We establish tighter uncertainty relations for arbitrary finite observables via(α,β,γ)weighted Wigner–Yanase–Dyson((α,β,γ)WWYD)skew information.The results are also applicable to the(α,γ)weighted Wigner–Yan...We establish tighter uncertainty relations for arbitrary finite observables via(α,β,γ)weighted Wigner–Yanase–Dyson((α,β,γ)WWYD)skew information.The results are also applicable to the(α,γ)weighted Wigner–Yanase–Dyson((α,γ)WWYD)skew information and the weighted Wigner–Yanase–Dyson(WWYD)skew information.We also present tighter lower bounds for quantum channels and unitary channels via(α,β,γ)modified weighted Wigner–Yanase–Dyson((α,β,γ)MWWYD)skew information.Detailed examples are provided to illustrate the tightness of our uncertainty relations.展开更多
We show that violation of the variance based local sum uncertainty relation(LSUR)for angular momentum operators of a bipartite system,proposed by Hofmann and Takeuchi[Phys.Rev.A 68032103(2003)],reflects entanglement i...We show that violation of the variance based local sum uncertainty relation(LSUR)for angular momentum operators of a bipartite system,proposed by Hofmann and Takeuchi[Phys.Rev.A 68032103(2003)],reflects entanglement in the equal bipartitions of an N-qubit symmetric state with even qubits.We establish the one-to-one connection with the violation of LSUR with negativity of covariance matrix[Phys.Lett.A 364203(2007)]of the two-qubit reduced system of a permutation symmetric N-qubit state.展开更多
Quantum mechanical uncertainty relations are fundamental consequences of the incompatible nature of noncommuting observables.In terms of the coherence measure based on the Wigner-Yanase skew information,we establish s...Quantum mechanical uncertainty relations are fundamental consequences of the incompatible nature of noncommuting observables.In terms of the coherence measure based on the Wigner-Yanase skew information,we establish several uncertainty relations for coherence with respect to von Neumann measurements,mutually unbiased bases(MUBs),and general symmetric informationally complete positive operator valued measurements(SIC-POVMs),respectively.Since coherence is intimately connected with quantum uncertainties,the obtained uncertainty relations are of intrinsically quantum nature,in contrast to the conventional uncertainty relations expressed in terms of variance,which are of hybrid nature(mixing both classical and quantum uncertainties).From a dual viewpoint,we also derive some uncertainty relations for coherence of quantum states with respect to a fixed measurement.In particular,it is shown that if the density operators representing the quantum states do not commute,then there is no measurement(reference basis)such that the coherence of these states can be simultaneously small.展开更多
In this paper,we use certain norm inequalities to obtain new uncertain relations based on the Wigner-Yanase skew information.First for an arbitrary finite number of observables we derive an uncertainty relation outper...In this paper,we use certain norm inequalities to obtain new uncertain relations based on the Wigner-Yanase skew information.First for an arbitrary finite number of observables we derive an uncertainty relation outperforming previous lower bounds.We then propose new weighted uncertainty relations for two noncompatible observables.Two separable criteria via skew information are also obtained.展开更多
It is found that the field of the combined mode of the probe wave and the phase conjugate wave in the process of non-degenerate four-wave mixing exhibits higher-order squeezing to all even orders. The higher-order squ...It is found that the field of the combined mode of the probe wave and the phase conjugate wave in the process of non-degenerate four-wave mixing exhibits higher-order squeezing to all even orders. The higher-order squeezed parameter and squeezed limit due to the modulation frequency are investigated. The smaller the modulation frequency is, the stronger the degree of higher-order squeezing becomes. Furthermore, the hlgher-order uncertainty relations in the process of non-degenerate four-wave mixing are presented for the first time. The product of higher-order noise moments is related to even order number N and the length L of the medium.展开更多
