16,000 research outputs found
Pooling quantum states obtained by indirect measurements
We consider the pooling of quantum states when Alice and Bob both have one
part of a tripartite system and, on the basis of measurements on their
respective parts, each infers a quantum state for the third part S. We denote
the conditioned states which Alice and Bob assign to S by alpha and beta
respectively, while the unconditioned state of S is rho. The state assigned by
an overseer, who has all the data available to Alice and Bob, is omega. The
pooler is told only alpha, beta, and rho. We show that for certain classes of
tripartite states, this information is enough for her to reconstruct omega by
the formula omega \propto alpha rho^{-1} beta. Specifically, we identify two
classes of states for which this pooling formula works: (i) all pure states for
which the rank of rho is equal to the product of the ranks of the states of
Alice's and Bob's subsystems; (ii) all mixtures of tripartite product states
that are mutually orthogonal on S.Comment: Corrected a mistake regarding the scope of our original result. This
version to be published in Phys. Rev. A. 6 pages, 1 figur
Nonlinear viscoelasticity of metastable complex fluids
Many metastable complex fluids such as colloidal glasses and gels show
distinct nonlinear viscoelasticity with increasing oscillatory-strain
amplitude; the storage modulus decreases monotonically as the strain amplitude
increases whereas the loss modulus has a distinct peak before it decreases at
larger strains. We present a qualitative argument to explain this ubiquitous
behavior and use mode coupling theory (MCT) to confirm it. We compare
theoretical predictions to the measured nonlinear viscoelasticity in a dense
hard sphere colloidal suspensions; reasonable agreement is obtained. The
argument given here can be used to obtain new information about linear
viscoelasticity of metastable complex fluids from nonlinear strain
measurements.Comment: 7 pages, 3 figures, accepted for publication in Europhys. Let
Quantum State Disturbance vs. Information Gain: Uncertainty Relations for Quantum Information
When an observer wants to identify a quantum state, which is known to be one
of a given set of non-orthogonal states, the act of observation causes a
disturbance to that state. We investigate the tradeoff between the information
gain and that disturbance. This issue has important applications in quantum
cryptography. The optimal detection method, for a given tolerated disturbance,
is explicitly found in the case of two equiprobable non-orthogonal pure states.Comment: 20 pages, standard LaTeX, four png figures (also available from the
authors: [email protected] and [email protected]
The mean-squared displacement of a molecule moving in a glassy system
The mean-squared displacement (MSD) of a hard sphere and of a dumbbell
molecule consisting of two fused hard spheres immersed in a dense hard-sphere
system is calculated within the mode-coupling theory for ideal liquid-glass
transitions. It is proven that the velocity correlator, which is the second
time derivative of the MSD, is the negative of a completely monotone function
for times within the structural-relaxation regime. The MSD is found to exhibit
a large time interval for structural relaxation prior to the onset of the
-process which cannot be described by the asymptotic formulas for the
mode-coupling-theory-bifurcation dynamics. The -process for molecules
with a large elongation is shown to exhibit an anomalously wide cross-over
interval between the end of the von-Schweidler decay and the beginning of
normal diffusion. The diffusivity of the molecule is predicted to vary
non-monotonically as function of its elongation.Comment: 18 pages, 12 figures, Phys. Rev. E, in prin
A quantitative test of the mode-coupling theory of the ideal glass transition for a binary Lennard-Jones system
Using a molecular dynamics computer simulation we determine the temperature
dependence of the partial structure factors for a binary Lennard-Jones system.
