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
The celebrated Majorana representation is exploited to investigate spin squeezing in different classes of pure symmetric states of N qubits with two distinct spinors,namely the Dicke-class of states.On obtaining a gen...The celebrated Majorana representation is exploited to investigate spin squeezing in different classes of pure symmetric states of N qubits with two distinct spinors,namely the Dicke-class of states.On obtaining a general expression for spin squeezing parameter,the variation of squeezing for different configurations is studied in detail.It is shown that the states in the Dicke-class,characterized by two-distinct non-orthogonal spinors,exhibit squeezing.展开更多
Using Majorana representation of symmetric N-qubit pure states, we have examined the monogamous nature of the family of states with two-distinct spinors, the W class of states. We have evaluated the N-concurrence tang...Using Majorana representation of symmetric N-qubit pure states, we have examined the monogamous nature of the family of states with two-distinct spinors, the W class of states. We have evaluated the N-concurrence tangle and showed that all the states in this family have vanishing concurrence tangle. The negativity tangle for the W class of states is shown to be non-zero, illustrating the fact that the concurrence tangle is always lesser than or equal to the negativity tangle in a pure N-qubit state.展开更多
Thermal entanglement of a two-qubit Ising chain subjected to an external magnetic field and Dzyaloshinsky–Moriya(DM)interaction is examined.The effect of magnetic field,strength of DM interaction and temperature are ...Thermal entanglement of a two-qubit Ising chain subjected to an external magnetic field and Dzyaloshinsky–Moriya(DM)interaction is examined.The effect of magnetic field,strength of DM interaction and temperature are analyzed by adopting negativity of partial transpose as the measure of entanglement.It is shown that when the DM interaction along the Ising axis is considerable,thermal entanglement can be sustained for a higher temperature.The usefulness of longitudinal DM interaction over the one that is perpendicular to the Ising axis,in the manipulation and control of entanglement at a feasible temperature,is illustrated.展开更多
Keeping in view of importance of exchange symmetry aspects in studies on spin squeezing of multiqubit states,we show that the one-dimensional Ising Hamiltonian with nearest neighbor interactions does not retain the ex...Keeping in view of importance of exchange symmetry aspects in studies on spin squeezing of multiqubit states,we show that the one-dimensional Ising Hamiltonian with nearest neighbor interactions does not retain the exchange symmetry of initially symmetric multiqubit states.Specifically we show that among 4-qubit states obeying exchange symmetry,all states except W class(and their linear combination)lose their symmetry under time evolution with Ising Hamiltonian.Attributing the loss of symmetry of the initially symmetric states to rotational asymmetry of the one-dimensional Ising Hamiltonian with more than 3 qubits,we indicate that all N-qubit states(N>5)obeying permutation symmetry lose their symmetry after time evolution with Ising Hamiltonian.展开更多
We examine here the proposition that all multiparty quantum states can be made monogamous by considering positive integral powers of any quantum correlation measure. With Rajagopal-Rendell quantum deficit as the measu...We examine here the proposition that all multiparty quantum states can be made monogamous by considering positive integral powers of any quantum correlation measure. With Rajagopal-Rendell quantum deficit as the measure of quantum correlations for symmetric 3-qubit pure states, we illustrate that monogamy inequality is satisfied for higher powers of quantum deficit. We discuss the drawbacks of this inequality in quantification of correlations in the state. We also prove a monogamy inequality in higher powers of classical mutual information and bring out the fact that such inequality needs not necessarily imply restricted shareability of correlations. We thus disprove the utility of higher powers of any correlation measure in establishing monogamous nature in multiparty quantum states.展开更多
We evaluate the monogamy inequality for symmetric, non-symmetric pure states of importance in terms of squared concurrence, squared entanglement of formation, squared negativity of partial transpose and compare the co...We evaluate the monogamy inequality for symmetric, non-symmetric pure states of importance in terms of squared concurrence, squared entanglement of formation, squared negativity of partial transpose and compare the corresponding tangles. We show that though concurrence and concurrence tangle are zero for two special classes of mixed entangled states, both negativity tangle and entanglement of formation（EOF） tangle turn out to be non-zero. A comparison of different tangles is carried out in each case and it is shown that while the concurrence tangle captures the genuine multiqubit entanglement in N-qubit pure states with N distinct spinors（containing GHZ and superposition of W-, obverse W states）either negativity tangle or EOF tangle is to be used as a better measure of entanglement in the W-class of states with two distinct spinors and in the special classes of mixed multiqubit states.展开更多
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.
