5,356 research outputs found
Entanglement of identical particles and reference phase uncertainty
We have recently introduced a measure of the bipartite entanglement of
identical particles, E_P, based on the principle that entanglement should be
accessible for use as a resource in quantum information processing. We show
here that particle entanglement is limited by the lack of a reference phase
shared by the two parties, and that the entanglement is constrained to
reference-phase invariant subspaces. The super-additivity of E_P results from
the fact that this constraint is weaker for combined systems. A shared
reference phase can only be established by transferring particles between the
parties, that is, with additional nonlocal resources. We show how this nonlocal
operation can increase the particle entanglement.Comment: 8 pages, no figures. Invited talk given at EQIS'03, Kyoto, September,
2003. Minor typos corrected, 1 reference adde
Measuring measurement--disturbance relationships with weak values
Using formal definitions for measurement precision {\epsilon} and disturbance
(measurement backaction) {\eta}, Ozawa [Phys. Rev. A 67, 042105 (2003)] has
shown that Heisenberg's claimed relation between these quantities is false in
general. Here we show that the quantities introduced by Ozawa can be determined
experimentally, using no prior knowledge of the measurement under investigation
--- both quantities correspond to the root-mean-squared difference given by a
weak-valued probability distribution. We propose a simple three-qubit
experiment which would illustrate the failure of Heisenberg's
measurement--disturbance relation, and the validity of an alternative relation
proposed by Ozawa
All-optical versus electro-optical quantum-limited feedback
All-optical feedback can be effected by putting the output of a source cavity
through a Faraday isolator and into a second cavity which is coupled to the
source cavity by a nonlinear crystal. If the driven cavity is heavily damped,
then it can be adiabatically eliminated and a master equation or quantum
Langevin equation derived for the first cavity alone. This is done for an input
bath in an arbitrary state, and for an arbitrary nonlinear coupling. If the
intercavity coupling involves only the intensity (or one quadrature) of the
driven cavity, then the effect on the source cavity is identical to that which
can be obtained from electro-optical feedback using direct (or homodyne)
detection. If the coupling involves both quadratures, this equivalence no
longer holds, and a coupling linear in the source amplitude can produce a
nonclassical state in the source cavity. The analogous electro-optic scheme
using heterodyne detection introduces extra noise which prevents the production
of nonclassical light. Unlike the electro-optic case, the all-optical feedback
loop has an output beam (reflected from the second cavity). We show that this
may be squeezed, even if the source cavity remains in a classical state.Comment: 21 pages. This is an old (1994) paper, but one which I thought was
worth posting because in addition to what is described in abstract it has:
(1) the first formulation (to my knowledge) of quantum trajectories for an
arbitrary (i.e. squeezed, thermal etc.) broadband bath; (2) the prediction of
a periodic modification to the detuning and damping of an oscillator for the
simplest sort of all-optical feedback (i.e. a mirror) as seen in the recent
experiment "Forces between a Single Atom and Its Distant Mirror Image", P.
Bushev et al, Phys. Rev. Lett. 92, 223602 (2004
The Consumption of Reference Resources
Under the operational restriction of the U(1)-superselection rule, states
that contain coherences between eigenstates of particle number constitute a
resource. Such resources can be used to facilitate operations upon systems that
otherwise cannot be performed. However, the process of doing this consumes
reference resources. We show this explicitly for an example of a unitary
operation that is forbidden by the U(1)-superselection rule.Comment: 4 pages 6x9 page format, 2 figure
Entanglement under restricted operations: Analogy to mixed-state entanglement
We show that the classification of bi-partite pure entangled states when
local quantum operations are restricted yields a structure that is analogous in
many respects to that of mixed-state entanglement. Specifically, we develop
this analogy by restricting operations through local superselection rules, and
show that such exotic phenomena as bound entanglement and activation arise
using pure states in this setting. This analogy aids in resolving several
conceptual puzzles in the study of entanglement under restricted operations. In
particular, we demonstrate that several types of quantum optical states that
possess confusing entanglement properties are analogous to bound entangled
states. Also, the classification of pure-state entanglement under restricted
operations can be much simpler than for mixed-state entanglement. For instance,
in the case of local Abelian superselection rules all questions concerning
distillability can be resolved.Comment: 10 pages, 2 figures; published versio
Atom Lasers, Coherent States, and Coherence:II. Maximally Robust Ensembles of Pure States
As discussed in Wiseman and Vaccaro [quant-ph/9906125], the stationary state
of an optical or atom laser far above threshold is a mixture of coherent field
states with random phase, or, equivalently, a Poissonian mixture of number
