We investigate the total variance of a quantum state with respect to a complete set of mutually complementary measurements and its relation to the Brukner–Zeilinger invariant information.By summing the variances over...We investigate the total variance of a quantum state with respect to a complete set of mutually complementary measurements and its relation to the Brukner–Zeilinger invariant information.By summing the variances over any complete set of mutually unbiased measurements and general symmetric informationally complete measurements respectively,we show that the Brukner–Zeilinger invariant information associated with such types of quantum measurements is equal to the difference between the maximal variance and the total variance obtained.These results provide an operational link between the previous interpretations of the Brukner–Zeilinger invariant information.展开更多
A non-Markovianity measure based on Brukner–Zeilinger invariant information to characterize nonMarkovian effect of open systems undergoing unital dynamical maps is proposed. The method takes advantage of non-increasi...A non-Markovianity measure based on Brukner–Zeilinger invariant information to characterize nonMarkovian effect of open systems undergoing unital dynamical maps is proposed. The method takes advantage of non-increasing property of the Brukner–Zeilinger invariant information under completely positive and trace-preserving unital maps. The simplicity of computing the Brukner–Zeilinger invariant information is the advantage of the proposed measure because of mainly depending on the purity of quantum state. The measure effectively captures the characteristics of non-Markovianity of unital dynamical maps. As some concrete application, we consider two typical non-Markovian noise channels, i.e., the phase damping channel and the random unitary channel to show the sensitivity of the proposed measure. By investigation, we find that the conditions of detecting the non-Markovianity for the phase damping channel are consistent with the results of existing measures for non-Markovianity, i.e., information flow, divisibility and quantum mutual information. However, for the random unitary channel non-Markovian conditions are same to that of the information flow, but is different from that of the divisibility and quantum mutual information.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.11805143 and 11675113Beijing Municipal Commission of Education under Grant No.KZ201810028042。
文摘We investigate the total variance of a quantum state with respect to a complete set of mutually complementary measurements and its relation to the Brukner–Zeilinger invariant information.By summing the variances over any complete set of mutually unbiased measurements and general symmetric informationally complete measurements respectively,we show that the Brukner–Zeilinger invariant information associated with such types of quantum measurements is equal to the difference between the maximal variance and the total variance obtained.These results provide an operational link between the previous interpretations of the Brukner–Zeilinger invariant information.
基金Supported by the National Natural Science Foundation of China under Grant No.61505053the Natural Science Foundation of Hunan Province under Grant No.2015JJ3092+1 种基金the Research Foundation of Education Bureau of Hunan Province,China under Grant No.16B177the School Foundation from the Hunan University of Arts and Science under Grant No.14ZD01
文摘A non-Markovianity measure based on Brukner–Zeilinger invariant information to characterize nonMarkovian effect of open systems undergoing unital dynamical maps is proposed. The method takes advantage of non-increasing property of the Brukner–Zeilinger invariant information under completely positive and trace-preserving unital maps. The simplicity of computing the Brukner–Zeilinger invariant information is the advantage of the proposed measure because of mainly depending on the purity of quantum state. The measure effectively captures the characteristics of non-Markovianity of unital dynamical maps. As some concrete application, we consider two typical non-Markovian noise channels, i.e., the phase damping channel and the random unitary channel to show the sensitivity of the proposed measure. By investigation, we find that the conditions of detecting the non-Markovianity for the phase damping channel are consistent with the results of existing measures for non-Markovianity, i.e., information flow, divisibility and quantum mutual information. However, for the random unitary channel non-Markovian conditions are same to that of the information flow, but is different from that of the divisibility and quantum mutual information.
