In weak measurement thought experiment, an ensemble consists of M quantum particles and N states. We observe that separability of the particles is lost, and hence we have fuzzy occupation numbers for the particles in ...In weak measurement thought experiment, an ensemble consists of M quantum particles and N states. We observe that separability of the particles is lost, and hence we have fuzzy occupation numbers for the particles in the ensemble. Without sharply measuring each particle state, quantum interferences add extra possible configurations of the ensemble, this explains the Quantum Pigeonhole Principle. This principle adds more entropy to the system;hence the particles seem to have a new kind of correlations emergent from particles not having a single, well-defined state. We formulated the Quantum Pigeonhole Principle in the language of abstract Hilbert spaces, then generalized it to systems consisting of mixed states. This insight into the fundamentals of quantum statistical mechanics could help us understand the interpretation of quantum mechanics more deeply, and possibly have implication on quantum computing and information theory.展开更多
Quantum uncertainty relations are mathematical inequalities that describe the lower bound of products of standard deviations of observables(i.e.,bounded or unbounded self-adjoint operators).By revealing a connection b...Quantum uncertainty relations are mathematical inequalities that describe the lower bound of products of standard deviations of observables(i.e.,bounded or unbounded self-adjoint operators).By revealing a connection between standard deviations of quantum observables and numerical radius of operators,we establish a universal uncertainty relation for k observables,of which the formulation depends on the even or odd quality of k.This universal uncertainty relation is tight at least for the cases k=2 and k=3.For two observables,the uncertainty relation is a simpler reformulation of Schr?dinger’s uncertainty principle,which is also tighter than Heisenberg’s and Robertson’s uncertainty relations.展开更多
文摘In weak measurement thought experiment, an ensemble consists of M quantum particles and N states. We observe that separability of the particles is lost, and hence we have fuzzy occupation numbers for the particles in the ensemble. Without sharply measuring each particle state, quantum interferences add extra possible configurations of the ensemble, this explains the Quantum Pigeonhole Principle. This principle adds more entropy to the system;hence the particles seem to have a new kind of correlations emergent from particles not having a single, well-defined state. We formulated the Quantum Pigeonhole Principle in the language of abstract Hilbert spaces, then generalized it to systems consisting of mixed states. This insight into the fundamentals of quantum statistical mechanics could help us understand the interpretation of quantum mechanics more deeply, and possibly have implication on quantum computing and information theory.
基金Supported by National Natural Science Foundation of China(Grant Nos.11771011,12071336)。
文摘Quantum uncertainty relations are mathematical inequalities that describe the lower bound of products of standard deviations of observables(i.e.,bounded or unbounded self-adjoint operators).By revealing a connection between standard deviations of quantum observables and numerical radius of operators,we establish a universal uncertainty relation for k observables,of which the formulation depends on the even or odd quality of k.This universal uncertainty relation is tight at least for the cases k=2 and k=3.For two observables,the uncertainty relation is a simpler reformulation of Schr?dinger’s uncertainty principle,which is also tighter than Heisenberg’s and Robertson’s uncertainty relations.
