903 research outputs found
Relations for classical communication capacity and entanglement capability of two-qubit operations
Bipartite operations underpin both classical communication and entanglement
generation. Using a superposition of classical messages, we show that the
capacity of a two-qubit operation for error-free entanglement-assisted
bidirectional classical communication can not exceed twice the entanglement
capability. In addition we show that any bipartite two-qubit operation can
increase the communication that may be performed using an ensemble by twice the
entanglement capability.Comment: 4 page
Dynamical fluctuations in classical adiabatic processes: General description and their implications
Dynamical fluctuations in classical adiabatic processes are not considered by
the conventional classical adiabatic theorem. In this work a general result is
derived to describe the intrinsic dynamical fluctuations in classical adiabatic
processes. Interesting implications of our general result are discussed via two
subtopics, namely, an intriguing adiabatic geometric phase in a dynamical model
with an adiabatically moving fixed-point solution, and the possible "pollution"
to Hannay's angle or to other adiabatic phase objects for adiabatic processes
involving non-fixed-point solutions.Comment: 19 pages, no figures, discussion significantly expanded, published
versio
Countering Quantum Noise with Supplementary Classical Information
We consider situations in which i) Alice wishes to send quantum information
to Bob via a noisy quantum channel, ii) Alice has a classical description of
the states she wishes to send and iii) Alice can make use of a finite amount of
noiseless classical information. After setting up the problem in general, we
focus attention on one specific scenario in which Alice sends a known qubit
down a depolarizing channel along with a noiseless cbit. We describe a protocol
which we conjecture is optimal and calculate the average fidelity obtained. A
surprising amount of structure is revealed even for this simple case which
suggests that relationships between quantum and classical information could in
general be very intricate.Comment: RevTeX, 5 pages, 2 figures Typo in reference 9 correcte
Faithful remote state preparation using finite classical bits and a non-maximally entangled state
We present many ensembles of states that can be remotely prepared by using
minimum classical bits from Alice to Bob and their previously shared entangled
state and prove that we have found all the ensembles in two-dimensional case.
Furthermore we show that any pure quantum state can be remotely and faithfully
prepared by using finite classical bits from Alice to Bob and their previously
shared nonmaximally entangled state though no faithful quantum teleportation
protocols can be achieved by using a nonmaximally entangled state.Comment: 6 page
On the Interpretation of Energy as the Rate of Quantum Computation
Over the last few decades, developments in the physical limits of computing
and quantum computing have increasingly taught us that it can be helpful to
think about physics itself in computational terms. For example, work over the
last decade has shown that the energy of a quantum system limits the rate at
which it can perform significant computational operations, and suggests that we
might validly interpret energy as in fact being the speed at which a physical
system is "computing," in some appropriate sense of the word. In this paper, we
explore the precise nature of this connection. Elementary results in quantum
theory show that the Hamiltonian energy of any quantum system corresponds
exactly to the angular velocity of state-vector rotation (defined in a certain
natural way) in Hilbert space, and also to the rate at which the state-vector's
components (in any basis) sweep out area in the complex plane. The total angle
traversed (or area swept out) corresponds to the action of the Hamiltonian
operator along the trajectory, and we can also consider it to be a measure of
the "amount of computational effort exerted" by the system, or effort for
short. For any specific quantum or classical computational operation, we can
(at least in principle) calculate its difficulty, defined as the minimum effort
required to perform that operation on a worst-case input state, and this in
turn determines the minimum time required for quantum systems to carry out that
operation on worst-case input states of a given energy. As examples, we
calculate the difficulty of some basic 1-bit and n-bit quantum and classical
operations in an simple unconstrained scenario.Comment: Revised to address reviewer comments. Corrects an error relating to
time-ordering, adds some additional references and discussion, shortened in a
few places. Figures now incorporated into tex
A note on the geometric phase in adiabatic approximation
The adiabatic theorem shows that the instantaneous eigenstate is a good
approximation of the exact solution for a quantum system in adiabatic
evolution. One may therefore expect that the geometric phase calculated by
using the eigenstate should be also a good approximation of exact geometric
phase. However, we find that the former phase may differ appreciably from the
latter if the evolution time is large enough.Comment: 11 pages, no figure, modified and Journal-ref adde
Measurement of coherent charge transfer in an adiabatic Cooper pair pump
We study adiabatic charge transfer in a superconducting Cooper pair pump,
focusing on the influence of current measurement on coherence. We investigate
the limit where the Josephson coupling energy between the various parts
of the system is small compared to the Coulomb charging energy . In this
case the charge transferred in a pumping cycle , the charge of one
Cooper pair: the main contribution is due to incoherent Cooper pair tunneling.
We are particularly interested in the quantum correction to , which is due
to coherent tunneling of pairs across the pump and which depends on the
superconducting phase difference between the electrodes: . A measurement of tends to destroy the phase
coherence. We first study an arbitrary measuring circuit and then specific
examples and show that coherent Cooper pair transfer can in principle be
detected using an inductively shunted ammeter
Decoherence as Decay of the Loschmidt Echo in a Lorentz Gas
Classical chaotic dynamics is characterized by the exponential sensitivity to
initial conditions. Quantum mechanics, however, does not show this feature. We
consider instead the sensitivity of quantum evolution to perturbations in the
Hamiltonian. This is observed as an atenuation of the Loschmidt Echo, ,
i.e. the amount of the original state (wave packet of width ) which is
recovered after a time reversed evolution, in presence of a classically weak
perturbation. By considering a Lorentz gas of size , which for large is
a model for an {\it unbounded} classically chaotic system, we find numerical
evidence that, if the perturbation is within a certain range, decays
exponentially with a rate determined by the Lyapunov exponent
of the corresponding classical dynamics. This exponential decay
extends much beyond the Eherenfest time and saturates at a time
, where is the effective dimensionality of the Hilbert space. Since quantifies the increasing uncontrollability of the quantum phase
(decoherence) its characterization and control has fundamental interest.Comment: 3 ps figures, uses Revtex and epsfig. Major revision to the text, now
including discussion and references on averaging and Ehrenfest time. Figures
2 and 3 content and order change
Weak-Localization in Chaotic Versus Non-Chaotic Cavities: A Striking Difference in the Line Shape
We report experimental evidence that chaotic and non-chaotic scattering
through ballistic cavities display distinct signatures in quantum transport. In
the case of non-chaotic cavities, we observe a linear decrease in the average
resistance with magnetic field which contrasts markedly with a Lorentzian
behavior for a chaotic cavity. This difference in line-shape of the
weak-localization peak is related to the differing distribution of areas
enclosed by electron trajectories. In addition, periodic oscillations are
observed which are probably associated with the Aharonov-Bohm effect through a
periodic orbit within the cavities.Comment: 4 pages revtex + 4 figures on request; amc.hub.94.
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