文摘The celebrated Majorana representation is exploited to investigate spin squeezing in different classes of pure symmetric states of N qubits with two distinct spinors,namely the Dicke-class of states.On obtaining a general expression for spin squeezing parameter,the variation of squeezing for different configurations is studied in detail.It is shown that the states in the Dicke-class,characterized by two-distinct non-orthogonal spinors,exhibit squeezing.
基金supported by Department of Science and Technology,Government of India through the award of INSPIRE fellowship
文摘Using Majorana representation of symmetric N-qubit pure states, we have examined the monogamous nature of the family of states with two-distinct spinors, the W class of states. We have evaluated the N-concurrence tangle and showed that all the states in this family have vanishing concurrence tangle. The negativity tangle for the W class of states is shown to be non-zero, illustrating the fact that the concurrence tangle is always lesser than or equal to the negativity tangle in a pure N-qubit state.
文摘Thermal entanglement of a two-qubit Ising chain subjected to an external magnetic field and Dzyaloshinsky–Moriya(DM)interaction is examined.The effect of magnetic field,strength of DM interaction and temperature are analyzed by adopting negativity of partial transpose as the measure of entanglement.It is shown that when the DM interaction along the Ising axis is considerable,thermal entanglement can be sustained for a higher temperature.The usefulness of longitudinal DM interaction over the one that is perpendicular to the Ising axis,in the manipulation and control of entanglement at a feasible temperature,is illustrated.
基金Supported by D.C.Pavate Foundation,Dharwad,India in collaboration with Sidney Sussex College,Cambridge,UK.
文摘Keeping in view of importance of exchange symmetry aspects in studies on spin squeezing of multiqubit states,we show that the one-dimensional Ising Hamiltonian with nearest neighbor interactions does not retain the exchange symmetry of initially symmetric multiqubit states.Specifically we show that among 4-qubit states obeying exchange symmetry,all states except W class(and their linear combination)lose their symmetry under time evolution with Ising Hamiltonian.Attributing the loss of symmetry of the initially symmetric states to rotational asymmetry of the one-dimensional Ising Hamiltonian with more than 3 qubits,we indicate that all N-qubit states(N>5)obeying permutation symmetry lose their symmetry after time evolution with Ising Hamiltonian.
文摘We examine here the proposition that all multiparty quantum states can be made monogamous by considering positive integral powers of any quantum correlation measure. With Rajagopal-Rendell quantum deficit as the measure of quantum correlations for symmetric 3-qubit pure states, we illustrate that monogamy inequality is satisfied for higher powers of quantum deficit. We discuss the drawbacks of this inequality in quantification of correlations in the state. We also prove a monogamy inequality in higher powers of classical mutual information and bring out the fact that such inequality needs not necessarily imply restricted shareability of correlations. We thus disprove the utility of higher powers of any correlation measure in establishing monogamous nature in multiparty quantum states.
基金support of the Department of Science and Technology (DST),Govt.of India through the award of the INSPIRE fellowship
文摘We evaluate the monogamy inequality for symmetric, non-symmetric pure states of importance in terms of squared concurrence, squared entanglement of formation, squared negativity of partial transpose and compare the corresponding tangles. We show that though concurrence and concurrence tangle are zero for two special classes of mixed entangled states, both negativity tangle and entanglement of formation（EOF） tangle turn out to be non-zero. A comparison of different tangles is carried out in each case and it is shown that while the concurrence tangle captures the genuine multiqubit entanglement in N-qubit pure states with N distinct spinors（containing GHZ and superposition of W-, obverse W states）either negativity tangle or EOF tangle is to be used as a better measure of entanglement in the W-class of states with two distinct spinors and in the special classes of mixed multiqubit states.
