Operational interpretations of quantum discord

Quantum discord quantifies non-classical correlations going beyond the standard classification of quantum states into entangled and unentangled ones. Although it has received considerable attention, it still lacks any precise interpretation in terms of some protocol in which quantum features are relevant. Here we give quantum discord its first operational meaning in terms of entanglement consumption in an extended quantum state merging protocol. We further relate the asymmetry of quantum discord with the performance imbalance in quantum state merging and dense coding.Comment: v4: 5 pages, 1 fig. Refs added, text improved. Main results unchanged. See arXiv:1008.4135v2 for a related work. v5: close to the published versio

Nonstationarities of regional climate model biases in European seasonal mean temperature and precipitation sums

Bias correcting climate models implicitly assumes stationarity of the correction function. This assumption is assessed for regional climate models in a pseudo reality for seasonal mean temperature and precipitation sums. An ensemble of regional climate models for Europe is used, all driven with the same transient boundary conditions. Although this model-dependent approach does not assess all possible bias non-stationarities, conclusions can be drawn for the real world. Generally, biases are relatively stable, and bias correction on average improves climate scenarios. For winter temperature, bias changes occur in the Alps and ice covered oceans caused by a biased forcing sensitivity of surface albedo; for summer temperature, bias changes occur due to a biased sensitivity of cloud cover and soil moisture. Precipitation correction is generally successful, but affected by internal variability in arid climates. As model sensitivities vary considerably in some regions, multi model ensembles are needed even after bias correction. Key Points: - Bias correction in general improves future climate simulations - Cloud cover, soil moisture and albedo changes may cause temperature bias changes - Precipitation biases in arid regions are affected by internal variabilit

A class of 2^N x 2^N bound entangled states revealed by non-decomposable maps

We use some general results regarding positive maps to exhibit examples of non-decomposable maps and 2^N x 2^N, N >= 2, bound entangled states, e.g. non distillable bipartite states of N + N qubits.Comment: 19 pages, 1 figur

Unified Framework for Correlations in Terms of Local Quantum Observables

We provide a unified framework for nonsignalling quantum and classical multipartite correlations, allowing all to be written as the trace of some local (quantum) measurements multiplied by an operator. The properties of this operator define the corresponding set of correlations.We then show that if the theory is such that all local quantum measurements are possible, one obtains the correlations corresponding to the extension of Gleason's Theorem to multipartite systems. Such correlations coincide with the quantum ones for one and two parties, but we prove the existence of a gap for three or more parties.Comment: 4 pages, final versio

Ancilla models for quantum operations: For what unitaries does the ancilla state have to be physical?

Any evolution described by a completely positive trace-preserving linear map can be imagined as arising from the interaction of the evolving system with an initially uncorrelated ancilla. The interaction is given by a joint unitary operator, acting on the system and the ancilla. Here we study the properties such a unitary operator must have in order to force the choice of a physical- that is, positive-state for the ancilla if the end result is to be a physical-that is, completely positive-evolution of the system.Comment: Quantum Information Processing, (2012

Characterising two-sided quantum correlations beyond entanglement via metric-adjusted f-correlations

We introduce an infinite family of quantifiers of quantum correlations beyond entanglement which vanish on both classical-quantum and quantum-classical states and are in one-to-one correspondence with the metric-adjusted skew informations. The `quantum $f-$correlations' are defined as the maximum metric-adjusted $f-$correlations between pairs of local observables with the same fixed equispaced spectrum. We show that these quantifiers are entanglement monotones when restricted to pure states of qubit-qudit systems. We also evaluate the quantum $f-$correlations in closed form for two-qubit systems and discuss their behaviour under local commutativity preserving channels. We finally provide a physical interpretation for the quantifier corresponding to the average of the Wigner-Yanase-Dyson skew informations.Comment: 20 pages, 1 figure. Published versio

Entanglement distribution and quantum discord

Establishing entanglement between distant parties is one of the most important problems of quantum technology, since long-distance entanglement is an essential part of such fundamental tasks as quantum cryptography or quantum teleportation. In this lecture we review basic properties of entanglement and quantum discord, and discuss recent results on entanglement distribution and the role of quantum discord therein. We also review entanglement distribution with separable states, and discuss important problems which still remain open. One such open problem is a possible advantage of indirect entanglement distribution, when compared to direct distribution protocols.Comment: 7 pages, 2 figures, contribution to "Lectures on general quantum correlations and their applications", edited by Felipe Fanchini, Diogo Soares-Pinto, and Gerardo Adess