Modifications of the Weyl-Heisenberg algebra are proposed where the classical limit corresponds to a metric in (curved) momentum spaces. In the simplest scenario, the 2D de Sitter metric of constant curvature in momen...Modifications of the Weyl-Heisenberg algebra are proposed where the classical limit corresponds to a metric in (curved) momentum spaces. In the simplest scenario, the 2D de Sitter metric of constant curvature in momentum space furnishes a hierarchy of modified uncertainty relations leading to a minimum value for the position uncertainty . The first uncertainty relation of this hierarchy has the same functional form as the stringy modified uncertainty relation with a Planck scale minimum value for at . We proceed with a discussion of the most general curved phase space scenario (cotangent bundle of spacetime) and provide the noncommuting phase space coordinates algebra in terms of the symmetric and nonsymmetric metric components of a Hermitian complex metric , such . Yang’s noncommuting phase-space coordinates algebra, combined with the Schrodinger-Robertson inequalities involving angular momentum eigenstates, reveals how a quantized area operator in units of emerges like it occurs in Loop Quantum Gravity (LQG). Some final comments are made about Fedosov deformation quantization, Noncommutative and Nonassociative gravity.展开更多
In this paper,we discuss quantum uncertainty relations of Tsallis relative α entropy coherence for a single qubit system based on three mutually unbiased bases.For α∈[1/2,1)U(1,2],the upper and lower bounds of sums...In this paper,we discuss quantum uncertainty relations of Tsallis relative α entropy coherence for a single qubit system based on three mutually unbiased bases.For α∈[1/2,1)U(1,2],the upper and lower bounds of sums of coherence are obtained.However,the above results cannot be verified directly for any α∈(0,1/2).Hence,we only consider the special case of α=1/n+1,where n is a positive integer,and we obtain the upper and lower bounds.By comparing the upper and lower bounds,we find that the upper bound is equal to the lower bound for the special α=1/2,and the differences between the upper and the lower bounds will increase as α increases.Furthermore,we discuss the tendency of the sum of coherence,and find that it has the same tendency with respect to the different θ or φ,which is opposite to the uncertainty relations based on the Rényi entropy and Tsallis entropy.展开更多
In this paper, we discuss quantum uncertainty relations of quantum coherence through a different method from Ref. [52]. Some lower bounds with parameters and their minimal bounds are obtained. Moreover, we find that f...In this paper, we discuss quantum uncertainty relations of quantum coherence through a different method from Ref. [52]. Some lower bounds with parameters and their minimal bounds are obtained. Moreover, we find that for two pairs of measurement bases with the same maximum overlap, quantum uncertainty relations and lower bounds with parameters are different, but the minimal bounds are the same. In addition, we discuss the dynamics of quantum uncertainty relations of quantum coherence and their lower bounds under the amplitude damping channel（ADC）. We find that the ADC will change the uncertainty relations and their lower bounds, and their tendencies depend on the initial state.展开更多
We study the uncertainty relation in the product form of variances and obtain some new uncertainty relations with weight, which are shown to be tighter than those derived from the Cauchy-Schwarz inequality.
