3,124 research outputs found
Optimal distinction between non-orthogonal quantum states
Given a finite set of linearly independent quantum states, an observer who
examines a single quantum system may sometimes identify its state with
certainty. However, unless these quantum states are orthogonal, there is a
finite probability of failure. A complete solution is given to the problem of
optimal distinction of three states, having arbitrary prior probabilities and
arbitrary detection values. A generalization to more than three states is
outlined.Comment: 9 pages LaTeX, one PostScript figure on separate pag
Quantum mechanics explained
The physical motivation for the mathematical formalism of quantum mechanics
is made clear and compelling by starting from an obvious fact - essentially,
the stability of matter - and inquiring into its preconditions: what does it
take to make this fact possible?Comment: 29 pages, 5 figures. v2: revised in response to referee comment
Quantum Field Theory with Null-Fronted Metrics
There is a large class of classical null-fronted metrics in which a free
scalar field has an infinite number of conservation laws. In particular, if the
scalar field is quantized, the number of particles is conserved. However, with
more general null-fronted metrics, field quantization cannot be interpreted in
terms of particle creation and annihilation operators, and the physical meaning
of the theory becomes obscure.Comment: 11 page
Information-disturbance tradeoff in quantum measurements
We present a simple information-disturbance tradeoff relation valid for any
general measurement apparatus: The disturbance between input and output states
is lower bounded by the information the apparatus provides in distinguishing
these two states.Comment: 4 Pages, 1 Figure. Published version (reference added and minor
changes performed
Minimum error discrimination problem for pure qubit states
The necessary and sufficient conditions for minimization of the generalized
rate error for discriminating among pure qubit states are reformulated in
terms of Bloch vectors representing the states. For the direct optimization
problem an algorithmic solution to these conditions is indicated. A solution to
the inverse optimization problem is given. General results are widely
illustrated by particular cases of equiprobable states and pure qubit
states given with different prior probabilities.Comment: English is corrected thanks to PRA edito
Non-linear operations in quantum information theory
Quantum information theory is used to analize various non-linear operations
on quantum states. The universal disentanglement machine is shown to be
impossible, and partial (negative) results are obtained in the state-dependent
case. The efficiency of the transformation of non-orthogonal states into
orthogonal ones is discussed.Comment: 11 pages, LaTeX, 3 figures on separate page
Wigner's little group and Berry's phase for massless particles
The ``little group'' for massless particles (namely, the Lorentz
transformations that leave a null vector invariant) is isomorphic to
the Euclidean group E2: translations and rotations in a plane. We show how to
obtain explicitly the rotation angle of E2 as a function of and we
relate that angle to Berry's topological phase. Some particles admit both signs
of helicity, and it is then possible to define a reduced density matrix for
their polarization. However, that density matrix is physically meaningless,
because it has no transformation law under the Lorentz group, even under
ordinary rotations.Comment: 4 pages revte
Power of unentangled measurements on two antiparallel spins
We consider a pair of antiparallel spins polarized in a random direction to
encode quantum information. We wish to extract as much information as possible
on the polarization direction attainable by an unentangled measurement, i.e.,
by a measurement, whose outcomes are associated with product states. We develop
analytically the upper bound 0.7935 bits to the Shannon mutual information
obtainable by an unentangled measurement, which is definitely less than the
value 0.8664 bits attained by an entangled measurement. This proves our main
result, that not every ensemble of product states can be optimally
distinguished by an unentangled measurement, if the measure of
distinguishability is defined in the sense of Shannon. We also present results
from numerical calculations and discuss briefly the case of parallel spins.Comment: Latex file, 18 pages, 1 figure; published versio
Violations of local realism with quNits up to N=16
Predictions for systems in entangled states cannot be described in local
realistic terms. However, after admixing some noise such a description is
possible. We show that for two quNits (quantum systems described by N
dimensional Hilbert spaces) in a maximally entangled state the minimal
admixture of noise increases monotonically with N. The results are a direct
extension of those of Kaszlikowski et. al., Phys. Rev. Lett. {\bf 85}, 4418
(2000), where results for were presented. The extension up to N=16 is
possible when one defines for each N a specially chosen set of observables. We
also present results concerning the critical detectors efficiency beyond which
a valid test of local realism for entangled quNits is possible.Comment: 5 pages, 3 ps picture
Generalized Schmidt decomposition and classification of three-quantum-bit states
We prove for any pure three-quantum-bit state the existence of local bases
which allow to build a set of five orthogonal product states in terms of which
the state can be written in a unique form. This leads to a canonical form which
generalizes the two-quantum-bit Schmidt decomposition. It is uniquely
characterized by the five entanglement parameters. It leads to a complete
classification of the three-quantum-bit states. It shows that the right outcome
of an adequate local measurement always erases all entanglement between the
other two parties.Comment: 4 pages, Revtex. Published version, minor changes and new references
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