97 research outputs found
Discord and quantum computational resources
Discordant states appear in a large number of quantum phenomena and seem to
be a good indicator of divergence from classicality. While there is evidence
that they are essential for a quantum algorithm to have an advantage over a
classical one, their precise role is unclear. We examine the role of discord in
quantum algorithms using the paradigmatic framework of `restricted distributed
quantum gates' and show that manipulating discordant states using local
operations has an associated cost in terms of entanglement and communication
resources. Changing discord reduces the total correlations and reversible
operations on discordant states usually require non-local resources. Discord
alone is, however, not enough to determine the need for entanglement. A more
general type of similar quantities, which we call K-discord, is introduced as a
further constraint on the kinds of operations that can be performed without
entanglement resources.Comment: Closer to published versio
Why should we care about quantum discord?
Entanglement is a central feature of quantum theory. Mathematical properties
and physical applications of pure state entanglement make it a template to
study quantum correlations. However, an extension of entanglement measures to
mixed states in terms of separability does not always correspond to all the
operational aspects. Quantum discord measures allow an alternative way to
extend the idea of quantum correlations to mixed states. In many cases these
extensions are motivated by physical scenarios and quantum information
protocols. In this chapter we discuss several settings involving correlated
quantum systems, ranging from distributed gates to detectors testing quantum
fields. In each setting we show how entanglement fails to capture the relevant
features of the correlated system, and discuss the role of discord as a
possible alternative.Comment: Written for "Lectures on general quantum correlations and their
applications
Quantum Correlations in Large-Dimensional States of High Symmetry
In this article, we investigate how quantum correlations behave for the
so-called Werner and pseudo-pure families of states. The latter refers to
states formed by mixing any pure state with the totally mixed state. We derive
closed expressions for the Quantum Discord (QD) and the Relative Entropy of
Quantumness (REQ) for these families of states. For Werner states, the
classical correlations are seen to vanish in high dimensions while the amount
of quantum correlations remain bounded and become independent of whether or not
the the state is entangled. For pseudo-pure states, nearly the opposite effect
is observed with both the quantum and classical correlations growing without
bound as the dimension increases and only as the system becomes more entangled.
Finally, we verify that pseudo-pure states satisfy the conjecture of
[\textit{Phys. Rev. A} \textbf{84}, 052110 (2011)] which says that the
Geometric Measure of Discord (GD) always upper bounds the squared Negativity of
the state
Vanishing quantum discord is not necessary for completely-positive maps
The description of the dynamics of a system that may be correlated with its
environment is only meaningful within the context of a specific framework.
Different frameworks rely upon different assumptions about the initial
system-environment state. We reexamine the connections between
complete-positivity and quantum discord within two different sets of
assumptions about the relevant family of initial states. We present an example
of a system-environment state with non-vanishing quantum discord that leads to
a completely-positive map. This invalidates an earlier claim on the necessity
of vanishing quantum discord for completely-positive maps. In our final remarks
we discuss the physical validity of each approach.Comment: close to published versio
Quantum discord and local demons
Quantum discord was proposed as a measure of the "quantumness" of
correlations. There are at least three different discord-like quantities, two
of which determine the difference between the efficiencies of a Szilard's
engine under different sets of restrictions. The three discord measures vanish
simulataneosly. We introduce an easy way to test for zero discord, relate it to
the Cerf-Adami conditional entropy and show that there is no relation between
the discord and the local disitnguishability.Comment: 7 pages, RevTeX. Some minor changes after comments from colleagues,
some references added. Similar to published versio
"Quantumness" versus "classicality" of quantum states and quantum protocols
Entanglement is one of the pillars of quantum mechanics and quantum information processing, and as a result, the quantumness of nonentangled states has typically been overlooked and unrecognized until the last decade. We give a robust definition for the classicality versus quantumness of a single multipartite quantum state, a set of states, and a protocol using quantum states. We show a variety of nonentangled (separable) states that exhibit interesting quantum properties, and we explore the "zoo" of separable states; several interesting subclasses are defined based on the diagonalizing bases of the states, and their nonclassical behavior is investigated.The work of BG was funded by EPSRC and Sidney Sussex College, Cambridge. T.M was funded by the Wolfson Foundation and the Israeli MOD Research and Technology Unit. AB and TM were partly supported The Gerald Schwartz & Heather Reis- man Foundation
Entanglement, discord and the power of quantum computation
We show that the ability to create entanglement is necessary for execution of
bipartite quantum gates even when they are applied to unentangled states and
create no entanglement. Starting with a simple example we demonstrate that to
execute such a gate bi-locally the local operations and classical
communications (LOCC) should be supplemented by shared entanglement. Our
results point to the changes in quantum discord, which is a measure of
quantumness of correlations even in the absence of entanglement, as the
indicator of failure of a LOCC implementation of the gates.Comment: Published version. More results are adde
Degree of quantum correlation required to speed up a computation
The one clean qubit model of quantum computation (DQC1) efficiently
implements a computational task that is not known to have a classical
alternative. During the computation, there is never more than a small but
finite amount of entanglement present, and it is typically vanishingly small in
the system size. In this paper, we demonstrate that there is nothing unexpected
hidden within the DQC1 model -- Grover's Search, when acting on a mixed state,
provably exhibits a speed-up over classical with guarantees as to the presence
of only vanishingly small amounts of quantum correlations (entanglement and
quantum discord) -- while arguing that this is not an artefact of the
oracle-based construction. We also present some important refinements in the
evaluation of how much entanglement may be present in DQC1, and how the typical
entanglement of the system must be evaluated.Comment: 7 pages, 3 figure
Exploring multipartite quantum correlations with the square of quantum discord
We explore the quantum correlation distribution in multipartite quantum
states based on the square of quantum discord (SQD). For tripartite quantum
systems, we derive the necessary and sufficient condition for the SQD to
satisfy the monogamy relation. Particularly, we prove that the SQD is
monogamous for three-qubit pure states, based on which a genuine tripartite
quantum correlation measure is introduced. In addition, we also address the
quantum correlation distributions in four-qubit pure states. As an example, we
investigate multipartite quantum correlations in the dynamical evolution of
multipartite cavity-reservoir systems.Comment: 8 pages, 5 figure
The classical-quantum boundary for correlations: discord and related measures
One of the best signatures of nonclassicality in a quantum system is the
existence of correlations that have no classical counterpart. Different methods
for quantifying the quantum and classical parts of correlations are amongst the
more actively-studied topics of quantum information theory over the past
decade. Entanglement is the most prominent of these correlations, but in many
cases unentangled states exhibit nonclassical behavior too. Thus distinguishing
quantum correlations other than entanglement provides a better division between
the quantum and classical worlds, especially when considering mixed states.
Here we review different notions of classical and quantum correlations
quantified by quantum discord and other related measures. In the first half, we
review the mathematical properties of the measures of quantum correlations,
relate them to each other, and discuss the classical-quantum division that is
common among them. In the second half, we show that the measures identify and
quantify the deviation from classicality in various
quantum-information-processing tasks, quantum thermodynamics, open-system
dynamics, and many-body physics. We show that in many cases quantum
correlations indicate an advantage of quantum methods over classical ones.Comment: Close to the published versio
- …