We study the uncertainty relation for three quantum systems in the N-dimensional space by using the virial theorem (VT). It is shown that this relation depends on the energy spectrum of the system as well as on the sp...We study the uncertainty relation for three quantum systems in the N-dimensional space by using the virial theorem (VT). It is shown that this relation depends on the energy spectrum of the system as well as on the space dimension N. It is pointed out that the form of lower bound of the inequality, which is governed by the ground state, depends on the system and on the space dimension N. A comparison between our result for the lower bound and recent results, based on information-theoretic approach, is pointed out. We examine and analyze these derived uncertainties for different angular momenta with a special attention made for the large N limit.展开更多
Quantum uncertainty relations constrain the precision of measurements across multiple non-commuting quantum mechanical observables.Here,we introduce the concept of optimal observable sets and define the tightest uncer...Quantum uncertainty relations constrain the precision of measurements across multiple non-commuting quantum mechanical observables.Here,we introduce the concept of optimal observable sets and define the tightest uncertainty constants to accurately describe these measurement uncertainties.For any quantum state,we establish optimal sets of three observables for both product and summation forms of uncertainty relations,and analytically derive the corresponding tightest uncertainty constants.We demonstrate that the optimality of these sets remains consistent regardless of the uncertainty relation form.Furthermore,the existence of the tightest constants excludes the validity of standard real quantum mechanics,underscoring the essential role of complex numbers in this field.Additionally,our findings resolve the conjecture posed in[Phys.Rev.Lett.118,180402(2017)],offering novel insights and potential applications in understanding preparation uncertainties.展开更多
We describe a setup for obtain!ing uncertainty relations for arbitrary pairs of observables related by a Fourier transform. The physical examples discussed here are the standard position and momentum, number and angle...We describe a setup for obtain!ing uncertainty relations for arbitrary pairs of observables related by a Fourier transform. The physical examples discussed here are the standard position and momentum, number and angle, finite qudit systems, and strings of qubits for quantum information applications. The uncertainty relations allow for an arbitrary choice of metric for the outcome distance, and the choice of an exponent distinguishing, e.g., absolute and root mean square deviations. The emphasis of this article is on developing a unified treatment, in which one observable takes on values in an arbitrary locally compact Abelian group and the other in the dual group. In all cases, the phase space symmetry implies the eciuality of measurement and preparation uncertainty bounds. There is also a straightforward method for determining the optimal bounds.展开更多
Uncertainty principle is one of the most fascinating features of the quantum world. It asserts a fundamental limit on the precision with which certain pairs of physical properties of a particle, such as position and m...Uncertainty principle is one of the most fascinating features of the quantum world. It asserts a fundamental limit on the precision with which certain pairs of physical properties of a particle, such as position and momentum, can not be si- multaneously known. The uncertainty principle has attracted considerable attention since the innovation of quantum me- chanics and has been investigated in terms of various types of uncertainty inequalities： in terms of the noise and dis- turbance, according to successive measurements, as informa- tional recourses in entropic terms, by means of majorization technique and based on sum of variances and standard devia- tions.展开更多
The uncertainty principle is a crucial aspect of quantum mechanics.It has been shown that quantum entanglement as well as more general notions of correlations,such as quantum discord,can relax or tighten the entropic ...The uncertainty principle is a crucial aspect of quantum mechanics.It has been shown that quantum entanglement as well as more general notions of correlations,such as quantum discord,can relax or tighten the entropic uncertainty relation in the presence of an ancillary system.We explored the behaviour of entropic uncertainty relations for system of two qubits—one of which subjects to several forms of independent quantum noise,in both Markovian and non-Markovian regimes.The uncertainties and their lower bounds,identified by the entropic uncertainty relations,increase under independent local unital Markovian noisy channels,but they may decrease under non-unital channels.The behaviour of the uncertainties(and lower bounds)exhibit periodical oscillations due to correlation dynamics under independent non-Markovian reservoirs.In addition,we compare different entropic uncertainty relations in several special cases and find that discord-tightened entropic uncertainty relations offer in general a better estimate of the uncertainties in play.展开更多
