479 research outputs found
Quantum Markov Process on a Lattice
We develop a systematic description of Weyl and Fano operators on a lattice
phase space. Introducing the so-called ghost variable even on an odd lattice,
odd and even lattices can be treated in a symmetric way. The Wigner function is
defined using these operators on the quantum phase space, which can be
interpreted as a spin phase space. If we extend the space with a dichotomic
variable, a positive distribution function can be defined on the new space. It
is shown that there exits a quantum Markov process on the extended space which
describes the time evolution of the distribution function.Comment: Lattice2003(theory
Optimal estimation of a physical observable's expectation value for pure states
We study the optimal way to estimate the quantum expectation value of a
physical observable when a finite number of copies of a quantum pure state are
presented. The optimal estimation is determined by minimizing the squared error
averaged over all pure states distributed in a unitary invariant way. We find
that the optimal estimation is "biased", though the optimal measurement is
given by successive projective measurements of the observable. The optimal
estimate is not the sample average of observed data, but the arithmetic average
of observed and "default nonobserved" data, with the latter consisting of all
eigenvalues of the observable.Comment: v2: 5pages, typos corrected, journal versio
Unitary-process discrimination with error margin
We investigate a discrimination scheme between unitary processes. By
introducing a margin for the probability of erroneous guess, this scheme
interpolates the two standard discrimination schemes: minimum-error and
unambiguous discrimination. We present solutions for two cases. One is the case
of two unitary processes with general prior probabilities. The other is the
case with a group symmetry: the processes comprise a projective representation
of a finite group. In the latter case, we found that unambiguous discrimination
is a kind of "all or nothing": the maximum success probability is either 0 or
1. We also closely analyze how entanglement with an auxiliary system improves
discrimination performance.Comment: 9 pages, 3 figures, presentation improved, typos corrected, final
versio
Complete solution for unambiguous discrimination of three pure states with real inner products
Complete solutions are given in a closed analytic form for unambiguous
discrimination of three general pure states with real mutual inner products.
For this purpose, we first establish some general results on unambiguous
discrimination of n linearly independent pure states. The uniqueness of
solution is proved. The condition under which the problem is reduced to an
(n-1)-state problem is clarified. After giving the solution for three pure
states with real mutual inner products, we examine some difficulties in
extending our method to the case of complex inner products. There is a class of
set of three pure states with complex inner products for which we obtain an
analytical solution.Comment: 13 pages, 3 figures, presentation improved, reference adde
Reexamination of optimal quantum state estimation of pure states
A direct derivation is given for the optimal mean fidelity of quantum state
estimation of a d-dimensional unknown pure state with its N copies given as
input, which was first obtained by M. Hayashi in terms of an infinite set of
covariant positive operator valued measures (POVM's) and by Bruss and
Macchiavello establishing a connection to optimal quantum cloning. An explicit
condition for POVM measurement operators for optimal estimators is obtained, by
which we construct optimal estimators with finite POVM using exact quadratures
on a hypersphere. These finite optimal estimators are not generally universal,
where universality means the fidelity is independent of input states. However,
any optimal estimator with finite POVM for M(>N) copies is universal if it is
used for N copies as input.Comment: v3(journal version): title changed, presentation improve
Discrimination with error margin between two states - Case of general occurrence probabilities -
We investigate a state discrimination problem which interpolates
minimum-error and unambiguous discrimination by introducing a margin for the
probability of error. We closely analyze discrimination of two pure states with
general occurrence probabilities. The optimal measurements are classified into
three types. One of the three types of measurement is optimal depending on
parameters (occurrence probabilities and error margin). We determine the three
domains in the parameter space and the optimal discrimination success
probability in each domain in a fully analytic form. It is also shown that when
the states to be discriminated are multipartite, the optimal success
probability can be attained by local operations and classical communication.
For discrimination of two mixed states, an upper bound of the optimal success
probability is obtained.Comment: Final version, 9 pages, references added, presentation improve
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