2,190 research outputs found
Optimal correlations in many-body quantum systems
Information and correlations in a quantum system are closely related through
the process of measurement. We explore such relation in a many-body quantum
setting, effectively bridging between quantum metrology and condensed matter
physics. To this aim we adopt the information-theory view of correlations, and
study the amount of correlations after certain classes of
Positive-Operator-Valued Measurements are locally performed. As many-body
system we consider a one-dimensional array of interacting two-level systems (a
spin chain) at zero temperature, where quantum effects are most pronounced. We
demonstrate how the optimal strategy to extract the correlations depends on the
quantum phase through a subtle interplay between local interactions and
coherence.Comment: 5 pages, 5 figures + supplementary material. To be published in PR
Chaotic Evolution in Quantum Mechanics
A quantum system is described, whose wave function has a complexity which
increases exponentially with time. Namely, for any fixed orthonormal basis, the
number of components required for an accurate representation of the wave
function increases exponentially.Comment: 8 pages (LaTeX 16 kB, followed by PostScript 2 kB for figure
Exact positivity of the Wigner and P-functions of a Markovian open system
We discuss the case of a Markovian master equation for an open system, as it
is frequently found from environmental decoherence. We prove two theorems for
the evolution of the quantum state. The first one states that for a generic
initial state the corresponding Wigner function becomes strictly positive after
a finite time has elapsed. The second one states that also the P-function
becomes exactly positive after a decoherence time of the same order. Therefore
the density matrix becomes exactly decomposable into a mixture of Gaussian
pointer states.Comment: 11 pages, references added, typo corrected, to appear in J. Phys.
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
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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Evolution of Liouville density of a chaotic system
An area-preserving map of the unit sphere, consisting of alternating twists
and turns, is mostly chaotic. A Liouville density on that sphere is specified
by means of its expansion into spherical harmonics. That expansion initially
necessitates only a finite number of basis functions. As the dynamical mapping
proceeds, it is found that the number of non-negligible coefficients increases
exponentially with the number of steps. This is to be contrasted with the
behavior of a Schr\"odinger wave function which requires, for the analogous
quantum system, a basis of fixed size.Comment: LaTeX 4 pages (27 kB) followed by four short PostScript files (2 kB +
2 kB + 1 kB + 4 kB
Quantum and classical descriptions of a measuring apparatus
A measuring apparatus is described by quantum mechanics while it interacts
with the quantum system under observation, and then it must be given a
classical description so that the result of the measurement appears as
objective reality. Alternatively, the apparatus may always be treated by
quantum mechanics, and be measured by a second apparatus which has such a dual
description. This article examines whether these two different descriptions are
mutually consistent. It is shown that if the dynamical variable used in the
first apparatus is represented by an operator of the Weyl-Wigner type (for
example, if it is a linear coordinate), then the conversion from quantum to
classical terminology does not affect the final result. However, if the first
apparatus encodes the measurement in a different type of operator (e.g., the
phase operator), the two methods of calculation may give different results.Comment: 18 pages LaTeX (including one encapsulated PostScript figure
Optimal manipulations with qubits: Universal quantum entanglers
We analyze various scenarios for entangling two initially unentangled qubits.
In particular, we propose an optimal universal entangler which entangles a
qubit in unknown state with a qubit in a reference (known) state
. That is, our entangler generates the output state which is as close as
possible to the pure (symmetrized) state . The most
attractive feature of this entangling machine, is that the fidelity of its
performance (i.e. the distance between the output and the ideally entangled --
symmetrized state) does not depend on the input and takes the constant value
. We also analyze how to optimally generate
from a single qubit initially prepared in an unknown state |\Psi\r a two
qubit entangled system which is as close as possible to a Bell state
, where \l\Psi|\Psi^\perp\r =0.Comment: 11 pages, 3 eps figures, accepted for publication in Phys. Rev.
Quantum copying: A network
We present a network consisting of quantum gates which produces two imperfect
copies of an arbitrary qubit. The quality of the copies does not depend on the
input qubit. We also show that for a restricted class of inputs it is possible
to use a very similar network to produce three copies instead of two. For
qubits in this class, the copy quality is again independent of the input and is
the same as the quality of the copies produced by the two-copy network.Comment: 10 pages LaTeX, with 1 figure, submitted to the Physical Review
Opposite Thermodynamic Arrows of Time
A model in which two weakly coupled systems maintain opposite running
thermodynamic arrows of time is exhibited. Each experiences its own retarded
electromagnetic interaction and can be seen by the other. The possibility of
opposite-arrow systems at stellar distances is explored and a relation to dark
matter suggested.Comment: To appear in Phys. Rev. Let
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