130 research outputs found
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
Quantum Machines
We discuss quantum information processing machines. We start with single
purpose machines that either redistribute quantum information or identify
quantum states. We then move on to machines that can perform a number of
functions, with the function they perform being determined by a program, which
is itself a quantum state. Examples of both deterministic and probabilistic
programmable machines are given, and we conclude with a discussion of the
utility of quantum programs.Comment: To appear in Contemporary Physic
Programmable discrimination with an error margin
The problem of optimally discriminating between two completely unknown qubit states is generalized by allowing an error margin. It is visualized as a device-the programmable discriminator-with one data and two program ports, each fed with a number of identically prepared qubits-the data and the programs. The device aims at correctly identifying the data state with one of the two program states. This scheme has the unambiguous and the minimum-error schemes as extremal cases, when the error margin is set to zero or it is sufficiently large, respectively. Analytical results are given in the two situations where the margin is imposed on the average error probability-weak condition-or it is imposed separately on the two probabilities of assigning the state of the data to the wrong program-strong condition. It is a general feature of our scheme that the success probability rises sharply as soon as a small error margin is allowed, thus providing a significant gain over the unambiguous scheme while still having high confidence results
Dealing with ignorance: universal discrimination, learning and quantum correlations
The problem of discriminating the state of a quantum system among a number of
hypothetical states is usually addressed under the assumption that one has
perfect knowledge of the possible states of the system. In this thesis, I
analyze the role of the prior information available in facing such problems,
and consider scenarios where the information regarding the possible states is
incomplete. In front of a complete ignorance of the possible states' identity,
I discuss a quantum "programmable" discrimination machine for qubit states that
accepts this information as input programs using a quantum encoding, rather
than as a classical description. The optimal performance of these machines is
studied for general qubit states when several copies are provided, in the
schemes of unambiguous, minimum-error, and error-margin discrimination. Then,
this type of automation in discrimination tasks is taken further. By realizing
a programmable machine as a device that is trained through quantum information
to perform a specific task, I propose a quantum "learning" machine for
classifying qubit states that does not require a quantum memory to store the
qubit programs and, nevertheless, performs as good as quantum mechanics
permits. Such learning machine thus allows for several optimal uses with no
need for retraining. A similar learning scheme is also discussed for coherent
states of light. I present it in the context of the readout of a classical
memory by means of classically correlated coherent signals, when these are
produced by an imperfect source. I show that, in this case, the retrieval of
information stored in the memory can be carried out more accurately when fully
general quantum measurements are used. Finally, as a transversal topic, I
propose an efficient algorithmic way of decomposing any quantum measurement
into convex combinations of simpler (extremal) measurements.Comment: Ph.D. Thesis, Universitat Aut\`onoma de Barcelona, 200 pages, 23
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Unambiguous coherent state identification: Searching a quantum database
We consider an unambiguous identification of an unknown coherent state with
one of two unknown coherent reference states. Specifically, we consider two
modes of an electromagnetic field prepared in unknown coherent states alpha_1
and alpha_2, respectively. The third mode is prepared either in the state
alpha_1 or in the state alpha_2. The task is to identify (unambiguously) which
of the two modes are in the same state. We present a scheme consisting of three
beamsplitters capable to perform this task. Although we don't prove the
optimality, we show that the performance of the proposed setup is better than
the generalization of the optimal measurement known for a finite-dimensional
case. We show that a single beamsplitter is capable to perform an unambiguous
quantum state comparison for coherent states optimally. Finally we propose an
experimental setup consisting of 2N-1 beamsplitters for unambiguous
identification among N unknown coherent states. This setup can be considered as
a search in a quantum database. The elements of the database are unknown
coherent states encoded in different modes of an electromagnetic field. The
task is to specify the two modes that are excited in the same, though unknown,
coherent state.Comment: version accepted for publication, 12 pages, 3 figure
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