420 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

### Unambiguous pure state identification without classical knowledge

We study how to unambiguously identify a given quantum pure state with one of
the two reference pure states when no classical knowledge on the reference
states is given but a certain number of copies of each reference quantum state
are presented. By the unambiguous identification, we mean that we are not
allowed to make a mistake but our measurement can produce an inconclusive
result. Assuming the two reference states are independently distributed over
the whole pure state space in a unitary invariant way, we determine the optimal
mean success probability for an arbitrary number of copies of the reference
states and a general dimension of the state space. It is explicitly shown that
the obtained optimal mean success probability asymptotically approaches that of
the unambiguous discrimination as the number of the copies of the reference
states increases.Comment: v3: 8 pages, minor corrections, journal versio

### Locality and nonlocality in quantum pure-state identification problems

Suppose we want to identify an input state with one of two unknown reference
states, where the input state is guaranteed to be equal to one of the reference
states. We assume that no classical knowledge of the reference states is given,
but a certain number of copies of them are available instead. Two reference
states are independently and randomly chosen from the state space in a unitary
invariant way. This is called the quantum state identification problem, and the
task is to optimize the mean identification success probability. In this paper,
we consider the case where each reference state is pure and bipartite, and
generally entangled. The question is whether the maximum mean identification
success probability can be attained by means of a local operations and
classical communication (LOCC) measurement scheme. Two types of identification
problems are considered when a single copy of each reference state is
available. We show that a LOCC scheme attains the globally achievable
identification probability in the minimum-error identification problem. In the
unambiguous identification problem, however, the maximal success probability by
means of LOCC is shown to be less than the globally achievable identification
probability.Comment: 11 pages, amalgamation of arXiv:0712.2906 and arXiv:0801.012

### 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

### Simple criterion for local distinguishability of generalized Bell states in prime dimension

Local distinguishability of sets of generalized Bell states (GBSs) is
investigated. We first clarify the conditions such that a set of GBSs can be
locally transformed to a certain type of GBS set that is easily distinguishable
within local operations and one-way classical communication. We then show that,
if the space dimension $d$ is a prime, these conditions are necessary and
sufficient for sets of $d$ GBSs in $\mathbb{C}^d \otimes \mathbb{C}^d$ to be
locally distinguishable. Thus we obtain a simple computable criterion for local
distinguishability of sets of $d$ GBSs in prime dimension $d$.Comment: 6 pages, presentation improved, final versio

- …