Wigner-Yanase skew information could quantify the quantum uncertainty of the observables that are not commuting with a conserved quantity.We present the uncertainty principle for two successive projective measurements...Wigner-Yanase skew information could quantify the quantum uncertainty of the observables that are not commuting with a conserved quantity.We present the uncertainty principle for two successive projective measurements in terms of Wigner-Yanase skew information based on a single quantum system.It could capture the incompatibility of the observables,i.e.the lower bound can be nontrivial for the observables that are incompatible with the state of the quanaim system.Furthermore,the lower bound is also constrained by the quantum Fisher information.In addition,we find the complementarity relation between the uncertainties of the observable which operated on the quantum state and the other observable that performed on the post-measured quantum state and the uncertainties formed by the non-degenerate quantum observables performed on the quantum state,respectively.展开更多
Maximal and total skew information is studied. For symmetric pure states of two-qubit, they are closely related to the linear entropy, the concurrence, and the spin squeezing parameter. For a two-qubit system implemen...Maximal and total skew information is studied. For symmetric pure states of two-qubit, they are closely related to the linear entropy, the concurrence, and the spin squeezing parameter. For a two-qubit system implemented in three nonlinear interaction models with an external field, we give the exact state vectors and the expectation value （Sz） at any time t. Based on （Sz）2, we give the maximal and the total skew information and a condition in which the maximal and the total skew information can reach 1 and 2, respectively.展开更多
Both the maximal and the total skew information have been studied. For a three-qubit system implemented in three nonlinear interaction models, we give the exact state vector at any time t. Beused on this, we give the ...Both the maximal and the total skew information have been studied. For a three-qubit system implemented in three nonlinear interaction models, we give the exact state vector at any time t. Beused on this, we give the maximal and the total skew information. It is found that they have the same form and their evolution periods are dependent on the energy difference between the ground state and the second excited state in these models. The maximal skew information is always in the （Sx, Sv） plane. We give the condition for the occurrence of IGHZ}sy, in which they can reach the extreme values of 9/4 and 15/4, respectively. In three different decoherence channels, two kinds of information and the concurrence are calculated. We find that the phenomenon of the concurrence of sudden death occurs, but the above two kinds of information do not die suddenly. In the phase-damping channel, the two kinds of information will not be lost completely.展开更多
In quantum mechanics, it is long recognized that there exist correlations between observables which are much stronger than the classical ones. These correlations are usually called entanglement, and cannot be accounte...In quantum mechanics, it is long recognized that there exist correlations between observables which are much stronger than the classical ones. These correlations are usually called entanglement, and cannot be accounted for by classical theory. In this paper, we will study correlations between observables in terms of covariance and the Wigner-Yanase correlation, and compare their merits in characterizing entanglement. We will show that the Wigner-Yanase correlation has some advantages over the conventional covariance.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
We quantify the nonclassicality of multimode bosonic field states by adopting an information-theoretic approach involving the Wigner-Yanase skew information.The fundamental properties of the quantifier such as convexi...We quantify the nonclassicality of multimode bosonic field states by adopting an information-theoretic approach involving the Wigner-Yanase skew information.The fundamental properties of the quantifier such as convexity,superadditivity,monotonicity,and conservation relations are revealed.The quantifier is illustrated by a variety of typical examples,and applications to the quantification of nonclassical correlations are discussed.Various extensions are indicated.展开更多
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.11771011,11775040,12011530014)the Natural Science Foundation of Shanxi Province,China(Grant Nos.201801D221032,201801D121016)Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi(Grant No.2019L0178).
文摘Wigner-Yanase skew information could quantify the quantum uncertainty of the observables that are not commuting with a conserved quantity.We present the uncertainty principle for two successive projective measurements in terms of Wigner-Yanase skew information based on a single quantum system.It could capture the incompatibility of the observables,i.e.the lower bound can be nontrivial for the observables that are incompatible with the state of the quanaim system.Furthermore,the lower bound is also constrained by the quantum Fisher information.In addition,we find the complementarity relation between the uncertainties of the observable which operated on the quantum state and the other observable that performed on the post-measured quantum state and the uncertainties formed by the non-degenerate quantum observables performed on the quantum state,respectively.
基金Project supported by the College Young Talents Foundation of Anhui Province,China (Grant No.2010SQRL107)
文摘Maximal and total skew information is studied. For symmetric pure states of two-qubit, they are closely related to the linear entropy, the concurrence, and the spin squeezing parameter. For a two-qubit system implemented in three nonlinear interaction models with an external field, we give the exact state vectors and the expectation value （Sz） at any time t. Based on （Sz）2, we give the maximal and the total skew information and a condition in which the maximal and the total skew information can reach 1 and 2, respectively.
基金Project supported by the College Young Talents Foundation of Anhui Province,China(Grant No.2010SQRL107)the Natural Science Foundation of the Education Department of Anhui Province,China(Grant No.KJ2008B83ZC)the Natural Science Foundation of Anhui Province,China(Grant No.KJ2011Z234)
文摘Both the maximal and the total skew information have been studied. For a three-qubit system implemented in three nonlinear interaction models, we give the exact state vector at any time t. Beused on this, we give the maximal and the total skew information. It is found that they have the same form and their evolution periods are dependent on the energy difference between the ground state and the second excited state in these models. The maximal skew information is always in the （Sx, Sv） plane. We give the condition for the occurrence of IGHZ}sy, in which they can reach the extreme values of 9/4 and 15/4, respectively. In three different decoherence channels, two kinds of information and the concurrence are calculated. We find that the phenomenon of the concurrence of sudden death occurs, but the above two kinds of information do not die suddenly. In the phase-damping channel, the two kinds of information will not be lost completely.
基金Supported by the National Natural Science Foundation of China (No.10131040).
文摘In quantum mechanics, it is long recognized that there exist correlations between observables which are much stronger than the classical ones. These correlations are usually called entanglement, and cannot be accounted for by classical theory. In this paper, we will study correlations between observables in terms of covariance and the Wigner-Yanase correlation, and compare their merits in characterizing entanglement. We will show that the Wigner-Yanase correlation has some advantages over the conventional covariance.
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supported by the National Key R&D Program of China,Grant No.2020YFA0712700the National Natural Science Foundation of China,Grant Nos.11875317and 61833010。
文摘We quantify the nonclassicality of multimode bosonic field states by adopting an information-theoretic approach involving the Wigner-Yanase skew information.The fundamental properties of the quantifier such as convexity,superadditivity,monotonicity,and conservation relations are revealed.The quantifier is illustrated by a variety of typical examples,and applications to the quantification of nonclassical correlations are discussed.Various extensions are indicated.
