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International Journal of Quantum Information

Using measurement induced disturbance to characterize correlations of multipartite non-k-classical states

Yinzhu Wang, Fangyu Zhou, Lili Yang, Donghua Yan, Huimei Wu

Published Mar 26, 2022• 1 citation
Publisher

Abstract

In [S. L. Luo, Using measurement induced disturbance to characterize correlations as classical or quantum, Phys. Rev. A77 (2008) 022301], the author presented a statistical correlation measure for bipartite quantum states using measurement induced disturbance. In this paper, motivated by this correlation measure, we obtain some necessary conditions for [Formula: see text]-classical states in multipartite quantum systems, and obtain a relation between the set of [Formula: see text]-classical states and the set of [Formula: see text]-product states; Secondly, we introduce a class of correlation measures based on trace distance using measurement induced disturbance in order to quantify the strength of correlation for non-[Formula: see text]-classical states; Lastly, we introduce the concept of quantum channel with respect to [Formula: see text]-partition, it is simply denoted by identical-[Formula: see text]-channel, and furthermore discuss the influences of the correlation measure under identical-[Formula: see text]-channel.

DOI
10.1142/s021974992250006x

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In [S. L. Luo, Using measurement induced disturbance to characterize correlations as classical or quantum, Phys. Rev. A77 (2008) 022301], the author presented a statistical correlation measure for bipartite quantum states using measurement induced disturbance. In this paper, motivated by this correlation measure, we obtain some necessary conditions for [Formula: see text]-classical states in multipartite quantum systems, and obtain a relation between the set of [Formula: see text]-classical states and the set of [Formula: see text]-product states; Secondly, we introduce a class of correlation measures based on trace distance using measurement induced disturbance in order to quantify the strength of correlation for non-[Formula: see text]-classical states; Lastly, we introduce the concept of quantum channel with respect to [Formula: see text]-partition, it is simply denoted by identical-[Formula: see text]-channel, and furthermore discuss the influences of the correlation measure under identical-[Formula: see text]-channel.
By using measurement-induced disturbance (S Luo 2008 Phys. Rev. A 77 022301 ), we propose a quantifier for genuine multipartite quantum correlations. The connection between this quantum correlations measure and the quantum advantage in multiport dense coding for pure three-qubit states is established. It is also used to investigate the dynamics of quantum correlations in a four-partite system. The phenomena of generation of quantum correlations and holding of quantum correlations in some time windows are found. As a byproduct, the monogamy score based on measurement-induced disturbance is related to the generalized geometric measure for pure three-qubit states.
Measure-induced non-classicality( MINC) in a family of bipartite separable qubit-qutrit correlated states was evaluated by using the MID method proposed by the reference [Luo S L. Using measurement-induced disturbance to characterize correlations as classical or quantum[J]. Phys Rev A,2008,77: 022301]. Specifically,classical correlation in each state was derived via the spectrum resolution technique and then the MINC( i. e.,quantum correlation) was extracted. The MINC was amply analyzed so that some distinct features were exposed.
In contrast to the seminal entanglement-separability paradigm widely used in quantum information theory, we introduce a quantum-classical dichotomy in order to classify and quantify statistical correlations in bipartite states. This is based on the idea that while in the classical description of nature measurements can be carried out without disturbance, in the quantum description, generic measurements often disturb the system and the disturbance can be exploited to quantify the quantumness of correlations therein. It turns out that certain separable states still possess correlations of a quantum nature and indicates that quantum correlations are more general than entanglement. The results are illustrated in the Werner states and the isotropic states, and are applied to quantify the quantum advantage of the model of quantum computation proposed by Knill and Laflamme [Phys. Rev. Lett. 81, 5672 (1998)].
Quantum correlations in a family of bipartite separable qubit-qutrit quantum-classical correlated states are investigated by using two popular measures, i.e., the original quantum discord (OQD) method by Ollivier and Zurek [ Phys. Rev. Lett. 88 (2001) 017901 ] and the measurement-induced disturbance (MID) method by Luo [ Phys. Rev. A 77 (2008) 022301 ]. It is found that both of them are functions of a parameter partially characterizing the concerned states, however, quantum correlations evaluated via the convenient MID method are somewhat overestimated.
Quantum channels, in general, will disturb quantum states and will lead to decoherence (i.e., information leakage to the environment). For bipartite systems, local channels often cause more decoherence for global states than for local states due to correlations. Intuitively, the difference between these two kinds of decoherence (i.e., global and local ones) may be regarded as a quantifier characterizing certain aspects of correlations in the global bipartite states. Based on this idea, we introduce a quantifier of correlations (relative to a local channel) as the coherence difference and investigate its basic properties. We probe and quantify correlations relative to various channels including the unitary channels, the twirling channels, the projective measurements, and the weak measurements. In particular, we show that both product states and some natural classical-quantum states can be operationally characterized in terms of local channels: The product states are just those states with vanishing coherence difference relative to the twirling channel induced by the unitary group, whereas these natural classical-quantum states are just those states with vanishing coherence difference relative to the twirling channel induced by the subgroup of the unitary group that does not disturb the local states. We further illustrate the results by various examples.
Quantifying the disturbance caused by a quantum measurement typically requires detailed knowledge of the underlying measurement channel. In this work, we introduce a statistical disturbance bound, which connects the statistical properties of a quantum measurement to the state disturbance induced by any compatible measurement channel. Specifically, we show that the average fidelity between input and output with respect to an arbitrary ensemble of pure input states is fundamentally bounded in terms of the measurement, described as a positive operator-valued measure (POVM). We further develop the weighted state exclusion technique, which enables an experimental determination of the statistical disturbance bound without requiring explicit knowledge of the measurement effects. To see the advantages of our approach over existing information-disturbance relations, we show that our bound distinguishes between measurements with equivalent informativeness. Furthermore, we demonstrate that the weighted state exclusion technique can detect and quantify measurement-induced disturbance using state preparations that are insufficient for tomographic reconstruction of the measurement operators. Finally, we illustrate how disturbance bounds defined with respect to specific input ensembles can be used to bound an eavesdropper's guessing probability in a simple protocol for quantum randomness generation.