149 research outputs found
Strengthened Bell inequalities for orthogonal spin directions
We strengthen the bound on the correlations of two spin-1/2 particles
(qubits) in separable (non-entangled) states for locally orthogonal spin
directions by much tighter bounds than the well-known Bell inequality. This
provides a sharper criterion for the experimental distinction between entangled
and separable states, and even one which is a necessary and sufficient
condition for separability. However, these improved bounds do not apply to
local hidden-variable theories, and hence they provide a criterion to test the
correlations allowed by local hidden-variable theories against those allowed by
separable quantum states. Furthermore, these bounds are stronger than some
recent alternative experimentally accessible entanglement criteria. We also
address the issue of finding a finite subset of these inequalities that would
already form a necessary and sufficient condition for non-entanglement. For
mixed state we have not been able to resolve this, but for pure states a set of
six inequalities using only three sets of orthogonal observables is shown to be
already necessary and sufficient for separability.Comment: v2: Considerably changed, many new and stronger results v3: Published
version; To appear in Physics Letters A. Online available from publishers
websit
Inequalities that test locality in quantum mechanics
Quantum theory violates Bell's inequality, but not to the maximum extent that
is logically possible. We derive inequalities (generalizations of Cirel'son's
inequality) that quantify the upper bound of the violation, both for the
standard formalism and the formalism of generalized observables (POVMs). These
inequalities are quantum analogues of Bell inequalities, and they can be used
to test the quantum version of locality. We discuss the nature of this kind of
locality. We also go into the relation of our results to an argument by Popescu
and Rohrlich (Found. Phys. 24, 379 (1994)) that there is no general connection
between the existence of Cirel'son's bound and locality.Comment: 5 pages, 1 figure; the argument has been made clearer in the revised
version; 1 reference adde
Uncertainty in prediction and in inference
The concepts of uncertainty in prediction and inference are introduced
and illustrated using the diffraction of light as an example. The close re-lationship
between the concepts of uncertainty in inference and resolving
power is noted. A general quantitative measure of uncertainty in infer-ence
can be obtained by means of the so-called statistical distance between
probability distributions. When applied to quantum mechanics, this dis-tance
leads to a measure of the distinguishability of quantum states, which
essentially is the absolute value of the matrix element between the states.
The importance of this result to the quantum mechanical uncertainty prin-ciple
is noted. The second part of the paper provides a derivation of the
statistical distance on basis of the so-called method of support
Partial separability and entanglement criteria for multiqubit quantum states
We explore the subtle relationships between partial separability and
entanglement of subsystems in multiqubit quantum states and give experimentally
accessible conditions that distinguish between various classes and levels of
partial separability in a hierarchical order. These conditions take the form of
bounds on the correlations of locally orthogonal observables. Violations of
such inequalities give strong sufficient criteria for various forms of partial
inseparability and multiqubit entanglement. The strength of these criteria is
illustrated by showing that they are stronger than several other well-known
entanglement criteria (the fidelity criterion, violation of Mermin-type
separability inequalities, the Laskowski-\.Zukowski criterion and the
D\"ur-Cirac criterion), and also by showing their great noise robustness for a
variety of multiqubit states, including N-qubit GHZ states and Dicke states.
Furthermore, for N greater than or equal to 3 they can detect bound entangled
states. For all these states, the required number of measurement settings for
implementation of the entanglement criteria is shown to be only N+1. If one
chooses the familiar Pauli matrices as single-qubit observables, the
inequalities take the form of bounds on the anti-diagonal matrix elements of a
state in terms of its diagonal matrix elements.Comment: 25 pages, 3 figures. v4: published versio
Addendum to "Sufficient conditions for three-particle entanglement and their tests in recent experiments"
A recent paper [M. Seevinck and J. Uffink, Phys. Rev. A 65, 012107 (2002)]
presented a bound for the three-qubit Mermin inequality such that the violation
of this bound indicates genuine three-qubit entanglement. We show that this
bound can be improved for a specific choice of observables. In particular, if
spin observables corresponding to orthogonal directions are measured at the
qubits (e.g., X and Y spin coordinates) then the bound is the same as the bound
for states with a local hidden variable model. As a consequence, it can
straightforwardly be shown that in the experiment described by J.-W. Pan et al.
[Nature 403, 515 (2000)] genuine three-qubit entanglement was detected.Comment: Two pages, no figures, revtex4; minor changes before publicatio
Translational Entanglement of Dipole-Dipole Interacting Atoms in Optical Lattices
We propose and investigate a realization of the position- and
momentum-correlated Einstein-Podolsky-Rosen (EPR) states [Phys. Rev. 47, 777
(1935)] that have hitherto eluded detection. The realization involves atom
pairs that are confined to adjacent sites of two mutually shifted optical
lattices and are entangled via laser-induced dipole-dipole interactions. The
EPR "paradox" with translational variables is then modified by
lattice-diffraction effects, and can be verified to a high degree of accuracy
in this scheme.Comment: 4 pages, 3 figures, to be published in PR
Geometric derivation of the quantum speed limit
The Mandelstam-Tamm and Margolus-Levitin inequalities play an important role
in the study of quantum mechanical processes in Nature, since they provide
general limits on the speed of dynamical evolution. However, to date there has
been only one derivation of the Margolus-Levitin inequality. In this paper,
alternative geometric derivations for both inequalities are obtained from the
statistical distance between quantum states. The inequalities are shown to hold
for unitary evolution of pure and mixed states, and a counterexample to the
inequalities is given for evolution described by completely positive
trace-preserving maps. The counterexample shows that there is no quantum speed
limit for non-unitary evolution.Comment: 8 pages, 1 figure
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