1,183 research outputs found
Better bound on the exponent of the radius of the multipartite separable ball
We show that for an m-qubit quantum system, there is a ball of radius
asymptotically approaching kappa 2^{-gamma m} in Frobenius norm, centered at
the identity matrix, of separable (unentangled) positive semidefinite matrices,
for an exponent gamma = (1/2)((ln 3/ln 2) - 1), roughly .29248125. This is much
smaller in magnitude than the best previously known exponent, from our earlier
work, of 1/2. For normalized m-qubit states, we get a separable ball of radius
sqrt(3^(m+1)/(3^m+3)) * 2^{-(1 + \gamma)m}, i.e. sqrt{3^{m+1}/(3^m+3)}\times
6^{-m/2} (note that \kappa = \sqrt{3}), compared to the previous 2 * 2^{-3m/2}.
This implies that with parameters realistic for current experiments, NMR with
standard pseudopure-state preparation techniques can access only unentangled
states if 36 qubits or fewer are used (compared to 23 qubits via our earlier
results). We also obtain an improved exponent for m-partite systems of fixed
local dimension d_0, although approaching our earlier exponent as d_0
approaches infinity.Comment: 30 pp doublespaced, latex/revtex, v2 added discussion of Szarek's
upper bound, and reference to work of Vidal, v3 fixed some errors (no effect
on results), v4 involves major changes leading to an improved constant, same
exponent, and adds references to and discussion of Szarek's work showing that
exponent is essentially optimal for qubit case, and Hildebrand's alternative
derivation for qubit case. To appear in PR
Local Quantum Measurement and No-Signaling Imply Quantum Correlations
We show that, assuming that quantum mechanics holds locally, the finite speed
of information is the principle that limits all possible correlations between
distant parties to be quantum mechanical as well. Local quantum mechanics means
that a Hilbert space is assigned to each party, and then all local
positive-operator-valued measurements are (in principle) available; however,
the joint system is not necessarily described by a Hilbert space. In
particular, we do not assume the tensor product formalism between the joint
systems. Our result shows that if any experiment would give nonlocal
correlations beyond quantum mechanics, quantum theory would be invalidated even
locally.Comment: Published version. 5 pages, 1 figure
Discord and non-classicality in probabilistic theories
Quantum discord quantifies non-classical correlations in quantum states. We
introduce discord for states in causal probabilistic theories, inspired by the
original definition proposed in Ref. [17]. We show that the only probabilistic
theory in which all states have null discord is classical probability theory.
Non-null discord is then not just a quantum feature, but a generic signature of
non-classicality.Comment: 5 pages, revtex styl
Generalization of entanglement to convex operational theories: Entanglement relative to a subspace of observables
We define what it means for a state in a convex cone of states on a space of
observables to be generalized-entangled relative to a subspace of the
observables, in a general ordered linear spaces framework for operational
theories. This extends the notion of ordinary entanglement in quantum
information theory to a much more general framework. Some important special
cases are described, in which the distinguished observables are subspaces of
the observables of a quantum system, leading to results like the identification
of generalized unentangled states with Lie-group-theoretic coherent states when
the special observables form an irreducibly represented Lie algebra. Some open
problems, including that of generalizing the semigroup of local operations with
classical communication to the convex cones setting, are discussed.Comment: 19 pages, to appear in proceedings of Quantum Structures VII, Int. J.
Theor. Phy
A violation of the uncertainty principle implies a violation of the second law of thermodynamics
Uncertainty relations state that there exist certain incompatible
measurements, to which the outcomes cannot be simultaneously predicted. While
the exact incompatibility of quantum measurements dictated by such uncertainty
relations can be inferred from the mathematical formalism of quantum theory,
the question remains whether there is any more fundamental reason for the
uncertainty relations to have this exact form. What, if any, would be the
operational consequences if we were able to go beyond any of these uncertainty
relations? We give a strong argument that justifies uncertainty relations in
quantum theory by showing that violating them implies that it is also possible
to violate the second law of thermodynamics. More precisely, we show that
violating the uncertainty relations in quantum mechanics leads to a
thermodynamic cycle with positive net work gain, which is very unlikely to
exist in nature.Comment: 8 pages, revte
On the "Security analysis and improvements of arbitrated quantum signature schemes"
Recently, Zou et al. [Phys. Rev. A 82, 042325 (2010)] pointed out that two
arbitrated quantum signature (AQS) schemes are not secure, because an
arbitrator cannot arbitrate the dispute between two users when a receiver
repudiates the integrity of a signature. By using a public board, they try to
propose two AQS schemes to solve the problem. This work shows that the same
security problem may exist in their schemes and also a malicious party can
reveal the other party's secret key without being detected by using the
Trojan-horse attacks. Accordingly, two basic properties of a quantum signature,
i.e. unforgeability and undeniability, may not be satisfied in their scheme
A subsystem-independent generalization of entanglement
We introduce a generalization of entanglement based on the idea that
entanglement is relative to a distinguished subspace of observables rather than
a distinguished subsystem decomposition. A pure quantum state is entangled
relative to such a subspace if its expectations are a proper mixture of those
of other states. Many information-theoretic aspects of entanglement can be
extended to the general setting, suggesting new ways of measuring and
classifying entanglement in multipartite systems. By going beyond the
distinguishable-subsystem framework, generalized entanglement also provides
novel tools for probing quantum correlations in interacting many-body systems.Comment: 5 pages, 1 encapsulated color figure, REVTeX4 styl
Introduction to Quantum Information Processing
As a result of the capabilities of quantum information, the science of
quantum information processing is now a prospering, interdisciplinary field
focused on better understanding the possibilities and limitations of the
underlying theory, on developing new applications of quantum information and on
physically realizing controllable quantum devices. The purpose of this primer
is to provide an elementary introduction to quantum information processing, and
then to briefly explain how we hope to exploit the advantages of quantum
information. These two sections can be read independently. For reference, we
have included a glossary of the main terms of quantum information.Comment: 48 pages, to appear in LA Science. Hyperlinked PDF at
http://www.c3.lanl.gov/~knill/qip/prhtml/prpdf.pdf, HTML at
http://www.c3.lanl.gov/~knill/qip/prhtm
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