Uncertainty relations are of profound significance in quantum mechanics and quantum information theory.The well-known Heisenberg-Robertson uncertainty relation presents the constraints on the spread of measurement out...Uncertainty relations are of profound significance in quantum mechanics and quantum information theory.The well-known Heisenberg-Robertson uncertainty relation presents the constraints on the spread of measurement outcomes caused by the non-commutability of a pair of observables.In this article,we study the uncertainty relation of triple observables to explore the relationship between the standard deviations and the commutators of the observables.We derive and tighten the multiplicative form and weighted summation form uncertainty relations,which are found to be dependent not only on the commutation relations of each pair of the observables but also on a newly defined commutator in terms of all the three observables.We experimentally test the uncertainty relations in a linear optical setup.The experimental and numerical results agree well and show that the uncer-tainty relations derived by us successfully present tight lower bounds in the cases of high-dimensional observables and the cases of mixed states.Our method of deriving the uncertainty relation can be extended to more than three observables.展开更多
In this paper, we consider the quantum uncertainty relations of two generalized relative entropies of coherence based on two measurement bases. First, we give quantum uncertainty relations for pure states in a d-dimen...In this paper, we consider the quantum uncertainty relations of two generalized relative entropies of coherence based on two measurement bases. First, we give quantum uncertainty relations for pure states in a d-dimensional quantum system by making use of the majorization technique; these uncertainty relations are then generalized to mixed states. We find that the lower bounds are always nonnegative for pure states but may be negative for some mixed states. Second, the quantum uncertainty relations for single qubit states are obtained by the analytical method. We show that the lower bounds obtained by this technique are always positive for single qubit states. Third, the lower bounds obtained by the two methods described above are compared for single qubit states.展开更多
This research work proceeds from the assumption, which was still considered by Einstein, that the quantization of gravity does not require additional external procedures: quantum phenomena can be a consequence of the ...This research work proceeds from the assumption, which was still considered by Einstein, that the quantization of gravity does not require additional external procedures: quantum phenomena can be a consequence of the properties of the universal gravitational interaction, which maps any physical field upon the space-time geometry. Therefore, an attempt is made in this research work to reduce the quantization of physical fields in GRT to the space-time quantization. Three reasons for quantum phenomena are considered: Partition of space-time into a set of unconnected Novikov’s R- and T-domains impenetrable for light paths;the set is generated by the invariance of Einstein’s equations with respect to dual mappings;The existence of electric charge quanta of wormholes, which geometrically describe elementary particles in GRT. This gives rise to a discrete spectrum of their physical and geometric parameters governed by Diophantine equations. It is shown that the fundamental constants (electric charge, rest masses of an electron and a proton) are interconnected arithmetically;The existence of the so-called Diophantine catastrophe, when fluctuations in the values of physical constants tending to zero lead to fluctuations in the number of electric charges and the number of nucleons at the wormhole throats, which tend to infinity, so that the product of the increments of these numbers by the increment of physical constants forms a relation equivalent to the uncertainty relation in quantum mechanics. This suggests that space-time cannot but fluctuate, and, moreover, its fluctuations are bounded from below, so that all processes become chaotic, and the observables become averaged over this chaos.展开更多
From the perspective of Markovian piecewise deterministic processes(PDPs),we investigate the derivation of a kinetic uncertainty relation(KUR),which was originally proposed in Markovian open quantum systems.First,stat...From the perspective of Markovian piecewise deterministic processes(PDPs),we investigate the derivation of a kinetic uncertainty relation(KUR),which was originally proposed in Markovian open quantum systems.First,stationary distributions of classical PDPs are explicitly constructed.Then,a tilting method is used to derive a rate functional of large deviations.Finally,based on an improved approximation scheme,we recover the KUR.These classical results are directly extended to the open quantum systems.We use a driven two-level quantum system to exemplify the quantum results.展开更多
