8,949 research outputs found
Optimal signal states for quantum detectors
Quantum detectors provide information about quantum systems by establishing
correlations between certain properties of those systems and a set of
macroscopically distinct states of the corresponding measurement devices. A
natural question of fundamental significance is how much information a quantum
detector can extract from the quantum system it is applied to. In the present
paper we address this question within a precise framework: given a quantum
detector implementing a specific generalized quantum measurement, what is the
optimal performance achievable with it for a concrete information readout task,
and what is the optimal way to encode information in the quantum system in
order to achieve this performance? We consider some of the most common
information transmission tasks - the Bayes cost problem (of which minimal error
discrimination is a special case), unambiguous message discrimination, and the
maximal mutual information. We provide general solutions to the Bayesian and
unambiguous discrimination problems. We also show that the maximal mutual
information has an interpretation of a capacity of the measurement, and derive
various properties that it satisfies, including its relation to the accessible
information of an ensemble of states, and its form in the case of a
group-covariant measurement. We illustrate our results with the example of a
noisy two-level symmetric informationally complete measurement, for whose
capacity we give analytical proofs of optimality. The framework presented here
provides a natural way to characterize generalized quantum measurements in
terms of their information readout capabilities.Comment: 13 pages, 1 figure, example section extende
Optimal discrimination of single-qubit mixed states
We consider the problem of minimum-error quantum state discrimination for
single-qubit mixed states. We present a method which uses the Helstrom
conditions constructively and analytically; this algebraic approach is
complementary to existing geometric methods, and solves the problem for any
number of arbitrary signal states with arbitrary prior probabilities.Comment: 8 pages, 1 figur
Optimal unambiguous filtering of a quantum state: An instance in mixed state discrimination
Deterministic discrimination of nonorthogonal states is forbidden by quantum
measurement theory. However, if we do not want to succeed all the time, i.e.
allow for inconclusive outcomes to occur, then unambiguous discrimination
becomes possible with a certain probability of success. A variant of the
problem is set discrimination: the states are grouped in sets and we want to
determine to which particular set a given pure input state belongs. We consider
here the simplest case, termed quantum state filtering, when the given
non-orthogonal states, , are divided into
two sets and the first set consists of one state only while the second consists
of all of the remaining states. We present the derivation of the optimal
measurement strategy, in terms of a generalized measurement (POVM), to
distinguish from the set and the
corresponding optimal success and failure probabilities. The results, but not
the complete derivation, were presented previously [\prl {\bf 90}, 257901
(2003)] as the emphasis there was on appplication of the results to novel
probabilistic quantum algorithms. We also show that the problem is equivalent
to the discrimination of a pure state and an arbitrary mixed state.Comment: 8 page
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