A fundamental feature of quantum mechanics radically different from classical theory lies in the role and consequence of quantum measurements, which usually cause disturbance to quantum states. For a bipartite state, the minimum disturbance caused by local measurements has been used to define quantum correlations from a measurement perspective. In contrast to this minimum approach, we investigate the maximum disturbance of local measurements, and define the nonlocal effect of a bipartite state as the maximum discrepancy between the global and local disturbances caused by local quantum measurements. Some analytical results are obtained and the significance of the maximum nonlocal effect is briefly discussed.
A fundamental feature of quantum mechanics radically different from classical theory lies in the role and consequence of quantum measurements, which usually cause disturbance to quantum states. For a bipartite state, the minimum disturbance caused by local measurements has been used to define quantum correlations from a measurement perspective. In contrast to this minimum approach, we investigate the maximum disturbance of local measurements, and define the nonlocal effect of a bipartite state as the maximum discrepancy between the global and local disturbances caused by local quantum measurements. Some analytical results are obtained and the significance of the maximum nonlocal effect is briefly discussed.
In quantum mechanics, general measurements often cause disturbance which may be exploited to quantify entanglement, nonlocality or quantumness. Imagine a bipartite state ρ ab shared by two parties a and b , and a von Neumann measurement performed locally on party a which does not disturb the local state ρ a ≔tr b ρ ab , but nevertheless may disturb the global state ρ ab . This disturbance is an indication of some kind of correlations or global effect in ρ ab which cannot be accounted for locally. We propose to use the maximum disturbance on ρ ab caused by locally non-disturbing measurements as a figure of merit quantifying the global effect (nonlocality), and investigate its fundamental properties. For general two-qubit states and some higher-dimensional symmetric states, we present analytic formulas for their global effects.
Finding physical principles lying behind quantum mechanics is essential to understand various quantum features, e.g., the quantum correlations, in a theory-independent manner. Here we propose such a principle, namely, no disturbance without uncertainty, stating that the disturbance caused by a measurement to a subsequent incompatible measurement is no larger than the uncertainty of the first measurement, equipped with suitable theory-independent measures for disturbance and uncertainty. When applied to local systems in a multipartite scenario, our principle imposes such a strong constraint on non-signaling correlations that quantum correlations can be recovered in many cases: i. it accounts for the Tsirelsons bound; ii. it provides the so far tightest boundary for a family of the noisy super-nonlocal box with 3 parameters, and iii. it rules out an almost quantum correlation from quantum correlations by which all the previous principles fail, as well as the celebrated quantum criterion due to Navascues, Pironio, and Acin. Our results pave the way to understand nonlocality exhibited in quantum correlations from local principles.
Nonlocality is one unique property of quantum mechanics that differs from the classical world. One of its quantifications can be properly described as the maximum global effect caused by locally invariant measurements, known as measurement-induced nonlocality (MIN) (2011 Phys. Rev. Lett. 106 120401). Here, we propose quantifying the MIN by the trace norm. We show explicitly that this measure is monotonically decreasing under the action of a completely positive trace-preserving map, which is the general local quantum operation, on the unmeasured party for the bipartite state. This property avoids the undesirable characteristic appearing in the known measure of MIN defined by the Hilbert–Schmidt norm which may be increased or decreased by trivial local reversible operations on the unmeasured party. We obtain analytical formulas of the trace-norm MIN for any -dimensional pure state, two-qubit state, and certain high-dimensional states. As with other quantum correlation measures, the newly defined MIN can be directly applied to various models for physical interpretations.
We interpret the maximum global effect caused by locally invariant measurements as measurement-induced nonlocality, which is in some sense dual to the geometric measure of quantum discord [Dakic, Vedral, and Brukner, Phys. Rev. Lett. 105, 190502 (2010)]. We quantify measurement-induced nonlocality from a geometric perspective in terms of measurements, and obtain analytical formulas for any dimensional pure states and 2 × n dimensional mixed states. We further derive a tight upper bound to measurement-induced nonlocality in general case. The physical significance of measurement-induced nonlocality is discussed in the context of correlations, entanglement, quantumness, and cryptographic communication.
We analyze the general nonclassicality of correlations of a composite quantum system as measured by the negativity of quantumness. The latter corresponds to the minimum entanglement, as quantified by the negativity that is created between the system and an apparatus that is performing local measurements on a selection of subsystems. The negativity of quantumness thus quantifies the degree of nonclassicality on the measured subsystems. We demonstrate a number of possible different interpretations for this measure and for the concept of quantumness of correlations in general. In particular, for general bipartite states in which the measured subsystem is a qubit, the negativity of quantumness acquires a geometric interpretation as the minimum trace distance from the set of classically correlated states. This can be further reinterpreted as minimum disturbance, with respect to trace norm, due to a local measurement or a nontrivial local unitary operation. We calculate the negativity of quantumness in closed form for Werner and isotropic states and for all two-qubit states for which the reduced state of the system that is locally measured is maximally mixed; this includes all Bell diagonal states. We discuss the operational significance and potential role of the negativity of quantumness in quantum information processing.
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.