states. We are interested in which, if either, of these descriptions of
, is more natural. In the preceding paper we concentrated upon
whether descriptions such as these are physically realizable (PR). In this
paper we investigate another relevant aspect of these ensembles, their
robustness. A robust ensemble is one for which the pure states that comprise it
survive relatively unchanged for a long time under the system evolution. We
determine numerically the most robust ensembles as a function of the parameters
in the laser model: the self-energy of the bosons in the laser mode, and
the excess phase noise . We find that these most robust ensembles are PR
ensembles, or similar to PR ensembles, for all values of these parameters. In
the ideal laser limit (), the most robust states are coherent
states. As the phase noise or phase dispersion is increased, the
most robust states become increasingly amplitude-squeezed. We find scaling laws
for these states. As the phase diffusion or dispersion becomes so large that
the laser output is no longer quantum coherent, the most robust states become
so squeezed that they cease to have a well-defined coherent amplitude. That is,
the quantum coherence of the laser output is manifest in the most robust PR
states having a well-defined coherent amplitude. This lends support to the idea
that robust PR ensembles are the most natural description of the state of the
laser mode. It also has interesting implications for atom lasers in particular,
for which phase dispersion due to self-interactions is expected to be large.Comment: 16 pages, 9 figures included. To be published in Phys. Rev. A, as
Part II of a two-part paper. The original version of quant-ph/9906125 is
shortly to be replaced by a new version which is Part I of the two-part
paper. This paper (Part II) also contains some material from the original
version of quant-ph/990612
Quantum phenomena modelled by interactions between many classical worlds
We investigate whether quantum theory can be understood as the continuum
limit of a mechanical theory, in which there is a huge, but finite, number of
classical 'worlds', and quantum effects arise solely from a universal
interaction between these worlds, without reference to any wave function. Here
a `world' means an entire universe with well-defined properties, determined by
the classical configuration of its particles and fields. In our approach each
world evolves deterministically; probabilities arise due to ignorance as to
which world a given observer occupies; and we argue that in the limit of
infinitely many worlds the wave function can be recovered (as a secondary
object) from the motion of these worlds. We introduce a simple model of such a
'many interacting worlds' approach and show that it can reproduce some generic
quantum phenomena---such as Ehrenfest's theorem, wavepacket spreading, barrier
tunneling and zero point energy---as a direct consequence of mutual repulsion
between worlds. Finally, we perform numerical simulations using our approach.
We demonstrate, first, that it can be used to calculate quantum ground states,
and second, that it is capable of reproducing, at least qualitatively, the
double-slit interference phenomenon.Comment: Published version (including further discussion of interpretation and
quantum limit
Continuous quantum error correction via quantum feedback control
We describe a protocol for continuously protecting unknown quantum states
from decoherence that incorporates design principles from both quantum error
correction and quantum feedback control. Our protocol uses continuous
measurements and Hamiltonian operations, which are weaker control tools than
are typically assumed for quantum error correction. We develop a cost function
appropriate for unknown quantum states and use it to optimize our
state-estimate feedback. Using Monte Carlo simulations, we study our protocol
for the three-qubit bit-flip code in detail and demonstrate that it can improve
the fidelity of quantum states beyond what is achievable using quantum error
correction when the time between quantum error correction cycles is limited.Comment: 12 pages, 6 figures, REVTeX; references fixe
State and dynamical parameter estimation for open quantum systems
Following the evolution of an open quantum system requires full knowledge of
its dynamics. In this paper we consider open quantum systems for which the
Hamiltonian is ``uncertain''. In particular, we treat in detail a simple system
similar to that considered by Mabuchi [Quant. Semiclass. Opt. 8, 1103 (1996)]:
a radiatively damped atom driven by an unknown Rabi frequency (as
would occur for an atom at an unknown point in a standing light wave). By
measuring the environment of the system, knowledge about the system state, and
about the uncertain dynamical parameter, can be acquired. We find that these
two sorts of knowledge acquisition (quantified by the posterior distribution
for , and the conditional purity of the system, respectively) are quite
distinct processes, which are not strongly correlated. Also, the quality and
quantity of knowledge gain depend strongly on the type of monitoring scheme. We
compare five different detection schemes (direct, adaptive, homodyne of the
quadrature, homodyne of the quadrature, and heterodyne) using four
different measures of the knowledge gain (Shannon information about ,
variance in , long-time system purity, and short-time system purity).Comment: 14 pages, 18 figure
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