701 research outputs found
Conditions for entanglement in multipartite systems
We introduce two entanglement conditions that take the form of inequalities
involving expectation values of operators. These conditions are sufficient
conditions for entanglement, that is if they are satisfied the state is
entangled, but if they are not, one can say nothing about the entanglement of
the state. These conditions are quite flexible, because the operators in them
are not specified, and they are particularly useful in detecting multipartite
entanglement. We explore the range of utility of these conditions by
considering a number of examples of entangled states, and seeing under what
conditions entanglement in them can be detected by the inequalities presented
here.Comment: accepted for publication in Physical Review
Universal state inversion and concurrence in arbitrary dimensions
Wootters [Phys. Rev. Lett. 80, 2245 (1998)] has given an explicit formula for
the entanglement of formation of two qubits in terms of what he calls the
concurrence of the joint density operator. Wootters's concurrence is defined
with the help of the superoperator that flips the spin of a qubit. We
generalize the spin-flip superoperator to a "universal inverter," which acts on
quantum systems of arbitrary dimension, and we introduce the corresponding
concurrence for joint pure states of (D1 X D2) bipartite quantum systems. The
universal inverter, which is a positive, but not completely positive
superoperator, is closely related to the completely positive universal-NOT
superoperator, the quantum analogue of a classical NOT gate. We present a
physical realization of the universal-NOT superoperator.Comment: Revtex, 25 page
Does the Third Law of Thermodynamics hold in the Quantum Regime?
The first in a long series of papers by John T. Lewis,
G. W. Ford and the present author, considered the problem of the most general
coupling of a quantum particle to a linear passive heat bath, in the course of
which they derived an exact formula for the free energy of an oscillator
coupled to a heat bath in thermal equilibrium at temperature T. This formula,
and its later extension to three dimensions to incorporate a magnetic field,
has proved to be invaluable in analyzing problems in quantum thermodynamics.
Here, we address the question raised in our title viz. Nernst's third law of
thermodynamics
Implementation of quantum maps by programmable quantum processors
A quantum processor is a device with a data register and a program register.
The input to the program register determines the operation, which is a
completely positive linear map, that will be performed on the state in the data
register. We develop a mathematical description for these devices, and apply it
to several different examples of processors. The problem of finding a processor
that will be able to implement a given set of mappings is also examined, and it
is shown that while it is possible to design a finite processor to realize the
phase-damping channel, it is not possible to do so for the amplitude-damping
channel.Comment: 10 revtex pages, no figure
Quantum models related to fouled Hamiltonians of the harmonic oscillator
We study a pair of canonoid (fouled) Hamiltonians of the harmonic oscillator
which provide, at the classical level, the same equation of motion as the
conventional Hamiltonian. These Hamiltonians, say and , result
to be explicitly time-dependent and can be expressed as a formal rotation of
two cubic polynomial functions, and , of the canonical variables
(q,p).
We investigate the role of these fouled Hamiltonians at the quantum level.
Adopting a canonical quantization procedure, we construct some quantum models
and analyze the related eigenvalue equations. One of these models is described
by a Hamiltonian admitting infinite self-adjoint extensions, each of them has a
discrete spectrum on the real line. A self-adjoint extension is fixed by
choosing the spectral parameter of the associated eigenvalue
equation equal to zero. The spectral problem is discussed in the context of
three different representations. For , the eigenvalue equation is
exactly solved in all these representations, in which square-integrable
solutions are explicity found. A set of constants of motion corresponding to
these quantum models is also obtained. Furthermore, the algebraic structure
underlying the quantum models is explored. This turns out to be a nonlinear
(quadratic) algebra, which could be applied for the determination of
approximate solutions to the eigenvalue equations.Comment: 24 pages, no figures, accepted for publication on JM
Multi-output programmable quantum processor
By combining telecloning and programmable quantum gate array presented by
Nielsen and Chuang [Phys.Rev.Lett. 79 :321(1997)], we propose a programmable
quantum processor which can be programmed to implement restricted set of
operations with several identical data outputs. The outputs are
approximately-transformed versions of input data. The processor successes with
certain probability.Comment: 5 pages and 2 PDF figure
Measurement models for time-resolved spectroscopy: a comment
We present an exactly solvable model for photon emission, which allows us to
examine the evolution of the photon wavefunction in space and time. We apply
this model to coherent phenomena in three-level systems with a special emphasis
on the photon detection process.Comment: 14 pages RevTex, 4 figure
Decoherence in a double-slit quantum eraser
We study and experimentally implement a double-slit quantum eraser in the
presence of a controlled decoherence mechanism. A two-photon state, produced in
a spontaneous parametric down conversion process, is prepared in a maximally
entangled polarization state. A birefringent double-slit is illuminated by one
of the down-converted photons, and it acts as a single-photon two-qubits
controlled not gate that couples the polarization with the transversal momentum
of these photons. The other photon, that acts as a which-path marker, is sent
through a Mach-Zehnder-like interferometer. When the interferometer is
partially unbalanced, it behaves as a controlled source of decoherence for
polarization states of down-converted photons. We show the transition from
wave-like to particle-like behavior of the signal photons crossing the
double-slit as a function of the decoherence parameter, which depends on the
length path difference at the interferometer.Comment: Accepted in Physical Review
Optimal unambiguous discrimination of two subspaces as a case in mixed state discrimination
We show how to optimally unambiguously discriminate between two subspaces of
a Hilbert space. In particular we suppose that we are given a quantum system in
either the state \psi_{1}, where \psi_{1} can be any state in the subspace
S_{1}, or \psi_{2}, where \psi_{2} can be any state in the subspace S_{2}, and
our task is to determine in which of the subspaces the state of our quantum
system lies. We do not want to make a mistake, which means that our procedure
will sometimes fail if the subspaces are not orthogonal. This is a special case
of the unambiguous discrimination of mixed states. We present the POVM that
solves this problem and several applications of this procedure, including the
discrimination of multipartite states without classical communication.Comment: 8 pages, replaced with published versio
Exponential quantum enhancement for distributed addition with local nonlinearity
We consider classical and entanglement-assisted versions of a distributed
computation scheme that computes nonlinear Boolean functions of a set of input
bits supplied by separated parties. Communication between the parties is
restricted to take place through a specific apparatus which enforces the
constraints that all nonlinear, nonlocal classical logic is performed by a
single receiver, and that all communication occurs through a limited number of
one-bit channels. In the entanglement-assisted version, the number of channels
required to compute a Boolean function of fixed nonlinearity can become
exponentially smaller than in the classical version. We demonstrate this
exponential enhancement for the problem of distributed integer addition.Comment: To appear in Quantum Information Processin
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