215 research outputs found
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
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
Coherent states engineering with linear optics: Possible and impossible tasks
The general transformation of the product of coherent states
to the output state (
or ), which is realizable with linear optical circuit, is
characterized with a linear map from the vector
to
. A correspondence between the
transformations of a product of coherent states and those of a single photon
state is established with such linear maps. It is convenient to apply this
linear transformation method to design any linear optical scheme working with
coherent states. The examples include message encoding and quantum database
searching. The limitation of manipulating entangled coherent states with linear
optics is also discussed.Comment: 6 pages, 2 figure
Quadratic squeezing: An overview
The amplitude of the electric field of a mode of the electromagnetic field is not a fixed quantity: there are always quantum mechanical fluctuations. The amplitude, having both a magnitude and a phase, is a complex number and is described by the mode annihilation operator a. It is also possible to characterize the amplitude by its real and imaginary parts which correspond to the Hermitian and anti-Hermitian parts of a, X sub 1 = 1/2(a(sup +) + a) and X sub 2 = i/2(a(sup +) - a), respectively. These operators do not commute and, as a result, obey the uncertainty relation (h = 1) delta X sub 1(delta X sub 2) greater than or = 1/4. From this relation we see that the amplitude fluctuates within an 'error box' in the complex plane whose area is at least 1/4. Coherent states, among them the vacuum state, are minimum uncertainty states with delta X sub 1 = delta X sub 2 = 1/2. A squeezed state, squeezed in the X sub 1 direction, has the property that delta X sub 1 is less than 1/2. A squeezed state need not be a minimum uncertainty state, but those that are can be obtained by applying the squeeze operator
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
Optimal unambiguous discrimination of two subspaces as a case in mixed state discrimination
We show how to optimally unambiguously discriminate between two subspaces of
a Hilbert space. In particular we suppose that we are given a quantum system in
either the state \psi_{1}, where \psi_{1} can be any state in the subspace
S_{1}, or \psi_{2}, where \psi_{2} can be any state in the subspace S_{2}, and
our task is to determine in which of the subspaces the state of our quantum
system lies. We do not want to make a mistake, which means that our procedure
will sometimes fail if the subspaces are not orthogonal. This is a special case
of the unambiguous discrimination of mixed states. We present the POVM that
solves this problem and several applications of this procedure, including the
discrimination of multipartite states without classical communication.Comment: 8 pages, replaced with published versio
Optimum unambiguous discrimination of two mixed states and application to a class of similar states
We study the measurement for the unambiguous discrimination of two mixed
quantum states that are described by density operators and of
rank d, the supports of which jointly span a 2d-dimensional Hilbert space.
Based on two conditions for the optimum measurement operators, and on a
canonical representation for the density operators of the states, two equations
are derived that allow the explicit construction of the optimum measurement,
provided that the expression for the fidelity of the states has a specific
simple form. For this case the problem is mathematically equivalent to
distinguishing pairs of pure states, even when the density operators are not
diagonal in the canonical representation. The equations are applied to the
optimum unambiguous discrimination of two mixed states that are similar states,
given by , and that belong to the class where the
unitary operator U can be decomposed into multiple rotations in the d mutually
orthogonal two-dimensional subspaces determined by the canonical
representation.Comment: 8 pages, changes in title and presentatio
Programmable quantum state discriminators with simple programs
We describe a class of programmable devices that can discriminate between two
quantum states. We consider two cases. In the first, both states are unknown.
One copy of each of the unknown states is provided as input, or program, for
the two program registers, and the data state, which is guaranteed to be
prepared in one of the program states, is fed into the data register of the
device. This device will then tell us, in an optimal way, which of the
templates stored in the program registers the data state matches. In the second
case, we know one of the states while the other is unknown. One copy of the
unknown state is fed into the single program register, and the data state which
is guaranteed to be prepared in either the program state or the known state, is
fed into the data register. The device will then tell us, again optimally,
whether the data state matches the template or is the known state. We determine
two types of optimal devices. The first performs discrimination with minimum
error, the second performs optimal unambiguous discrimination. In all cases we
first treat the simpler problem of only one copy of the data state and then
generalize the treatment to n copies. In comparison to other works we find that
providing n > 1 copies of the data state yields higher success probabilities
than providing n > 1 copies of the program states.Comment: 17 pages, 5 figure
Optimal minimum-cost quantum measurements for imperfect detection
Knowledge of optimal quantum measurements is important for a wide range of
situations, including quantum communication and quantum metrology. Quantum
measurements are usually optimised with an ideal experimental realisation in
mind. Real devices and detectors are, however, imperfect. This has to be taken
into account when optimising quantum measurements. In this paper, we derive the
optimal minimum-cost and minimum-error measurements for a general model of
imperfect detection.Comment: 5 page
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