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 picture of the quantum steering ellipsoids (QSE). The phenomenon of locally increased quantum correlation 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 non-radial line segment. For states with higer-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 QSEs of either qubit $A$ or qubit $B$, for the needle-shape QSE states, as well as the Bell diagonal states with higher-dimensional QSE.Comment: 6 pages, 2 figures. Comments are welcom

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.Comment: almost published versio

Upper bound and shareability of quantum discord based on entropic uncertainty relations

By using the quantum-memory-assisted entropic uncertainty relation (EUR), we derive a computable tight upper bound for quantum discord, which applies to an arbitrary bipartite state. Detailed examples show that this upper bound is tighter than other known bounds in a wide regime. Furthermore, we show that for any tripartite pure state, the quantum-memory-assisted EUR imposes a constraint on the shareability of quantum correlations among the constituent parties. This conclusion amends the well accepted result that quantum discord is not monogamous.Comment: 5 pages, 1 figure, the final version as that published in Phys. Rev.

Measurement-induced nonlocality based on the trace norm

Nonlocality is one unique property of quantum mechanics differing from classical world. One of its quantifications can be properly described as the maximum global effect caused by locally invariant measurements, termed as measurement-induced nonlocality (MIN) (2011 \emph{Phys. Rev. Lett.} {\bf 106} 120401). Here, we propose to quantify the MIN by the trace norm. We show explicitly that this measure is monotonically decreasing under the action of 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 that 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 $2\times n$ dimensional pure state, two-qubit state, and certain high-dimensional states. As other quantum correlation measures, the new defined MIN can be directly applied to various models for physical interpretations.Comment: 6 pages, 1 figure, the final version as that published in New J. Phy

Evolution equation for quantum coherence

The estimation of the decoherence process of an open quantum system is of both theoretical significance and experimental appealing. Practically, the decoherence can be easily estimated if the coherence evolution satisfies some simple relations. Based on the coherence quantification method, we prove a simple factorization relation for the $l_1$ norm measure of coherence, and analyze under which condition this relation holds. We also obtain a more general relation which applies to arbitrary $N$-qubit state, and determine a condition for the transformation matrix of the quantum channel which can support permanently freezing of the $l_1$ norm of coherence. These results simplify determination of a general decoherence dynamics to that the investigation of evolution about the representative probe state.Comment: 9 pages (including the Supplemental Material), 1 figure, minor corrections being mad

Evolution equation for geometric quantum correlation measures

A simple relation is established for the evolution equation of quantum information processing protocols such as quantum teleportation, remote state preparation, Bell-inequality violation and particularly dynamics of the geometric quantum correlation measures. This relation shows that when the system traverses the local quantum channel, various figures of merit of the quantum correlations for different protocols demonstrate a factorization decay behavior for dynamics. We identified the family of quantum states for different kinds of quantum channels under the action of which the relation holds. This relation simplifies the assessment of many quantum tasks.Comment: 7 pages, 2 figure

Nonlocal advantage of quantum coherence in high-dimensional states

By local measurements on party $A$ of a system $AB$ and classical communication between its two parties, one can achieve a nonlocal advantage of quantum coherence (NAQC) on party $B$. For the $l_1$ norm of coherence and the relative entropy of coherence, we generalized the framework of NAQC for two qubits and derived the criteria which capture NAQC in the $(d\times d)$-dimensional states when $d$ is a power of a prime. We also presented a new framework for formulating NAQC, and showed through explicit examples its capacity on capturing the NAQC states. Moreover, we proved that any bipartite state with NAQC is quantum entangled, thus the obtained criteria can also be used as an entanglement witness.Comment: 5 pages, 2 figures; Final version to be published in Phys. Rev.

Dynamics of entropic measurement-induced nonlocality in structured reservoirs

We propose the entropic measurement-induced nonlocality (MIN) as the maximal increment of von Neumann entropy induced by the locally non-disturbing measurement, and study behaviors of it both in the independent and common structured reservoirs. We present schemes for preserving the MIN, and show that for certain initial states the MIN, including the quantum correlations, can even be enhanced by the common reservoir. Additionally, we also show that the different measures of MIN may give different qualitative characterizations of nonlocal properties, i.e., it is rather measure dependent than state dependent.Comment: 8 pages, 6 figure

Competitions between quantum correlations in the quantum-memory-assisted entropic uncertainty relation

With the aid of a quantum memory, the uncertainty about the measurement outcomes of two incompatible observables of a quantum system can be reduced. We investigate this measurement uncertainty bound by considering an additional quantum system connected with both the quantum memory and the measured quantum system. We find that the reduction of the uncertainty bound induced by a quantum memory, on the other hand, implies its increasing for a third participant. We also show that the properties of the uncertainty bound can be viewed from perspectives of both quantum and classical correlations, in particular, the behavior of the uncertainty bound is a result of competitions of various correlations between different parties.Comment: 5 pages, 2 figures, the final version as that published in Phys. Rev.

Quantum coherence of multiqubit states in correlated noisy channels

The long-time maintenance of quantum coherence is crucial for its practical applications. We explore decoherence process of a multiqubit system passing through a correlated channel (phase flip, bit flip, bit-phase flip, and depolarizing). The results show that the decay of coherence was evidently delayed when the consecutive actions of the channel on the sequence of qubits has some classical correlations. In particular, the relative entropy of coherence for a system with large number of qubits is more robust than that with small number of qubits. We also provide an explanation for the delayed decoherence by exploring the interplay between the change of the unlocalized quantum coherence and the total correlation gain of the multiqubit system.Comment: 6 pages, 3 figure