A new uncertainty relation(UR) is obtained for a system of N identical pure entangled particles if we use symmetrized observables when deriving the inequality. This new expression can be written in a form where we ide...A new uncertainty relation(UR) is obtained for a system of N identical pure entangled particles if we use symmetrized observables when deriving the inequality. This new expression can be written in a form where we identify a term which explicitly shows the quantum correlations among the particles that constitute the system. For the particular cases of two and three particles, making use of the Schwarz inequality, we obtain new lower bounds for the UR that are different from the standard one.展开更多
We investigate the quantum-memory-assisted entropic uncertainty relation(QMA-EUR)in a Heisenberg XYZ mixed-spin(1/2,1)model.Coupling strength,Dzyaloshinskii–Moriya(DM)interaction and inhomogeneous magnetic field,resp...We investigate the quantum-memory-assisted entropic uncertainty relation(QMA-EUR)in a Heisenberg XYZ mixed-spin(1/2,1)model.Coupling strength,Dzyaloshinskii–Moriya(DM)interaction and inhomogeneous magnetic field,respectively,contributing to QMA-EUR by a thermal entanglement in the hybrid-spin model are studied in detail.Furthermore,we compare the uncertainty of the bipartite hybrid model with those of qubit–qubit and qutrit–qutrit systems.Meanwhile,the effects of local PT-symmetric operation and weak measurement on the steering of entropic uncertainty are analyzed.We find that the local PT-symmetric operation can reduce the entropic uncertainty,and the entropic uncertainty can also be decreased by weak measurement reversal.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.12161056,12075159,12171044)Jiangxi Provincial Natural Science Foundation(Grant No.20232ACB211003)the Academician Innovation Platform of Hainan Province。
文摘We establish tighter uncertainty relations for arbitrary finite observables via(α,β,γ)weighted Wigner–Yanase–Dyson((α,β,γ)WWYD)skew information.The results are also applicable to the(α,γ)weighted Wigner–Yanase–Dyson((α,γ)WWYD)skew information and the weighted Wigner–Yanase–Dyson(WWYD)skew information.We also present tighter lower bounds for quantum channels and unitary channels via(α,β,γ)modified weighted Wigner–Yanase–Dyson((α,β,γ)MWWYD)skew information.Detailed examples are provided to illustrate the tightness of our uncertainty relations.
基金the support of NCN,SHENG(Grant No.2018/30/Q/ST2/00625)supported by the Department of Science and Technology,India(Grant No.DST/ICPS/QUST/Theme-2/2019)。
文摘We show that violation of the variance based local sum uncertainty relation(LSUR)for angular momentum operators of a bipartite system,proposed by Hofmann and Takeuchi[Phys.Rev.A 68032103(2003)],reflects entanglement in the equal bipartitions of an N-qubit symmetric state with even qubits.We establish the one-to-one connection with the violation of LSUR with negativity of covariance matrix[Phys.Lett.A 364203(2007)]of the two-qubit reduced system of a permutation symmetric N-qubit state.
基金Supported by the National Natural Science Foundation of China under Grant No.11875317the National Center for Mathematics and Interdisciplinary Sciences,and Chinese Academy of Sciences under Grant No.Y029152K51
文摘Quantum mechanical uncertainty relations are fundamental consequences of the incompatible nature of noncommuting observables.In terms of the coherence measure based on the Wigner-Yanase skew information,we establish several uncertainty relations for coherence with respect to von Neumann measurements,mutually unbiased bases(MUBs),and general symmetric informationally complete positive operator valued measurements(SIC-POVMs),respectively.Since coherence is intimately connected with quantum uncertainties,the obtained uncertainty relations are of intrinsically quantum nature,in contrast to the conventional uncertainty relations expressed in terms of variance,which are of hybrid nature(mixing both classical and quantum uncertainties).From a dual viewpoint,we also derive some uncertainty relations for coherence of quantum states with respect to a fixed measurement.In particular,it is shown that if the density operators representing the quantum states do not commute,then there is no measurement(reference basis)such that the coherence of these states can be simultaneously small.
基金the National Natural Science Foundation of China(grant Nos.11861031 and 11531004)the Education Department of Hainan Province Hnky2020ZD10Simons Foundation grant No.523868。
文摘In this paper,we use certain norm inequalities to obtain new uncertain relations based on the Wigner-Yanase skew information.First for an arbitrary finite number of observables we derive an uncertainty relation outperforming previous lower bounds.We then propose new weighted uncertainty relations for two noncompatible observables.Two separable criteria via skew information are also obtained.
文摘It is found that the field of the combined mode of the probe wave and the phase conjugate wave in the process of non-degenerate four-wave mixing exhibits higher-order squeezing to all even orders. The higher-order squeezed parameter and squeezed limit due to the modulation frequency are investigated. The smaller the modulation frequency is, the stronger the degree of higher-order squeezing becomes. Furthermore, the hlgher-order uncertainty relations in the process of non-degenerate four-wave mixing are presented for the first time. The product of higher-order noise moments is related to even order number N and the length L of the medium.
