44 research outputs found
Fidelity for displaced squeezed states and the oscillator semigroup
The fidelity for two displaced squeezed thermal states is computed using the
fact that the corresponding density operators belong to the oscillator
semigroup.Comment: 3 pages, REVTEX, no figures, submitted to Journal of Physics A, May
5, 199
Quantum discord and related measures of quantum correlations in XY chains
We examine the quantum correlations of spin pairs in the ground state of
finite XY chains in a transverse field, by evaluating the quantum discord as
well as other related entropic measures of quantum correlations. A brief review
of the latter, based on generalized entropic forms, is also included. It is
shown that parity effects are of crucial importance for describing the behavior
of these measures below the critical field. It is also shown that these
measures reach full range in the immediate vicinity of the factorizing field,
where they become independent of separation and coupling range. Analytical and
numerical results for the quantum discord, the geometric discord and other
measures in spin chains with nearest neighbor coupling and in fully connected
spin arrays are also provided.Comment: accepted in Int. J. Mod. Phys. B, special issue "Classical Vs Quantum
correlations in composite systems" edited by L. Amico, S. Bose, V. Korepin
and V. Vedra
Dense coding with multipartite quantum states
We consider generalisations of the dense coding protocol with an arbitrary
number of senders and either one or two receivers, sharing a multiparty quantum
state, and using a noiseless channel. For the case of a single receiver, the
capacity of such information transfer is found exactly. It is shown that the
capacity is not enhanced by allowing the senders to perform joint operations.
We provide a nontrivial upper bound on the capacity in the case of two
receivers. We also give a classification of the set of all multiparty states in
terms of their usefulness for dense coding. We provide examples for each of
these classes, and discuss some of their properties.Comment: 14 pages, 1 figure, RevTeX
Chow's theorem and universal holonomic quantum computation
A theorem from control theory relating the Lie algebra generated by vector
fields on a manifold to the controllability of the dynamical system is shown to
apply to Holonomic Quantum Computation. Conditions for deriving the holonomy
algebra are presented by taking covariant derivatives of the curvature
associated to a non-Abelian gauge connection. When applied to the Optical
Holonomic Computer, these conditions determine that the holonomy group of the
two-qubit interaction model contains . In particular, a
universal two-qubit logic gate is attainable for this model.Comment: 13 page
Universality of optimal measurements
We present optimal and minimal measurements on identical copies of an unknown
state of a qubit when the quality of measuring strategies is quantified with
the gain of information (Kullback of probability distributions). We also show
that the maximal gain of information occurs, among isotropic priors, when the
state is known to be pure. Universality of optimal measurements follows from
our results: using the fidelity or the gain of information, two different
figures of merits, leads to exactly the same conclusions. We finally
investigate the optimal capacity of copies of an unknown state as a quantum
channel of information.Comment: Revtex, 5 pages, no figure
Statistical distinguishability between unitary operations
The problem of distinguishing two unitary transformations, or quantum gates,
is analyzed and a function reflecting their statistical distinguishability is
found. Given two unitary operations, and , it is proved that there
always exists a finite number such that and are perfectly distinguishable, although they were not in the single-copy
case. This result can be extended to any finite set of unitary transformations.
Finally, a fidelity for one-qubit gates, which satisfies many useful properties
from the point of view of quantum information theory, is presented.Comment: 6 pages, REVTEX. The perfect distinguishability result is extended to
any finite set of gate
Non-adaptive Measurement-based Quantum Computation and Multi-party Bell Inequalities
Quantum correlations exhibit behaviour that cannot be resolved with a local
hidden variable picture of the world. In quantum information, they are also
used as resources for information processing tasks, such as Measurement-based
Quantum Computation (MQC). In MQC, universal quantum computation can be
achieved via adaptive measurements on a suitable entangled resource state. In
this paper, we look at a version of MQC in which we remove the adaptivity of
measurements and aim to understand what computational abilities still remain in
the resource. We show that there are explicit connections between this model of
computation and the question of non-classicality in quantum correlations. We
demonstrate this by focussing on deterministic computation of Boolean
functions, in which natural generalisations of the Greenberger-Horne-Zeilinger
(GHZ) paradox emerge; we then explore probabilistic computation, via which
multipartite Bell Inequalities can be defined. We use this correspondence to
define families of multi-party Bell inequalities, which we show to have a
number of interesting contrasting properties.Comment: 13 pages, 4 figures, final version accepted for publicatio
Generic Quantum Block Compression
A generic approach for compiling any classical block compression algorithm
into a quantum block compression algorithm is presented. Using this technique,
compression asymptoticaly approaching the von Neumann entropy of a qubit source
can be achieved. The automatically compiled algorithms are competitive (in time
and space complexity) with hand constructed quantum block compression
algorithms
Bures distance between two displaced thermal states
The Bures distance between two displaced thermal states and the corresponding
geometric quantities (statistical metric, volume element, scalar curvature) are
computed. Under nonunitary (dissipative) dynamics, the statistical distance
shows the same general features previously reported in the literature by
Braunstein and Milburn for two--state systems. The scalar curvature turns out
to have new interesting properties when compared to the curvature associated
with squeezed thermal states.Comment: 3 pages, RevTeX, no figure
Measuring the Quantum State of a Large Angular Momentum
We demonstrate a general method to measure the quantum state of an angular
momentum of arbitrary magnitude. The (2F+1) x (2F+1) density matrix is
completely determined from a set of Stern-Gerlach measurements with (4F+1)
different orientations of the quantization axis. We implement the protocol for
laser cooled Cesium atoms in the 6S_{1/2}(F=4) hyperfine ground state and apply
it to a variety of test states prepared by optical pumping and Larmor
precession. A comparison of input and measured states shows typical
reconstruction fidelities of about 0.95.Comment: 4 pages, 6 figures, submitted to PR