8,189 research outputs found
Entanglement at distance: qubits versus continuous variables
We consider the problem of obtaining maximally entangled photon states at
distance in the presence of loss. We compare the efficiency of two different
schemes in establishing shared ebits: i) single ebit states with the
qubit encoded on polarization; ii) a single continuous variable entangled state
(emode) assisted by optimal local operation and classical communication (LOCC)
protocol in order to obtain a -dimensional maximally entangled state, with
qubits encoded on the photon number.Comment: 5 pages. 4 eps files. Use fortschritte.sty (included
Purification of noisy quantum measurements
We consider the problem of improving noisy quantum measurements by suitable
preprocessing strategies making many noisy detectors equivalent to a single
ideal detector. For observables pertaining to finite-dimensional systems (e.g.
qubits or spins) we consider preprocessing strategies that are reminiscent of
quantum error correction procedures and allows one to perfectly measure an
observable on a single quantum system for increasing number of inefficient
detectors. For measurements of observables with unbounded spectrum (e.g. photon
number, homodyne and heterodyne detection), the purification of noisy quantum
measurements can be achieved by preamplification as suggested by H. P. Yuen
[1].Comment: 13 pages, 8 figures; minor correction
Joint estimation of real squeezing and displacement
We study the problem of joint estimation of real squeezing and amplitude of
the radiation field, deriving the measurement that maximizes the probability
density of detecting the true value of the unknown parameters. More generally,
we provide a solution for the problem of estimating the unknown unitary action
of a nonunimodular group in the maximum likelihood approach. Remarkably, in
this case the optimal measurements do not coincide with the so called
square-root measurements. In the case of squeezing and displacement we analyze
in detail the sensitivity of estimation for coherent states and displaced
squeezed states, deriving the asymptotic relation between the uncertainties in
the joint estimation and the corresponding uncertainties in the optimal
separate measurements of squeezing and displacement. A two-mode setup is also
analyzed, showing how entanglement between optical modes can be used to
approximate perfect estimation.Comment: 14 pages, 3 eps figures; a section has been added with new results in
terms of Heisenberg uncertainty relations for the joint measuremen
Informationally complete measurements on bipartite quantum systems: comparing local with global measurements
Informationally complete measurements allow the estimation of expectation
values of any operator on a quantum system, by changing only the
data-processing of the measurement outcomes. In particular, an informationally
complete measurement can be used to perform quantum tomography, namely to
estimate the density matrix of the quantum state. The data-processing is
generally nonunique, and can be optimized according to a given criterion. In
this paper we provide the solution of the optimization problem which minimizes
the variance in the estimation. We then consider informationally complete
measurements performed over bipartite quantum systems focusing attention on
universally covariant measurements, and compare their statistical efficiency
when performed either locally or globally on the two systems. Among global
measurements we consider the special case of Bell measurements, which allow to
estimate the expectation of a restricted class of operators. We compare the
variance in the three cases: local, Bell, and unrestricted global--and derive
conditions for the operators to be estimated such that one type of measurement
is more efficient than the other. In particular, we find that for factorized
operators and Bell projectors the Bell measurement always performs better than
the unrestricted global measurement, which in turn outperforms the local one.
For estimation of the matrix elements of the density operator, the relative
performances depend on the basis on which the state is represented, and on the
matrix element being diagonal or off-diagonal, however, with the global
unrestricted measurement generally performing better than the local one.Comment: 8 pages, no figure
Optimization of quantum universal detectors
The expectation value of an arbitrary operator O can be obtained via a
universal measuring apparatus that is independent of O, by changing only the
data-processing of the outcomes. Such a ``universal detector'' performs a joint
measurement on the system and on a suitable ancilla prepared in a fixed state,
and is equivalent to a positive operator valued measure (POVM) for the system
that is ``informationally complete''. The data processing functions generally
are not unique, and we pose the problem of their optimization, providing some
examples for covariant POVM's, in particular for SU(d) covariance group.Comment: 8 pages, no figures. Proceedingsof the 8th International Conference
on Squeezed States and Uncertainty Relations ICSSUR' 2003, Puebla, Mexico -
June 9-13, 200
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