592 research outputs found
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
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
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
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
Quantum key distribution using non-classical photon number correlations in macroscopic light pulses
We propose a new scheme for quantum key distribution using macroscopic
non-classical pulses of light having of the order 10^6 photons per pulse.
Sub-shot-noise quantum correlation between the two polarization modes in a
pulse gives the necessary sensitivity to eavesdropping that ensures the
security of the protocol. We consider pulses of two-mode squeezed light
generated by a type-II seeded parametric amplification process. We analyze the
security of the system in terms of the effect of an eavesdropper on the bit
error rates for the legitimate parties in the key distribution system. We also
consider the effects of imperfect detectors and lossy channels on the security
of the scheme.Comment: Modifications:added new eavesdropping attack, added more references
Submitted to Physical Review A [email protected]
Multiphoton communication in lossy channels with photon-number entangled states
We address binary and quaternary communication channels based on correlated
multiphoton two-mode states of radiation in the presence of losses. The
protocol are based on photon number correlations and realized upon choosing a
shared set of thresholds to convert the outcome of a joint photon number
measurement into a symbol from a discrete alphabet. In particular, we focus on
channels build using feasible photon-number entangled states (PNES) as two-mode
coherently-correlated (TMC) or twin-beam (TWB) states and compare their
performances with that of channels built using feasible classically correlated
(separable) states. We found that PNES provide larger channel capacity in the
presence of loss, and that TWB-based channels may transmit a larger amount of
information than TMC-based ones at fixed energy and overall loss. Optimized bit
discrimination thresholds, as well as the corresponding maximized mutual
information, are explicitly evaluated as a function of the beam intensity and
the loss parameter. The propagation of TMC and TWB in lossy channels is
analyzed and the joint photon number distribution is evaluated, showing that
the beam statistics, either sub-Poissonian for TMC or super-Poissonian for TWB,
is not altered by losses. Although entanglement is not strictly needed to
establish the channels, which are based on photon-number correlations owned
also by separable mixed states, purity of the support state is relevant to
increase security. The joint requirement of correlation and purity individuates
PNES as a suitable choice to build effective channels. The effects of losses on
channel security are briefly discussed.Comment: 8 pages, 19 figure
Quantum signature scheme with single photons
Quantum digital signature combines quantum theory with classical digital
signature. The main goal of this field is to take advantage of quantum effects
to provide unconditionally secure signature. We present a quantum signature
scheme with message recovery without using entangle effect. The most important
property of the proposed scheme is that it is not necessary for the scheme to
use Greenberger-Horne-Zeilinger states. The present scheme utilizes single
photons to achieve the aim of signature and verification. The security of the
scheme relies on the quantum one-time pad and quantum key distribution. The
efficiency analysis shows that the proposed scheme is an efficient scheme
Generation of Entangled N-Photon States in a Two-Mode Jaynes-Cummings Model
We describe a mathematical solution for the generation of entangled N-photon
states in two field modes. A simple and compact solution is presented for a
two-mode Jaynes-Cummings model by combining the two field modes in a way that
only one of the two resulting quasi-modes enters in the interaction term. The
formalism developed is then applied to calculate various generation
probabilities analytically. We show that entanglement, starting from an initial
field and an atom in one defined state may be obtained in a single step. We
also show that entanglement may be built up in the case of an empty cavity and
excited atoms whose final states are detected, as well as in the case when the
final states of the initially excited atoms are not detected.Comment: v2: 5 pages, RevTeX4, minor text changes + 1 figure added, revised
version to be published in PRA, May 200
SU(2) and SU(1,1) algebra eigenstates: A unified analytic approach to coherent and intelligent states
We introduce the concept of algebra eigenstates which are defined for an
arbitrary Lie group as eigenstates of elements of the corresponding complex Lie
algebra. We show that this concept unifies different definitions of coherent
states associated with a dynamical symmetry group. On the one hand, algebra
eigenstates include different sets of Perelomov's generalized coherent states.
On the other hand, intelligent states (which are squeezed states for a system
of general symmetry) also form a subset of algebra eigenstates. We develop the
general formalism and apply it to the SU(2) and SU(1,1) simple Lie groups.
Complete solutions to the general eigenvalue problem are found in the both
cases, by a method that employs analytic representations of the algebra
eigenstates. This analytic method also enables us to obtain exact closed
expressions for quantum statistical properties of an arbitrary algebra
eigenstate. Important special cases such as standard coherent states and
intelligent states are examined and relations between them are studied by using
their analytic representations.Comment: LaTeX, 24 pages, 1 figure (compressed PostScript, available at
http://www.technion.ac.il/~brif/abstracts/AES.html ). More information on
http://www.technion.ac.il/~brif/science.htm
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