7,183 research outputs found
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 -side two-qubit discordant state can be
locally prepared from a classical state by a trace-preserving channel on qubit
if and only if its QSE of 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 or
qubit , 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 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 norm measure of coherence, and
analyze under which condition this relation holds. We also obtain a more
general relation which applies to arbitrary -qubit state, and determine a
condition for the transformation matrix of the quantum channel which can
support permanently freezing of the 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
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
Nonlocal advantage of quantum coherence in high-dimensional states
By local measurements on party of a system and classical
communication between its two parties, one can achieve a nonlocal advantage of
quantum coherence (NAQC) on party . For the 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 -dimensional states when 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.
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
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