Experimental investigation of classical and quantum correlations under decoherence

It is well known that many operations in quantum information processing depend largely on a special kind of quantum correlation, that is, entanglement. However, there are also quantum tasks that display the quantum advantage without entanglement. Distinguishing classical and quantum correlations in quantum systems is therefore of both fundamental and practical importance. In consideration of the unavoidable interaction between correlated systems and the environment, understanding the dynamics of correlations would stimulate great interest. In this study, we investigate the dynamics of different kinds of bipartite correlations in an all-optical experimental setup. The sudden change in behaviour in the decay rates of correlations and their immunity against certain decoherences are shown. Moreover, quantum correlation is observed to be larger than classical correlation, which disproves the early conjecture that classical correlation is always greater than quantum correlation. Our observations may be important for quantum information processing.Comment: 7 pages, 4 figures, to appear in Nature Communication

Dynamics of multipartite quantum correlations under decoherence

Quantum discord is an optimal resource for the quantification of classical and non-classical correlations as compared to other related measures. Geometric measure of quantum discord is another measure of quantum correlations. Recently, the geometric quantum discord for multipartite states has been introduced by Jianwei Xu [arxiv:quant/ph.1205.0330]. Motivated from the recent study [Ann. Phys. 327 (2012) 851] for the bipartite systems, I have investigated global quantum discord (QD) and geometric quantum discord (GQD) under the influence of external environments for different multipartite states. Werner-GHZ type three-qubit and six-qubit states are considered in inertial and non-inertial settings. The dynamics of QD and GQD is investigated under amplitude damping, phase damping, depolarizing and flipping channels. It is seen that the quantum discord vanishes for p>0.75 in case of three-qubit GHZ states and for p>0.5 for six qubit GHZ states. This implies that multipartite states are more fragile to decoherence for higher values of N. Surprisingly, a rapid sudden death of discord occurs in case of phase flip channel. However, for bit flip channel, no sudden death happens for the six-qubit states. On the other hand, depolarizing channel heavily influences the QD and GQD as compared to the amplitude damping channel. It means that the depolarizing channel has the most destructive influence on the discords for multipartite states. From the perspective of accelerated observers, it is seen that effect of environment on QD and GQD is much stronger than that of the acceleration of non-inertial frames. The degradation of QD and GQD happens due to Unruh effect. Furthermore, QD exhibits more robustness than GQD when the multipartite systems are exposed to environment.Comment: 15 pages, 4 figures, 4 table

Additivity and non-additivity of multipartite entanglement measures

We study the additivity property of three multipartite entanglement measures, i.e. the geometric measure of entanglement (GM), the relative entropy of entanglement and the logarithmic global robustness. First, we show the additivity of GM of multipartite states with real and non-negative entries in the computational basis. Many states of experimental and theoretical interests have this property, e.g. Bell diagonal states, maximally correlated generalized Bell diagonal states, generalized Dicke states, the Smolin state, and the generalization of D\"{u}r's multipartite bound entangled states. We also prove the additivity of other two measures for some of these examples. Second, we show the non-additivity of GM of all antisymmetric states of three or more parties, and provide a unified explanation of the non-additivity of the three measures of the antisymmetric projector states. In particular, we derive analytical formulae of the three measures of one copy and two copies of the antisymmetric projector states respectively. Third, we show, with a statistical approach, that almost all multipartite pure states with sufficiently large number of parties are nearly maximally entangled with respect to GM and relative entropy of entanglement. However, their GM is not strong additive; what's more surprising, for generic pure states with real entries in the computational basis, GM of one copy and two copies, respectively, are almost equal. Hence, more states may be suitable for universal quantum computation, if measurements can be performed on two copies of the resource states. We also show that almost all multipartite pure states cannot be produced reversibly with the combination multipartite GHZ states under asymptotic LOCC, unless relative entropy of entanglement is non-additive for generic multipartite pure states.Comment: 45 pages, 4 figures. Proposition 23 and Theorem 24 are revised by correcting a minor error from Eq. (A.2), (A.3) and (A.4) in the published version. The abstract, introduction, and summary are also revised. All other conclusions are unchange