25,864 research outputs found
Parity Measurement is Sufficient for Phase Estimation at the Quantum Cramer-Rao Bound for Path-Symmetric States
In this letter, we show that for all the so-called path-symmetric states, the
measurement of parity of photon number at the output of an optical
interferometer achieves maximal phase sensitivity at the quantum Cramer-Rao
bound. Such optimal phase sensitivity with parity is attained at a suitable
bias phase, which can be determined a priori. Our scheme is applicable for
local phase estimation
Efficient Optimal Minimum Error Discrimination of Symmetric Quantum States
This paper deals with the quantum optimal discrimination among mixed quantum
states enjoying geometrical uniform symmetry with respect to a reference
density operator . It is well-known that the minimal error probability
is given by the positive operator-valued measure (POVM) obtained as a solution
of a convex optimization problem, namely a set of operators satisfying
geometrical symmetry, with respect to a reference operator , and
maximizing . In this paper, by resolving the dual
problem, we show that the same result is obtained by minimizing the trace of a
semidefinite positive operator commuting with the symmetry operator and
such that . The new formulation gives a deeper insight into the
optimization problem and allows to obtain closed-form analytical solutions, as
shown by a simple but not trivial explanatory example. Besides the theoretical
interest, the result leads to semidefinite programming solutions of reduced
complexity, allowing to extend the numerical performance evaluation to quantum
communication systems modeled in Hilbert spaces of large dimension.Comment: 5 pages, 1 Table, no figure
Comparing the states of many quantum systems
We investigate how to determine whether the states of a set of quantum
systems are identical or not. This paper treats both error-free comparison, and
comparison where errors in the result are allowed. Error-free comparison means
that we aim to obtain definite answers, which are known to be correct, as often
as possible. In general, we will have to accept also inconclusive results,
giving no information. To obtain a definite answer that the states of the
systems are not identical is always possible, whereas, in the situation
considered here, a definite answer that they are identical will not be
possible. The optimal universal error-free comparison strategy is a projection
onto the totally symmetric and the different non-symmetric subspaces, invariant
under permutations and unitary transformations. We also show how to construct
optimal comparison strategies when allowing for some errors in the result,
minimising either the error probability, or the average cost of making an
error. We point out that it is possible to realise universal error-free
comparison strategies using only linear elements and particle detectors, albeit
with less than ideal efficiency. Also minimum-error and minimum-cost strategies
may sometimes be realised in this way. This is of great significance for
practical applications of quantum comparison.Comment: 13 pages, 2 figures. Corrected a misprint on p. 7 and added a few
references. Accepted for publication in J Mod Op
Distinguishing two single-mode Gaussian states by homodyne detection: An information-theoretic approach
It is known that the quantum fidelity, as a measure of the closeness of two
quantum states, is operationally equivalent to the minimal overlap of the
probability distributions of the two states over all possible POVMs; the POVM
realizing the minimum is optimal. We consider the ability of homodyne detection
to distinguish two single-mode Gaussian states, and investigate to what extent
it is optimal in this information-theoretic sense. We completely identify the
conditions under which homodyne detection makes an optimal distinction between
two single-mode Gaussian states of the same mean, and show that if the Gaussian
states are pure, they are always optimally distinguished.Comment: 6 pages, 4 figures, published version with a detailed discussio
Quantum state discrimination
It is a fundamental consequence of the superposition principle for quantum
states that there must exist non-orthogonal states, that is states that,
although different, have a non-zero overlap. This finite overlap means that
there is no way of determining with certainty in which of two such states a
given physical system has been prepared. We review the various strategies that
have been devised to discriminate optimally between non-orthogonal states and
some of the optical experiments that have been performed to realise these.Comment: 43 pages, submitted to Advances in Optics and Photonic
Coherent and Squeezed Vacuum Light Interferometry: Parity detection hits the Heisenberg limit
The interference between coherent and squeezed vacuum light can produce path
entangled states with very high fidelities. We show that the phase sensitivity
of the above interferometric scheme with parity detection saturates the quantum
Cramer-Rao bound, which reaches the Heisenberg-limit when the coherent and
squeezed vacuum light are mixed in roughly equal proportions. For the same
interferometric scheme, we draw a detailed comparison between parity detection
and a symmetric-logarithmic-derivative-based detection scheme suggested by Ono
and Hofmann.Comment: Change in the format from aps to iop since we decided to submit it to
NJP; Minor changes in tex
Measurement-induced disturbances and nonclassical correlations of Gaussian states
We study quantum correlations beyond entanglement in two-mode Gaussian states
of continuous variable systems, by means of the measurement-induced disturbance
(MID) and its ameliorated version (AMID). In analogy with the recent studies of
the Gaussian quantum discord, we define a Gaussian AMID by constraining the
optimization to all bi-local Gaussian positive operator valued measurements. We
solve the optimization explicitly for relevant families of states, including
squeezed thermal states. Remarkably, we find that there is a finite subset of
two-mode Gaussian states, comprising pure states, where non-Gaussian
measurements such as photon counting are globally optimal for the AMID and
realize a strictly smaller state disturbance compared to the best Gaussian
measurements. However, for the majority of two--mode Gaussian states the
unoptimized MID provides a loose overestimation of the actual content of
quantum correlations, as evidenced by its comparison with Gaussian discord.
This feature displays strong similarity with the case of two qubits. Upper and
lower bounds for the Gaussian AMID at fixed Gaussian discord are identified. We
further present a comparison between Gaussian AMID and Gaussian entanglement of
formation, and classify families of two-mode states in terms of their Gaussian
AMID, Gaussian discord, and Gaussian entanglement of formation. Our findings
provide a further confirmation of the genuinely quantum nature of general
Gaussian states, yet they reveal that non-Gaussian measurements can play a
crucial role for the optimized extraction and potential exploitation of
classical and nonclassical correlations in Gaussian states.Comment: 16 pages, 5 figures; new results added; to appear in Phys. Rev.
- …