文摘Modifications of the Weyl-Heisenberg algebra are proposed where the classical limit corresponds to a metric in (curved) momentum spaces. In the simplest scenario, the 2D de Sitter metric of constant curvature in momentum space furnishes a hierarchy of modified uncertainty relations leading to a minimum value for the position uncertainty . The first uncertainty relation of this hierarchy has the same functional form as the stringy modified uncertainty relation with a Planck scale minimum value for at . We proceed with a discussion of the most general curved phase space scenario (cotangent bundle of spacetime) and provide the noncommuting phase space coordinates algebra in terms of the symmetric and nonsymmetric metric components of a Hermitian complex metric , such . Yang’s noncommuting phase-space coordinates algebra, combined with the Schrodinger-Robertson inequalities involving angular momentum eigenstates, reveals how a quantized area operator in units of emerges like it occurs in Loop Quantum Gravity (LQG). Some final comments are made about Fedosov deformation quantization, Noncommutative and Nonassociative gravity.
基金This paper is supported by Startup Foundation for Doctors of Nanchang Hangkong University(No.EA201907210).
文摘In this paper,we discuss quantum uncertainty relations of Tsallis relative α entropy coherence for a single qubit system based on three mutually unbiased bases.For α∈[1/2,1)U(1,2],the upper and lower bounds of sums of coherence are obtained.However,the above results cannot be verified directly for any α∈(0,1/2).Hence,we only consider the special case of α=1/n+1,where n is a positive integer,and we obtain the upper and lower bounds.By comparing the upper and lower bounds,we find that the upper bound is equal to the lower bound for the special α=1/2,and the differences between the upper and the lower bounds will increase as α increases.Furthermore,we discuss the tendency of the sum of coherence,and find that it has the same tendency with respect to the different θ or φ,which is opposite to the uncertainty relations based on the Rényi entropy and Tsallis entropy.
基金Project supported by the National Natural Science Foundation of China(Grant No.11671244)the Higher School Doctoral Subject Foundation of Ministry of Education of China(Grant No.20130202110001)Fundamental Research Funds for the Central Universities,China(Grant No.2016CBY003)
文摘In this paper, we discuss quantum uncertainty relations of quantum coherence through a different method from Ref. [52]. Some lower bounds with parameters and their minimal bounds are obtained. Moreover, we find that for two pairs of measurement bases with the same maximum overlap, quantum uncertainty relations and lower bounds with parameters are different, but the minimal bounds are the same. In addition, we discuss the dynamics of quantum uncertainty relations of quantum coherence and their lower bounds under the amplitude damping channel（ADC）. We find that the ADC will change the uncertainty relations and their lower bounds, and their tendencies depend on the initial state.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11501153,11461018,and 11531003)the Simons Foundation(Grant No.523868)
文摘We study the uncertainty relation in the product form of variances and obtain some new uncertainty relations with weight, which are shown to be tighter than those derived from the Cauchy-Schwarz inequality.
文摘We study the uncertainty relation for three quantum systems in the N-dimensional space by using the virial theorem (VT). It is shown that this relation depends on the energy spectrum of the system as well as on the space dimension N. It is pointed out that the form of lower bound of the inequality, which is governed by the ground state, depends on the system and on the space dimension N. A comparison between our result for the lower bound and recent results, based on information-theoretic approach, is pointed out. We examine and analyze these derived uncertainties for different angular momenta with a special attention made for the large N limit.
基金supported by the National Natural Science Foundation of China(NSFC)(Grant Nos.12065021,12075159,12171044,and 12175147)。
文摘Quantum uncertainty relations constrain the precision of measurements across multiple non-commuting quantum mechanical observables.Here,we introduce the concept of optimal observable sets and define the tightest uncertainty constants to accurately describe these measurement uncertainties.For any quantum state,we establish optimal sets of three observables for both product and summation forms of uncertainty relations,and analytically derive the corresponding tightest uncertainty constants.We demonstrate that the optimality of these sets remains consistent regardless of the uncertainty relation form.Furthermore,the existence of the tightest constants excludes the validity of standard real quantum mechanics,underscoring the essential role of complex numbers in this field.Additionally,our findings resolve the conjecture posed in[Phys.Rev.Lett.118,180402(2017)],offering novel insights and potential applications in understanding preparation uncertainties.
