8,498 research outputs found
Optimal Entanglement Enhancement for Mixed States
We consider the actions of protocols involving local quantum operations and
classical communication (LQCC) on a single system consisting of two separated
qubits. We give a complete description of the orbits of the space of states
under LQCC and characterise the representatives with maximal entanglement of
formation. We thus obtain a LQCC entanglement concentration protocol for a
single given state (pure or mixed) of two qubits which is optimal in the sense
that the protocol produces, with non-zero probability, a state of maximal
possible entanglement of formation. This defines a new entanglement measure,
the maximum extractable entanglement.Comment: Final version: to appear in Phys. Rev. Let
Variable Bias Coin Tossing
Alice is a charismatic quantum cryptographer who believes her parties are
unmissable; Bob is a (relatively) glamorous string theorist who believes he is
an indispensable guest. To prevent possibly traumatic collisions of
self-perception and reality, their social code requires that decisions about
invitation or acceptance be made via a cryptographically secure variable bias
coin toss (VBCT). This generates a shared random bit by the toss of a coin
whose bias is secretly chosen, within a stipulated range, by one of the
parties; the other party learns only the random bit. Thus one party can
secretly influence the outcome, while both can save face by blaming any
negative decisions on bad luck.
We describe here some cryptographic VBCT protocols whose security is
guaranteed by quantum theory and the impossibility of superluminal signalling,
setting our results in the context of a general discussion of secure two-party
computation. We also briefly discuss other cryptographic applications of VBCT.Comment: 14 pages, minor correction
Systematic study of d-wave superconductivity in the 2D repulsive Hubbard model
The cluster size dependence of superconductivity in the conventional
two-dimensional Hubbard model, commonly believed to describe high-temperature
superconductors, is systematically studied using the Dynamical Cluster
Approximation and Quantum Monte Carlo simulations as cluster solver. Due to the
non-locality of the d-wave superconducting order parameter, the results on
small clusters show large size and geometry effects. In large enough clusters,
the results are independent of the cluster size and display a finite
temperature instability to d-wave superconductivity.Comment: 4 pages, 3 figures; updated with version published in PRL; added
values of Tc obtained from fit
Security of Quantum Bit-String Generation
We consider the cryptographic task of bit-string generation. This is a
generalisation of coin tossing in which two mistrustful parties wish to
generate a string of random bits such that an honest party can be sure that the
other cannot have biased the string too much. We consider a quantum protocol
for this task, originally introduced in Phys. Rev. A {\bf 69}, 022322 (2004),
that is feasible with present day technology. We introduce security conditions
based on the average bias of the bits and the Shannon entropy of the string.
For each, we prove rigorous security bounds for this protocol in both noiseless
and noisy conditions under the most general attacks allowed by quantum
mechanics. Roughly speaking, in the absence of noise, a cheater can only bias
significantly a vanishing fraction of the bits, whereas in the presence of
noise, a cheater can bias a constant fraction, with this fraction depending
quantitatively on the level of noise. We also discuss classical protocols for
the same task, deriving upper bounds on how well a classical protocol can
perform. This enables the determination of how much noise the quantum protocol
can tolerate while still outperforming classical protocols. We raise several
conjectures concerning both quantum and classical possibilities for large n
cryptography. An experiment corresponding to the scheme analysed in this paper
has been performed and is reported elsewhere.Comment: 16 pages. No figures. Accepted for publication in Phys. Rev. A. A
corresponding experiment is reported in quant-ph/040812
Density-density functionals and effective potentials in many-body electronic structure calculations
We demonstrate the existence of different density-density functionals
designed to retain selected properties of the many-body ground state in a
non-interacting solution starting from the standard density functional theory
ground state. We focus on diffusion quantum Monte Carlo applications that
require trial wave functions with optimal Fermion nodes. The theory is
extensible and can be used to understand current practices in several
electronic structure methods within a generalized density functional framework.
The theory justifies and stimulates the search of optimal empirical density
functionals and effective potentials for accurate calculations of the
properties of real materials, but also cautions on the limits of their
applicability. The concepts are tested and validated with a near-analytic
model.Comment: five figure
A Comparison of Quantum Oracles
A standard quantum oracle for a general function is
defined to act on two input states and return two outputs, with inputs
and () returning outputs and
. However, if is known to be a one-to-one function, a
simpler oracle, , which returns given , can also be
defined. We consider the relative strengths of these oracles. We define a
simple promise problem which minimal quantum oracles can solve exponentially
faster than classical oracles, via an algorithm which cannot be naively adapted
to standard quantum oracles. We show that can be constructed by invoking
and once each, while invocations of
and/or are required to construct .Comment: 4 pages, 1 figure; Final version, with an extended discussion of
oracle inverses. To appear in Phys Rev
Zinc-blende and wurtzite AlxGa1-xN bulk crystals grown by molecular beam epitaxy
There is a significant difference in the lattice parameters of GaN and AlN and for many device applications AlxGa1-xN substrates would be preferable to either GaN or AlN. We have studied the growth of free-standing zinc-blende and wurtzite AlxGa1-xN bulk crystals by plasma-assisted molecular beam epitaxy (PA-MBE). Thick (similar to 10 mu m) zinc-blende and wurtzite AlxGa1-xN films were grown by PA-MBE on 2-in. GaAs (0 0 1) and GaAs (1 1 1)B substrates respectively and were removed from the GaAs substrate after the growth. We demonstrate that free-standing zinc-blende and wurtzite AlxGa1-xN wafers can be achieved by PA-MBE for a wide range of Al compositions. (C) 2011 Elsevier B.V. All rights reserved
Monte Carlo energy and variance minimization techniques for optimizing many-body wave functions
We investigate Monte Carlo energy and variance minimization techniques for
optimizing many-body wave functions. Several variants of the basic techniques
are studied, including limiting the variations in the weighting factors which
arise in correlated sampling estimations of the energy and its variance. We
investigate the numerical stability of the techniques and identify two reasons
why variance minimization exhibits superior numerical stability to energy
minimization. The characteristics of each method are studied using a
non-interacting 64-electron model of crystalline silicon. While our main
interest is in solid state systems, the issues investigated are relevant to
Monte Carlo studies of atoms, molecules and solids. We identify a robust and
efficient variance minimization scheme for optimizing wave functions for large
systems.Comment: 14 pages, including 7 figures. To appear in Phys. Rev. B. For related
publications see http://www.tcm.phy.cam.ac.uk/Publications/many_body.htm
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