Xueyuan Hu

Necessary and sufficient conditions for local creation of quantum correlation

Quantum correlation can be created by a local operation from some initially classical states. We prove that the necessary and sufficient condition for a local trace-preserving channel to create quantum correlation is that it is not a commutativity-preserving channel. This condition is valid for arbitrary finite dimension systems. We also derive the explicit form of commutativity-preserving channels. For a qubit, a commutativity-preserving channel is either a completely decohering channel or a mixing channel. For a three-dimensional system (qutrit), a commutativity-preserving channel is either a completely decohering channel or an isotropic channel.

Quantum correlating power of local quantum channels

We define quantum-correlating power (QCP) of a local quantum channel acting on the left part of a bipartite quantum system as the maximum amount of left quantum correlation that can be created by this channel. We prove that for any local channel, the optimal input state, which corresponds to the maximum quantum correlation in the output state, must be a classical-classical state. Further, the single-qubit channels with maximum QCP can be found in the class of channels which take their optimal input states to rank-two quantum-classical states. A superactivation property of QCP, that is, two zero-QCP channels can constitute a positive-QCP channel, is observed and discussed for single-qubit phase damping channels. The analytic expression for QCP of single-qubit amplitude damping channel is obtained. DOI: 10.1103/PhysRevA.87.032340

Quantum coherence of steered states

Lying at the heart of quantum mechanics, coherence has recently been studied as a key resource in quantum information theory. Quantum steering, a fundamental notion originally considered by Schödinger, has also recently received much attention. When Alice and Bob share a correlated quantum system, Alice can perform a local measurement to ‘steer’ Bob’s reduced state. We introduce the maximal steered coherence as a measure describing the extent to which steering can remotely create coherence; more precisely, we find the maximal coherence of Bob’s steered state in the eigenbasis of his original reduced state, where maximization is performed over all positive-operator valued measurements for Alice. We prove that maximal steered coherence vanishes for quantum-classical states whilst reaching a maximum for pure entangled states with full Schmidt rank. Although invariant under local unitary operations, maximal steered coherence may be increased when Bob performs a channel. For a two-qubit state we find that Bob’s channel can increase maximal steered coherence if and only if it is neither unital nor semi-classical, which coincides with the condition for increasing discord. Our results show that the power of steering for coherence generation, though related to discord, is distinct from existing measures of quantum correlation.

Extracting quantum coherence via steering

As the precious resource for quantum information processing, quantum coherence can be created remotely if the involved two sites are quantum correlated. It can be expected that the amount of coherence created should depend on the quantity of the shared quantum correlation, which is also a resource. Here, we establish an operational connection between coherence induced by steering and the quantum correlation. We find that the steering-induced coherence quantified by such as relative entropy of coherence and trace-norm of coherence is bounded from above by a known quantum correlation measure defined as the one-side measurement-induced disturbance. The condition that the upper bound saturated by the induced coherence varies for different measures of coherence. The tripartite scenario is also studied and similar conclusion can be obtained. Our results provide the operational connections between local and non-local resources in quantum information processing.

Genuine correlations of tripartite system

We define genuine total, classical and quantum correlations in tripartite systems. The genuine tripartite quantum discord can be interpreted as ‘quantum advantage’ in tripartite superdense coding. We find in a symmetrical tripartite state, for total correlation and classical correlation, the genuine tripartite correlations are no less than the pair-wise correlations. However, the genuine quantum tripartite correlation can be surpassed by the pair-wise quantum correlations. Analytical expressions for genuine tripartite correlations are obtained for pure states and rank-2 symmetrical states. The genuine correlations in both entangled and separable states are calculated.

Effect of local channels on quantum steering ellipsoids

The effect of a local trace-preserving single-qubit channel on a two-qubit state is investigated in the frame of quantum steering ellipsoids (QSEs). The phenomenon of locally increased quantum discord is visualized in this picture. We strictly prove that a B-side two-qubit discordant state can be locally prepared from a classical state by a trace-preserving channel on qubit B if and only if its QSE of B is a nonradial line segment. For states with higher-dimensional QSEs, the phenomenon of locally increased quantum correlation generally happens when the shape of the QSE is like a baguette. Based on this observation, we find a class of entangled states whose quantum discord can be increased by the local amplitude-damping channel. Further, we find that the local quantum channel does not increase the size of the QSEs of either qubit A or qubit B, for the needle-shaped QSE states, or for the Bell diagonal states with higher-dimensional QSEs.

Quantum coherence and geometric quantum discord

Quantum coherence and quantum correlations are of fundamental and practical significance for the development of quantum mechanics.They are also cornerstones of quantum computation and quantum communication theory. Searching physically meaningful and mathematically rigorous quantifiers of them are long-standing concerns of the community of quantum information science, and various faithful measures have been introduced so far. We review in this paper the measures of discordlike quantum correlations for bipartite and multipartite systems, the measures of quantum coherence for any single quantum system, and their relationship in different settings. Our aim is to provide a full review about the resource theory of quantum coherence, including its application in many-body systems, and the discordlike quantum correlations which were defined based on the various distance measures of states. We discuss the interrelations between quantum coherence and quantum correlations established in an operational way, and the fundamental characteristics of quantum coherence such as their complementarity under different basis sets, their duality with path information of an interference experiment, their distillation and dilution under different operations, and some new viewpoints of the superiority of the quantum algorithms from the perspective of quantum coherence. Additionally, we review properties of geometric quantum correlations and quantum coherence under noisy quantum channels. Finally, the main progresses for the study of quantum correlations and quantum coherence in the relativistic settings are reviewed. All these results provide an overview for the conceptual implications and basic connections of quantum coherence, quantum correlations, and their potential applications in various related subjects of physics.

Superadditivity of quantum-correlating power

We investigate the superadditivity property of quantum-correlating power (QCP), which is the power of generating quantum correlation by a local quantum channel. We prove that, when two local quantum channels are used in parallel, the QCP of the composed channel is no less than the sum of QCP of the two channels. For local channels with zero QCP, the superactivation of QCP is a fairly common effect, and it is proven to exist widely except for the trivial case where both of the channels are completely decohering channels or unitary operators. For general quantum channels, we show that the (not-so-common) additivity of QCP can be observed for the situation where a measuring-and-preparing channel is used together with a completely decohering channel.

Measurement-Induced Nonlocality and Quantum Correlations Under Local Operations

One significant feature of quantum theory is the existence of non-local quantum correlations which have no classical counterpart. There are various measures quantifying quantum correlations from different view points. Here, we present some recent developments about the quantum correlation measures known as measurement-induced nonlocality, in the sense that quantum measurement may destroy the quantum correlations for quantum states resulting in measures of nonlocality. Quantum correlations remain invariant under local unitary operations, they may decrease under general local operations, however, sometimes they can also show increasing for some local operations. We will review the properties of quantum correlations under local operations.