文摘We describe a setup for obtain!ing uncertainty relations for arbitrary pairs of observables related by a Fourier transform. The physical examples discussed here are the standard position and momentum, number and angle, finite qudit systems, and strings of qubits for quantum information applications. The uncertainty relations allow for an arbitrary choice of metric for the outcome distance, and the choice of an exponent distinguishing, e.g., absolute and root mean square deviations. The emphasis of this article is on developing a unified treatment, in which one observable takes on values in an arbitrary locally compact Abelian group and the other in the dual group. In all cases, the phase space symmetry implies the eciuality of measurement and preparation uncertainty bounds. There is also a straightforward method for determining the optimal bounds.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11275131, 11371247, 11571313, and 11675113)
文摘Uncertainty principle is one of the most fascinating features of the quantum world. It asserts a fundamental limit on the precision with which certain pairs of physical properties of a particle, such as position and momentum, can not be si- multaneously known. The uncertainty principle has attracted considerable attention since the innovation of quantum me- chanics and has been investigated in terms of various types of uncertainty inequalities： in terms of the noise and dis- turbance, according to successive measurements, as informa- tional recourses in entropic terms, by means of majorization technique and based on sum of variances and standard devia- tions.
基金supported by the National Natural Science Foundation of China(Grant Nos.61144006,11201427 and 10901103)the Foundation of China Scholarship Council,the Project Fund of Hunan Provincial Scienceand Technology Department(Grant No.2010FJ3147)the Fund of Hunan Provincial Key Laboratory of Photoelectric Information Integration and Optical Manufacturing Technology,the Educational Committee of the Hunan Province of China through the Overseas Famous Teachers Programme
文摘The uncertainty principle is a crucial aspect of quantum mechanics.It has been shown that quantum entanglement as well as more general notions of correlations,such as quantum discord,can relax or tighten the entropic uncertainty relation in the presence of an ancillary system.We explored the behaviour of entropic uncertainty relations for system of two qubits—one of which subjects to several forms of independent quantum noise,in both Markovian and non-Markovian regimes.The uncertainties and their lower bounds,identified by the entropic uncertainty relations,increase under independent local unital Markovian noisy channels,but they may decrease under non-unital channels.The behaviour of the uncertainties(and lower bounds)exhibit periodical oscillations due to correlation dynamics under independent non-Markovian reservoirs.In addition,we compare different entropic uncertainty relations in several special cases and find that discord-tightened entropic uncertainty relations offer in general a better estimate of the uncertainties in play.
基金supported by the National Natural Science Foundation of China(Grant Nos.12175052,11775065,62105086,and 11935012).
文摘Uncertainty relations are of profound significance in quantum mechanics and quantum information theory.The well-known Heisenberg-Robertson uncertainty relation presents the constraints on the spread of measurement outcomes caused by the non-commutability of a pair of observables.In this article,we study the uncertainty relation of triple observables to explore the relationship between the standard deviations and the commutators of the observables.We derive and tighten the multiplicative form and weighted summation form uncertainty relations,which are found to be dependent not only on the commutation relations of each pair of the observables but also on a newly defined commutator in terms of all the three observables.We experimentally test the uncertainty relations in a linear optical setup.The experimental and numerical results agree well and show that the uncer-tainty relations derived by us successfully present tight lower bounds in the cases of high-dimensional observables and the cases of mixed states.Our method of deriving the uncertainty relation can be extended to more than three observables.