These structure factors are used as input data to solve numerically the
wave-vector dependent mode-coupling equations in the long time limit. Using the
so determined solutions, we compare the predictions of mode-coupling theory
(MCT) with the results of a previously done molecular dynamics computer
simulation [Phys. Rev. E 51, 4626 (1995), ibid. 52, 4134 (1995)]. From this
comparison we conclude that MCT gives a fair estimate of the critical coupling
constant, a good estimate of the exponent parameter, predicts the wave-vector
dependence of the various nonergodicity parameters very well, except for very
large wave-vectors, and gives also a very good description of the space
dependence of the various critical amplitudes. In an attempt to correct for
some of the remaining discrepancies between the theory and the results of the
simulation, we investigate two small (ad hoc) modifications of the theory. We
find that one modification gives a worse agreement between theory and
simulation, whereas the second one leads to an improved agreement.Comment: Figures available from W. Ko
Information Tradeoff Relations for Finite-Strength Quantum Measurements
In this paper we give a new way to quantify the folklore notion that quantum
measurements bring a disturbance to the system being measured. We consider two
observers who initially assign identical mixed-state density operators to a
two-state quantum system. The question we address is to what extent one
observer can, by measurement, increase the purity of his density operator
without affecting the purity of the other observer's. If there were no
restrictions on the first observer's measurements, then he could carry this out
trivially by measuring the initial density operator's eigenbasis. If, however,
the allowed measurements are those of finite strength---i.e., those
measurements strictly within the interior of the convex set of all
measurements---then the issue becomes significantly more complex. We find that
for a large class of such measurements the first observer's purity increases
the most precisely when there is some loss of purity for the second observer.
More generally the tradeoff between the two purities, when it exists, forms a
monotonic relation. This tradeoff has potential application to quantum state
control and feedback.Comment: 15 pages, revtex3, 3 eps figure
A mode-coupling theory for the glassy dynamics of a diatomic probe molecule immersed in a simple liquid
Generalizing the mode-coupling theory for ideal liquid-glass transitions,
equations of motion are derived for the correlation functions describing the
glassy dynamics of a diatomic probe molecule immersed in a simple glass-forming
system. The molecule is described in the interaction-site representation and
the equations are solved for a dumbbell molecule consisting of two fused hard
spheres in a hard-sphere system. The results for the molecule's arrested
position in the glass state and the reorientational correlators for
angular-momentum index and near the glass transition are
compared with those obtained previously within a theory based on a
tensor-density description of the molecule in order to demonstrate that the two
approaches yield equivalent results. For strongly hindered reorientational
motion, the dipole-relaxation spectra for the -process can be mapped on
the dielectric-loss spectra of glycerol if a rescaling is performed according
to a suggestion by Dixon et al. [Phys. Rev. Lett. {\bf 65}, 1108 (1990)]. It is
demonstrated that the glassy dynamics is independent of the molecule's inertia
parameters.Comment: 19 pages, 10 figures, Phys. Rev. E, in prin
Optimal Universal and State-Dependent Quantum Cloning
We establish the best possible approximation to a perfect quantum cloning
machine which produces two clones out of a single input. We analyze both
universal and state-dependent cloners. The maximal fidelity of cloning is shown
to be 5/6 for universal cloners. It can be achieved either by a special unitary
evolution or by a novel teleportation scheme. We construct the optimal
state-dependent cloners operating on any prescribed two non-orthogonal states,
discuss their fidelities and the use of auxiliary physical resources in the
process of cloning. The optimal universal cloners permit us to derive a new
upper bound on the quantum capacity of the depolarizing quantum channel.Comment: 30 pages (RevTeX), 2 figures (epsf), further results and further
authors added, to appear in Physical Review
On bit-commitment based quantum coin flipping
In this paper, we focus on a special framework for quantum coin flipping
protocols,_bit-commitment based protocols_, within which almost all known
protocols fit. We show a lower bound of 1/16 for the bias in any such protocol.
We also analyse a sequence of multi-round protocol that tries to overcome the
drawbacks of the previously proposed protocols, in order to lower the bias. We
show an intricate cheating strategy for this sequence, which leads to a bias of
1/4. This indicates that a bias of 1/4 might be optimal in such protocols, and
also demonstrates that a cleverer proof technique may be required to show this
optimality.Comment: The lower bound shown in this paper is superceded by a result of
Kitaev (personal communication, 2001
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