337 research outputs found
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
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
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
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
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
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
Multipartite Asymmetric Quantum Cloning
We investigate the optimal distribution of quantum information over
multipartite systems in asymmetric settings. We introduce cloning
transformations that take identical replicas of a pure state in any
dimension as input, and yield a collection of clones with non-identical
fidelities. As an example, if the clones are partitioned into a set of
clones with fidelity and another set of clones with fidelity ,
the trade-off between these fidelities is analyzed, and particular cases of
optimal cloning machines are exhibited. We also present an
optimal cloning machine, which is the first known example of a
tripartite fully asymmetric cloner. Finally, it is shown how these cloning
machines can be optically realized.Comment: 5 pages, 2 figure
Measurement uncertainty relations
Measurement uncertainty relations are quantitative bounds on the errors in an
approximate joint measurement of two observables. They can be seen as a
generalization of the error/disturbance tradeoff first discussed heuristically
by Heisenberg. Here we prove such relations for the case of two canonically
conjugate observables like position and momentum, and establish a close
connection with the more familiar preparation uncertainty relations
constraining the sharpness of the distributions of the two observables in the
same state. Both sets of relations are generalized to means of order
rather than the usual quadratic means, and we show that the optimal constants
are the same for preparation and for measurement uncertainty. The constants are
determined numerically and compared with some bounds in the literature. In both
cases the near-saturation of the inequalities entails that the state (resp.
observable) is uniformly close to a minimizing one.Comment: This version 2 contains minor corrections and reformulation
Direct detection of quantum entanglement
Quantum entanglement, after playing a significant role in the development of
the foundations of quantum mechanics, has been recently rediscovered as a new
physical resource with potential commercial applications such as, for example,
quantum cryptography, better frequency standards or quantum-enhanced
positioning and clock synchronization. On the mathematical side the studies of
entanglement have revealed very interesting connections with the theory of
positive maps. The capacity to generate entangled states is one of the basic
requirements for building quantum computers. Hence, efficient experimental
methods for detection, verification and estimation of quantum entanglement are
of great practical importance. Here, we propose an experimentally viable,
\emph{direct} detection of quantum entanglement which is efficient and does not
require any \emph{a priori} knowledge about the quantum state. In a particular
case of two entangled qubits it provides an estimation of the amount of
entanglement. We view this method as a new form of quantum computation, namely,
as a decision problem with quantum data structure.Comment: 4 pages, 1 eps figure, RevTe
On Nonzero Kronecker Coefficients and their Consequences for Spectra
A triple of spectra (r^A, r^B, r^{AB}) is said to be admissible if there is a
density operator rho^{AB} with (Spec rho^A, Spec rho^B, Spec rho^{AB})=(r^A,
r^B, r^{AB}). How can we characterise such triples? It turns out that the
admissible spectral triples correspond to Young diagrams (mu, nu, lambda) with
nonzero Kronecker coefficient [M. Christandl and G. Mitchison, to appear in
Comm. Math. Phys., quant-ph/0409016; A. Klyachko, quant-ph/0409113]. This means
that the irreducible representation V_lambda is contained in the tensor product
of V_mu and V_nu. Here, we show that such triples form a finitely generated
semigroup, thereby resolving a conjecture of Klyachko. As a consequence we are
able to obtain stronger results than in [M. Ch. and G. M. op. cit.] and give a
complete information-theoretic proof of the correspondence between triples of
spectra and representations. Finally, we show that spectral triples form a
convex polytope.Comment: 13 page
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