1,261 research outputs found
Interpreting quantum discord through quantum state merging
We present an operational interpretation of quantum discord based on the
quantum state merging protocol. Quantum discord is the markup in the cost of
quantum communication in the process of quantum state merging, if one discards
relevant prior information. Our interpretation has an intuitive explanation
based on the strong subadditivity of von Neumann entropy. We use our result to
provide operational interpretations of other quantities like the local purity
and quantum deficit. Finally, we discuss in brief some instances where our
interpretation is valid in the single copy scenario.Comment: 5 pages, no figures. See http://arxiv.org/abs/1008.3205 for similar
results. Typos fixed, references and acknowledgements updated. End note adde
Nonzero Classical Discord
Quantum discord is the quantitative difference between two alternative
expressions for bipartite mutual information, given respectively in terms of
two distinct definitions for the conditional entropy. By constructing a
stochastic model of shared states, classical discord can be similarly defined,
quantifying the presence of some stochasticity in the measurement process.
Therefore, discord can generally be understood as a quantification of the
system's state disturbance due to local measurements, be it quantum or
classical. We establish an operational meaning of classical discord in the
context of state merging with noisy measurement and thereby show the
quantum-classical separation in terms of a negative conditional entropy.Comment: Replaced by the published versio
Computing quantum discord is NP-complete
We study the computational complexity of quantum discord (a measure of
quantum correlation beyond entanglement), and prove that computing quantum
discord is NP-complete. Therefore, quantum discord is computationally
intractable: the running time of any algorithm for computing quantum discord is
believed to grow exponentially with the dimension of the Hilbert space so that
computing quantum discord in a quantum system of moderate size is not possible
in practice. As by-products, some entanglement measures (namely entanglement
cost, entanglement of formation, relative entropy of entanglement, squashed
entanglement, classical squashed entanglement, conditional entanglement of
mutual information, and broadcast regularization of mutual information) and
constrained Holevo capacity are NP-hard/NP-complete to compute. These
complexity-theoretic results are directly applicable in common randomness
distillation, quantum state merging, entanglement distillation, superdense
coding, and quantum teleportation; they may offer significant insights into
quantum information processing. Moreover, we prove the NP-completeness of two
typical problems: linear optimization over classical states and detecting
classical states in a convex set, providing evidence that working with
classical states is generically computationally intractable.Comment: The (published) journal version
http://iopscience.iop.org/1367-2630/16/3/033027/article is more updated than
the arXiv versions, and is accompanied with a general scientific summary for
non-specialists in computational complexit
On the Necessity of Entanglement for the Explanation of Quantum Speedup
In this paper I argue that entanglement is a necessary component for any
explanation of quantum speedup and I address some purported counter-examples
that some claim show that the contrary is true. In particular, I address Biham
et al.'s mixed-state version of the Deutsch-Jozsa algorithm, and Knill &
Laflamme's deterministic quantum computation with one qubit (DQC1) model of
quantum computation. I argue that these examples do not demonstrate that
entanglement is unnecessary for the explanation of quantum speedup, but that
they rather illuminate and clarify the role that entanglement does play.Comment: Many clarificatory changes, and improved argumentation. Comments and
criticisms are still welcom
Quantum mutual information and quantumness vectors for multi-qubit systems
We introduce a new information theoretic measure of quantum correlations for
multiparticle systems. We use a form of multivariate mutual information -- the
interaction information and generalize it to multiparticle quantum systems.
There are a number of different possible generalizations. We consider two of
them. One of them is related to the notion of quantum discord and the other to
the concept of quantum dissension. This new measure, called dissension vector,
is a set of numbers -- quantumness vector. This can be thought of as a
fine-grained measure, as opposed to measures that quantify some average quantum
properties of a system. These quantities quantify/characterize the correlations
present in multiparticle states. We consider some multiqubit states and find
that these quantities are responsive to different aspects of quantumness, and
correlations present in a state. We find that different dissension vectors can
track the correlations (both classical and quantum), or quantumness only. As
physical applications, we find that these vectors might be useful in several
information processing tasks. We consider the role of dissension vectors -- (a)
in deciding the security of BB84 protocol against an eavesdropper and (b) in
determining the possible role of correlations in the performance of Grover
search algorithm. Especially, in the Grover search algorithm, we find that
dissension vectors can detect the correlations and show the maximum
correlations when one expects.Comment: 18 pages 8 figures. Updated. Comments are welcom
Remote transfer of Gaussian quantum discord
Quantum discord quantifies quantum correlation between quantum systems, which
has potential application in quantum information processing. In this paper, we
propose a scheme realizing the remote transfer of Gaussian quantum discord, in
which another quantum discordant state or an Einstein-Podolsky-Rosen entangled
state serves as ancillary state. The calculation shows that two independent
optical modes that without direct interaction become quantum correlated after
the transfer. The output Gaussian quantum discord can be higher than the
initial Gaussian quantum discord when optimal gain of the classical channel and
the ancillary state are chosen. The physical reason for this result comes from
the fact that the quantum discord of an asymmetric Gaussian quantum discordant
state can be higher than that of a symmetric one. The presented scheme has
potential application in quantum information network
Geometric measure of quantum discord and the geometry of a class of two-qubit states
We investigate the geometric picture of the level surfaces of quantum
entanglement and geometric measure of quantum discord (GMQD) of a class of
X-states, respectively. This pictorial approach provides us a direct
understanding of the structure of entanglement and GMQD. The dynamic evolution
of GMQD under two typical kinds of quantum decoherence channels is also
investigated. It is shown that there exists a class of initial states for which
the GMQD is not destroyed by decoherence in a finite time interval.
Furthermore, we establish a factorization law between the initial and final
GMQD, which allows us to infer the evolution of entanglement under the
influences of the environment.Comment: 10 pages, 4 figures, comments are welcom
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