274 research outputs found
On Haag Duality for Pure States of Quantum Spin Chain
We consider quantum spin chains and their translationally invariant pure
states. We prove Haag duality for quasilocal observables localized in
semi-infinite intervals when the von Neumann algebras generated by observables
localized in these intervals are not type I
Uncertainty Relations for Joint Localizability and Joint Measurability in Finite-Dimensional Systems
Two quantities quantifying uncertainty relations are examined. In
J.Math.Phys. 48, 082103 (2007), Busch and Pearson investigated the limitation
on joint localizability and joint measurement of position and momentum by
introducing overall width and error bar width. In this paper, we show a simple
relationship between these quantities for finite-dimensional systems. Our
result indicates that if there is a bound on joint localizability, it is
possible to obtain a similar bound on joint measurability. For
finite-dimensional systems, uncertainty relations for a pair of general
projection-valued measures are obtained as by-products.Comment: 10 pages. To appear in Journal of Mathematical Physic
Estimating the spectrum of a density operator
Given N quantum systems prepared according to the same density operator \rho,
we propose a measurement on the N-fold system which approximately yields the
spectrum of \rho. The projections of the proposed observable decompose the
Hilbert space according to the irreducible representations of the permutations
on N points, and are labeled by Young frames, whose relative row lengths
estimate the eigenvalues of \rho in decreasing order. We show convergence of
these estimates in the limit N\to\infty, and that the probability for errors
decreases exponentially with a rate we compute explicitly.Comment: 4 Pages, RevTeX, one figur
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
Decoherence of multi-dimensional entangled coherent states
For entangled states of light both the amount of entanglement and the
sensitivity to noise generally increase with the number of photons in the
state. The entanglement-sensitivity tradeoff is investigated for a particular
set of states, multi-dimensional entangled coherent states. Those states
possess an arbitrarily large amount of entanglement provided the number of
photons is at least of order . We calculate how fast that entanglement
decays due to photon absorption losses and how much entanglement is left. We
find that for very small losses the amount of entanglement lost is equal to
ebits per absorbed photon, irrespective of the amount
of pure-state entanglement one started with. In contrast, for larger losses
it tends to be the remaining amount of entanglement that is independent of .
This may provide a useful strategy for creating states with a fixed amount of
entanglement.Comment: 6 pages, 5 figure
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
Quantum Walks with Non-Orthogonal Position States
Quantum walks have by now been realized in a large variety of different
physical settings. In some of these, particularly with trapped ions, the walk
is implemented in phase space, where the corresponding position states are not
orthogonal. We develop a general description of such a quantum walk and show
how to map it into a standard one with orthogonal states, thereby making
available all the tools developed for the latter. This enables a variety of
experiments, which can be implemented with smaller step sizes and more steps.
Tuning the non-orthogonality allows for an easy preparation of extended states
such as momentum eigenstates, which travel at a well-defined speed with low
dispersion. We introduce a method to adjust their velocity by momentum shifts,
which allows to investigate intriguing effects such as the analog of Bloch
oscillations.Comment: 5 pages, 4 figure
Experimental Purification of Single Qubits
We report the experimental realization of the purification protocol for
single qubits sent through a depolarization channel. The qubits are associated
with polarization encoded photon particles and the protocol is achieved by
means of passive linear optical elements. The present approach may represent a
convenient alternative to the distillation and error correction protocols of
quantum information.Comment: 10 pages, 2 figure
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