208 research outputs found
Entanglement, Haag-duality and type properties of infinite quantum spin chains
We consider an infinite spin chain as a bipartite system consisting of the
left and right half-chain and analyze entanglement properties of pure states
with respect to this splitting. In this context we show that the amount of
entanglement contained in a given state is deeply related to the von Neumann
type of the observable algebras associated to the half-chains. Only the type I
case belongs to the usual entanglement theory which deals with density
operators on tensor product Hilbert spaces, and only in this situation
separable normal states exist. In all other cases the corresponding state is
infinitely entangled in the sense that one copy of the system in such a state
is sufficient to distill an infinite amount of maximally entangled qubit pairs.
We apply this results to the critical XY model and show that its unique ground
state provides a particular example for this type of entanglement.Comment: LaTeX2e, 34 pages, 1 figure (pstricks
Optimal probabilistic cloning and purification of quantum states
We investigate the probabilistic cloning and purification of quantum states.
The performance of these probabilistic operations is quantified by the average
fidelity between the ideal and actual output states. We provide a simple
formula for the maximal achievable average fidelity and we explictly show how
to construct a probabilistic operation that achieves this fidelity. We
illustrate our method on several examples such as the phase covariant cloning
of qubits, cloning of coherent states, and purification of qubits transmitted
via depolarizing channel and amplitude damping channel. Our examples reveal
that the probabilistic cloner may yield higher fidelity than the best
deterministic cloner even when the states that should be cloned are linearly
dependent and are drawn from a continuous set.Comment: 9 pages, 2 figure
Numerical simulations of mixed states quantum computation
We describe quantum-octave package of functions useful for simulations of
quantum algorithms and protocols. Presented package allows to perform
simulations with mixed states. We present numerical implementation of important
quantum mechanical operations - partial trace and partial transpose. Those
operations are used as building blocks of algorithms for analysis of
entanglement and quantum error correction codes. Simulation of Shor's algorithm
is presented as an example of package capabilities.Comment: 6 pages, 4 figures, presented at Foundations of Quantum Information,
16th-19th April 2004, Camerino, Ital
Local distinguishability of quantum states in infinite dimensional systems
We investigate local distinguishability of quantum states by use of the
convex analysis about joint numerical range of operators on a Hilbert space. We
show that any two orthogonal pure states are distinguishable by local
operations and classical communications, even for infinite dimensional systems.
An estimate of the local discrimination probability is also given for some
family of more than two pure states
A generalization of Schur-Weyl duality with applications in quantum estimation
Schur-Weyl duality is a powerful tool in representation theory which has many
applications to quantum information theory. We provide a generalization of this
duality and demonstrate some of its applications. In particular, we use it to
develop a general framework for the study of a family of quantum estimation
problems wherein one is given n copies of an unknown quantum state according to
some prior and the goal is to estimate certain parameters of the given state.
In particular, we are interested to know whether collective measurements are
useful and if so to find an upper bound on the amount of entanglement which is
required to achieve the optimal estimation. In the case of pure states, we show
that commutativity of the set of observables that define the estimation problem
implies the sufficiency of unentangled measurements.Comment: The published version, Typos corrected, 40 pages, 2 figure
Single-copy entanglement in critical spin chains
We introduce the single-copy entanglement as a quantity to assess quantum
correlations in the ground state in quantum many-body systems. We show for a
large class of models that already on the level of single specimens of spin
chains, criticality is accompanied with the possibility of distilling a
maximally entangled state of arbitrary dimension from a sufficiently large
block deterministically, with local operations and classical communication.
These analytical results -- which refine previous results on the divergence of
block entropy as the rate at which EPR pairs can be distilled from many
identically prepared chains, and which apply to single systems as encountered
in actual experimental situations -- are made quantitative for general
isotropic translationally invariant spin chains that can be mapped onto a
quasi-free fermionic system, and for the anisotropic XY model. For the XX
model, we provide the asymptotic scaling of ~(1/6) log_2(L), and contrast it
with the block entropy. The role of superselection rules on single-copy
entanglement in systems consisting of indistinguishable particles is
emphasized.Comment: 5 pages, RevTeX, final versio
Universal approximation of multi-copy states and universal quantum lossless data compression
We have proven that there exists a quantum state approximating any multi-copy
state universally when we measure the error by means of the normalized relative
entropy. While the qubit case was proven by Krattenthaler and Slater (IEEE
Trans. IT, 46, 801-819 (2000); quant-ph/9612043), the general case has been
open for more than ten years. For a deeper analysis, we have solved the
mini-max problem concerning `approximation error' up to the second order.
Furthermore, we have applied this result to quantum lossless data compression,
and have constructed a universal quantum lossless data compression
Universal and phase covariant superbroadcasting for mixed qubit states
We describe a general framework to study covariant symmetric broadcasting
maps for mixed qubit states. We explicitly derive the optimal N to M
superbroadcasting maps, achieving optimal purification of the single-site
output copy, in both the universal and the phase covariant cases. We also study
the bipartite entanglement properties of the superbroadcast states.Comment: 19 pages, 8 figures, strictly related to quant-ph/0506251 and
quant-ph/051015
Radon-Nikodym derivatives of quantum operations
Given a completely positive (CP) map , there is a theorem of the
Radon-Nikodym type [W.B. Arveson, Acta Math. {\bf 123}, 141 (1969); V.P.
Belavkin and P. Staszewski, Rep. Math. Phys. {\bf 24}, 49 (1986)] that
completely characterizes all CP maps such that is also a CP map. This
theorem is reviewed, and several alternative formulations are given along the
way. We then use the Radon-Nikodym formalism to study the structure of order
intervals of quantum operations, as well as a certain one-to-one correspondence
between CP maps and positive operators, already fruitfully exploited in many
quantum information-theoretic treatments. We also comment on how the
Radon-Nikodym theorem can be used to derive norm estimates for differences of
CP maps in general, and of quantum operations in particular.Comment: 22 pages; final versio
The optimal cloning of quantum coherent states is non-Gaussian
We consider the optimal cloning of quantum coherent states with single-clone
and joint fidelity as figures of merit. Both optimal fidelities are attained
for phase space translation covariant cloners. Remarkably, the joint fidelity
is maximized by a Gaussian cloner, whereas the single-clone fidelity can be
enhanced by non-Gaussian operations: a symmetric non-Gaussian 1-to-2 cloner can
achieve a single-clone fidelity of approximately 0.6826, perceivably higher
than the optimal fidelity of 2/3 in a Gaussian setting. This optimal cloner can
be realized by means of an optical parametric amplifier supplemented with a
particular source of non-Gaussian bimodal states. Finally, we show that the
single-clone fidelity of the optimal 1-to-infinity cloner, corresponding to a
measure-and-prepare scheme, cannot exceed 1/2. This value is achieved by a
Gaussian scheme and cannot be surpassed even with supplemental bound entangled
states.Comment: 4 pages, 2 figures, revtex; changed title, extended list of authors,
included optical implementation of optimal clone
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