1,536 research outputs found

### Optimum unambiguous discrimination of two mixed quantum states

We investigate generalized measurements, based on positive-operator-valued
measures, and von Neumann measurements for the unambiguous discrimination of
two mixed quantum states that occur with given prior probabilities. In
particular, we derive the conditions under which the failure probability of the
measurement can reach its absolute lower bound, proportional to the fidelity of
the states. The optimum measurement strategy yielding the fidelity bound of the
failure probability is explicitly determined for a number of cases. One example
involves two density operators of rank d that jointly span a 2d-dimensional
Hilbert space and are related in a special way. We also present an application
of the results to the problem of unambiguous quantum state comparison,
generalizing the optimum strategy for arbitrary prior probabilities of the
states.Comment: final versio

### 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 $N$ given
non-orthogonal states, $\{|\psi_{1} >,..., |\psi_{N} > \}$, 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 $|\psi_1>$ from the set $\{|\psi_2 >,...,|\psi_N > \}$ 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

### Optimum measurement for unambiguously discriminating two mixed states: General considerations and special cases

Based on our previous publication [U. Herzog and J. A. Bergou, Phys.Rev. A
71, 050301(R) (2005)] we investigate the optimum measurement for the
unambiguous discrimination of two mixed quantum states that occur with given
prior probabilities. Unambiguous discrimination of nonorthogonal states is
possible in a probabilistic way, at the expense of a nonzero probability of
inconclusive results, where the measurement fails. Along with a discussion of
the general problem, we give an example illustrating our method of solution. We
also provide general inequalities for the minimum achievable failure
probability and discuss in more detail the necessary conditions that must be
fulfilled when its absolute lower bound, proportional to the fidelity of the
states, can be reached.Comment: Submitted to Journal of Physics:Conference Series (Proceedings of the
12th Central European Workshop on Quantum Optics, Ankara, June 2005

### Optical realization of optimal unambiguous discrimination for pure and mixed quantum states

Quantum mechanics forbids deterministic discrimination among non-orthogonal
states. Nonetheless, the capability to distinguish nonorthogonal states
unambiguously is an important primitive in quantum information processing. In
this work, we experimentally implement generalized measurements in an optical
system and demonstrate the first optimal unambiguous discrimination between
three nonorthogonal states, with a success rate of 55%, to be compared with the
25% maximum achievable using projective measurements. Furthermore we present
the first realization of unambiguous discrimination between a pure state and a
nonorthogonal mixed state.Comment: Some minor revision

### Minimal optimal generalized quantum measurements

Optimal and finite positive operator valued measurements on a finite number
$N$ of identically prepared systems have been presented recently. With physical
realization in mind we propose here optimal and minimal generalized quantum
measurements for two-level systems.
We explicitly construct them up to N=7 and verify that they are minimal up to
N=5. We finally propose an expression which gives the size of the minimal
optimal measurements for arbitrary $N$.Comment: 9 pages, Late

### Maximum-confidence discrimination among symmetric qudit states

We study the maximum-confidence (MC) measurement strategy for discriminating
among nonorthogonal symmetric qudit states. Restricting to linearly dependent
and equally likely pure states, we find the optimal positive operator valued
measure (POVM) that maximizes our confidence in identifying each state in the
set and minimizes the probability of obtaining inconclusive results. The
physical realization of this POVM is completely determined and it is shown that
after an inconclusive outcome, the input states may be mapped into a new set of
equiprobable symmetric states, restricted, however, to a subspace of the
original qudit Hilbert space. By applying the MC measurement again onto this
new set, we can still gain some information about the input states, although
with less confidence than before. This leads us to introduce the concept of
"sequential maximum-confidence" (SMC) measurements, where the optimized MC
strategy is iterated in as many stages as allowed by the input set, until no
further information can be extracted from an inconclusive result. Within each
stage of this measurement our confidence in identifying the input states is the
highest possible, although it decreases from one stage to the next. In
addition, the more stages we accomplish within the maximum allowed, the higher
will be the probability of correct identification. We will discuss an explicit
example of the optimal SMC measurement applied in the discrimination among four
symmetric qutrit states and propose an optical network to implement it.Comment: 14 pages, 4 figures. Published versio

### Minimum-error discrimination between three mirror-symmetric states

We present the optimal measurement strategy for distinguishing between three
quantum states exhibiting a mirror symmetry. The three states live in a
two-dimensional Hilbert space, and are thus overcomplete. By mirror symmetry we
understand that the transformation {|+> -> |+>, |-> -> -|->} leaves the set of
states invariant. The obtained measurement strategy minimizes the error
probability. An experimental realization for polarized photons, realizable with
current technology, is suggested.Comment: 4 pages, 2 figure

### On Interferometric Duality in Multibeam Experiments

We critically analyze the problem of formulating duality between fringe
visibility and which-way information, in multibeam interference experiments. We
show that the traditional notion of visibility is incompatible with any
intuitive idea of complementarity, but for the two-beam case. We derive a
number of new inequalities, not present in the two-beam case, one of them
coinciding with a recently proposed multibeam generalization of the inequality
found by Greenberger and YaSin. We show, by an explicit procedure of
optimization in a three-beam case, that suggested generalizations of Englert's
inequality, do not convey, differently from the two-beam case, the idea of
complementarity, according to which an increase of visibility is at the cost of
a loss in path information, and viceversa.Comment: 26 pages, 1 figure, substantial changes in the text, new material has
been added in Section 3. Version to appear in J.Phys.

### A two-qubit Bell inequality for which POVM measurements are relevant

A bipartite Bell inequality is derived which is maximally violated on the
two-qubit state space if measurements describable by positive operator valued
measure (POVM) elements are allowed rather than restricting the possible
measurements to projective ones. In particular, the presented Bell inequality
requires POVMs in order to be maximally violated by a maximally entangled
two-qubit state. This answers a question raised by N. Gisin.Comment: 7 pages, 1 figur

### Kochen-Specker theorem for a single qubit using positive operator-valued measures

A proof of the Kochen-Specker theorem for a single two-level system is
presented. It employs five eight-element positive operator-valued measures and
a simple algebraic reasoning based on the geometry of the dodecahedron.Comment: REVTeX4, 4 pages, 2 figure

- â€¦