102 research outputs found
Optimal Cloning of Pure States, Judging Single Clones
We consider quantum devices for turning a finite number N of d-level quantum
systems in the same unknown pure state \sigma into M>N systems of the same
kind, in an approximation of the M-fold tensor product of the state \sigma. In
a previous paper it was shown that this problem has a unique optimal solution,
when the quality of the output is judged by arbitrary measurements, involving
also the correlations between the clones. We show in this paper, that if the
quality judgement is based solely on measurements of single output clones,
there is again a unique optimal cloning device, which coincides with the one
found previously.Comment: 16 Pages, REVTe
Quantum erasure of decoherence
We consider the classical algebra of observables that are diagonal in a given
orthonormal basis, and define a complete decoherence process as a completely
positive map that asymptotically converts any quantum observable into a
diagonal one, while preserving the elements of the classical algebra. For
quantum systems in dimension two and three any decoherence process can be
undone by collecting classical information from the environment and using such
an information to restore the initial system state. As a relevant example, we
illustrate the quantum eraser of Scully et al. [Nature 351, 111 (1991)] as an
example of environment-assisted correction. Moreover, we present the
generalization of the eraser setup for d-dimensional systems, showing that any
von Neumann measurement on a system can be undone by a complementary
measurement on the environment.Comment: 10 pages, 1 figur
Quantum Channels and Representation Theory
In the study of d-dimensional quantum channels , an assumption
which is not very restrictive, and which has a natural physical interpretation,
is that the corresponding Kraus operators form a representation of a Lie
algebra. Physically, this is a symmetry algebra for the interaction
Hamiltonian. This paper begins a systematic study of channels defined by
representations; the famous Werner-Holevo channel is one element of this
infinite class. We show that the channel derived from the defining
representation of SU(n) is a depolarizing channel for all , but for most
other representations this is not the case. Since the Bloch sphere is not
appropriate here, we develop technology which is a generalization of Bloch's
technique. Our method works by representing the density matrix as a polynomial
in symmetrized products of Lie algebra generators, with coefficients that are
symmetric tensors. Using these tensor methods we prove eleven theorems, derive
many explicit formulas and show other interesting properties of quantum
channels in various dimensions, with various Lie symmetry algebras. We also
derive numerical estimates on the size of a generalized ``Bloch sphere'' for
certain channels. There remain many open questions which are indicated at
various points through the paper.Comment: 28 pages, 1 figur
Distilling entanglement from arbitrary resources
We obtain the general formula for the optimal rate at which singlets can be
distilled from any given noisy and arbitrarily correlated entanglement
resource, by means of local operations and classical communication (LOCC). Our
formula, obtained by employing the quantum information spectrum method, reduces
to that derived by Devetak and Winter, in the special case of an i.i.d.
resource. The proofs rely on a one-shot version of the so-called "hashing
bound," which in turn provides bounds on the one-shot distillable entanglement
under general LOCC.Comment: 24 pages, article class, no figure. v2: references added, published
versio
Semiquantum key distribution using entangled states
Recently, Boyer et al. presented a novel semiquantum key distribution
protocol [M. Boyer, D. Kenigsberg, and T. Mor, Phys. Rev. Lett. 99, 140501
(2007)], by using four quantum states, each of which is randomly prepared by Z
basis or X basis. Here we present a semiquantum key distribution protocol by
using entangled states in which quantum Alice shares a secret key with
classical Bob. We also show the protocol is secure against eavesdropping.Comment: 6 page
Interference of Quantum Channels
We show how interferometry can be used to characterise certain aspects of
general quantum processes, in particular, the coherence of completely positive
maps. We derive a measure of coherent fidelity, maximum interference visibility
and the closest unitary operator to a given physical process under this
measure.Comment: 4 pages, 5 figures, REVTeX 4, typographical corrections and added
acknowledgemen
Maximal Commutative Subalgebras Invariant for CP-Maps: (Counter-)Examples
We solve, mainly by counterexamples, many natural questions regarding maximal
commutative subalgebras invariant under CP-maps or semigroups of CP-maps on a
von Neumann algebra. In particular, we discuss the structure of the generators
of norm continuous semigroups on B(G) leaving a maximal commutative subalgebra
invariant and show that there exists Markov CP-semigroups on M_d without
invariant maximal commutative subalgebras for any d>2.Comment: After the elemenitation in Version 2 of a false class of examples in
Version 1, we now provide also correct examples for unital CP-maps and Markov
semigroups on M_d for d>2 without invariant masa
Lazy states: sufficient and necessary condition for zero quantum entropy rates under any coupling to the environment
We find the necessary and sufficient conditions for the entropy rate of the
system to be zero under any system-environment Hamiltonian interaction. We call
the class of system-environment states that satisfy this condition lazy states.
They are a generalization of classically correlated states defined by quantum
discord, but based on projective measurements of any rank. The concept of lazy
states permits the construction of a protocol for detecting global quantum
correlations using only local dynamical information. We show how quantum
correlations to the environment provide bounds to the entropy rate, and how to
estimate dissipation rates for general non-Markovian open quantum systems.Comment: 4 page
Tsirelson's problem and Kirchberg's conjecture
Tsirelson's problem asks whether the set of nonlocal quantum correlations
with a tensor product structure for the Hilbert space coincides with the one
where only commutativity between observables located at different sites is
assumed. Here it is shown that Kirchberg's QWEP conjecture on tensor products
of C*-algebras would imply a positive answer to this question for all bipartite
scenarios. This remains true also if one considers not only spatial
correlations, but also spatiotemporal correlations, where each party is allowed
to apply their measurements in temporal succession; we provide an example of a
state together with observables such that ordinary spatial correlations are
local, while the spatiotemporal correlations reveal nonlocality. Moreover, we
find an extended version of Tsirelson's problem which, for each nontrivial Bell
scenario, is equivalent to the QWEP conjecture. This extended version can be
conveniently formulated in terms of steering the system of a third party.
Finally, a comprehensive mathematical appendix offers background material on
complete positivity, tensor products of C*-algebras, group C*-algebras, and
some simple reformulations of the QWEP conjecture.Comment: 57 pages, to appear in Rev. Math. Phy
Operational distance and fidelity for quantum channels
We define and study a fidelity criterion for quantum channels, which we term
the minimax fidelity, through a noncommutative generalization of maximal
Hellinger distance between two positive kernels in classical probability
theory. Like other known fidelities for quantum channels, the minimax fidelity
is well-defined for channels between finite-dimensional algebras, but it also
applies to a certain class of channels between infinite-dimensional algebras
(explicitly, those channels that possess an operator-valued Radon--Nikodym
density with respect to the trace in the sense of Belavkin--Staszewski) and
induces a metric on the set of quantum channels which is topologically
equivalent to the CB-norm distance between channels, precisely in the same way
as the Bures metric on the density operators associated with statistical states
of quantum-mechanical systems, derived from the well-known fidelity
(`generalized transition probability') of Uhlmann, is topologically equivalent
to the trace-norm distance.Comment: 26 pages, amsart.cls; improved intro, fixed typos, added a reference;
accepted by J. Math. Phy
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