基金supported by the National Natural Science Foundation of China(Grant Nos.11671244,61373150,and 61602291)the Higher School Doctoral Subject Foundation of Ministry of Education of China(Grant No.20130202110001)the Fundamental Research Funds for the Central Universities(Grant No.2016CBY003)
文摘In this paper, we consider the quantum uncertainty relations of two generalized relative entropies of coherence based on two measurement bases. First, we give quantum uncertainty relations for pure states in a d-dimensional quantum system by making use of the majorization technique; these uncertainty relations are then generalized to mixed states. We find that the lower bounds are always nonnegative for pure states but may be negative for some mixed states. Second, the quantum uncertainty relations for single qubit states are obtained by the analytical method. We show that the lower bounds obtained by this technique are always positive for single qubit states. Third, the lower bounds obtained by the two methods described above are compared for single qubit states.
文摘This research work proceeds from the assumption, which was still considered by Einstein, that the quantization of gravity does not require additional external procedures: quantum phenomena can be a consequence of the properties of the universal gravitational interaction, which maps any physical field upon the space-time geometry. Therefore, an attempt is made in this research work to reduce the quantization of physical fields in GRT to the space-time quantization. Three reasons for quantum phenomena are considered: Partition of space-time into a set of unconnected Novikov’s R- and T-domains impenetrable for light paths;the set is generated by the invariance of Einstein’s equations with respect to dual mappings;The existence of electric charge quanta of wormholes, which geometrically describe elementary particles in GRT. This gives rise to a discrete spectrum of their physical and geometric parameters governed by Diophantine equations. It is shown that the fundamental constants (electric charge, rest masses of an electron and a proton) are interconnected arithmetically;The existence of the so-called Diophantine catastrophe, when fluctuations in the values of physical constants tending to zero lead to fluctuations in the number of electric charges and the number of nucleons at the wormhole throats, which tend to infinity, so that the product of the increments of these numbers by the increment of physical constants forms a relation equivalent to the uncertainty relation in quantum mechanics. This suggests that space-time cannot but fluctuate, and, moreover, its fluctuations are bounded from below, so that all processes become chaotic, and the observables become averaged over this chaos.
基金supported by the National Natural Science Foundation of China under Grant No.12075016,No.11575016。
文摘From the perspective of Markovian piecewise deterministic processes(PDPs),we investigate the derivation of a kinetic uncertainty relation(KUR),which was originally proposed in Markovian open quantum systems.First,stationary distributions of classical PDPs are explicitly constructed.Then,a tilting method is used to derive a rate functional of large deviations.Finally,based on an improved approximation scheme,we recover the KUR.These classical results are directly extended to the open quantum systems.We use a driven two-level quantum system to exemplify the quantum results.
基金supported by Fundacao de Amparo à Pesquisa do Estado de Sao Paulo(FAPESP)
文摘A new uncertainty relation(UR) is obtained for a system of N identical pure entangled particles if we use symmetrized observables when deriving the inequality. This new expression can be written in a form where we identify a term which explicitly shows the quantum correlations among the particles that constitute the system. For the particular cases of two and three particles, making use of the Schwarz inequality, we obtain new lower bounds for the UR that are different from the standard one.
基金supported by the National Natural Science Foundation of China under Grant Nos.91950112 and 11174081the National Key Research and Development Program of China under Grant No.2016YFB0501601。
文摘We investigate the quantum-memory-assisted entropic uncertainty relation(QMA-EUR)in a Heisenberg XYZ mixed-spin(1/2,1)model.Coupling strength,Dzyaloshinskii–Moriya(DM)interaction and inhomogeneous magnetic field,respectively,contributing to QMA-EUR by a thermal entanglement in the hybrid-spin model are studied in detail.Furthermore,we compare the uncertainty of the bipartite hybrid model with those of qubit–qubit and qutrit–qutrit systems.Meanwhile,the effects of local PT-symmetric operation and weak measurement on the steering of entropic uncertainty are analyzed.We find that the local PT-symmetric operation can reduce the entropic uncertainty,and the entropic uncertainty can also be decreased by weak measurement reversal.
