4,661 research outputs found
Single-shot discrimination of quantum unitary processes
We formulate minimum-error and unambiguous discrimination problems for
quantum processes in the language of process positive operator valued measures
(PPOVM). In this framework we present the known solution for minimum-error
discrimination of unitary channels. We derive a "fidelity-like" lower bound on
the failure probability of the unambiguous discrimination of arbitrary quantum
processes. This bound is saturated (in a certain range of apriori
probabilities) in the case of unambiguous discrimination of unitary channels.
Surprisingly, the optimal solution for both tasks is based on the optimization
of the same quantity called completely bounded process fidelity.Comment: 11 pages, 1 figur
Single-shot discrimination of quantum unitary processes
We formulate minimum-error and unambiguous discrimination problems for
quantum processes in the language of process positive operator valued measures
(PPOVM). In this framework we present the known solution for minimum-error
discrimination of unitary channels. We derive a "fidelity-like" lower bound on
the failure probability of the unambiguous discrimination of arbitrary quantum
processes. This bound is saturated (in a certain range of apriori
probabilities) in the case of unambiguous discrimination of unitary channels.
Surprisingly, the optimal solution for both tasks is based on the optimization
of the same quantity called completely bounded process fidelity.Comment: 11 pages, 1 figur
Atemporal diagrams for quantum circuits
A system of diagrams is introduced that allows the representation of various
elements of a quantum circuit, including measurements, in a form which makes no
reference to time (hence ``atemporal''). It can be used to relate quantum
dynamical properties to those of entangled states (map-state duality), and
suggests useful analogies, such as the inverse of an entangled ket. Diagrams
clarify the role of channel kets, transition operators, dynamical operators
(matrices), and Kraus rank for noisy quantum channels. Positive (semidefinite)
operators are represented by diagrams with a symmetry that aids in
understanding their connection with completely positive maps. The diagrams are
used to analyze standard teleportation and dense coding, and for a careful
study of unambiguous (conclusive) teleportation. A simple diagrammatic argument
shows that a Kraus rank of 3 is impossible for a one-qubit channel modeled
using a one-qubit environment in a mixed state.Comment: Minor changes in references. Latex 32 pages, 13 figures in text using
PSTrick
Unambiguous quantum state filtering
In this paper, we consider the generalized measurement where one particular
quantum signal is unambiguously extracted from a set of non-commutative quantum
signals and the other signals are filtered out. Simple expressions for the
maximum detection probability and its POVM are derived. We applyl such
unambiguous quantum state filtering to evaluation of the sensing of decoherence
channels. The bounds of the precision limit for a given quantum state of probes
and possible device implementations are discussed.Comment: 7 pages, 5 figure
Unambiguous discrimination among oracle operators
We address the problem of unambiguous discrimination among oracle operators.
The general theory of unambiguous discrimination among unitary operators is
extended with this application in mind. We prove that entanglement with an
ancilla cannot assist any discrimination strategy for commuting unitary
operators. We also obtain a simple, practical test for the unambiguous
distinguishability of an arbitrary set of unitary operators on a given system.
Using this result, we prove that the unambiguous distinguishability criterion
is the same for both standard and minimal oracle operators. We then show that,
except in certain trivial cases, unambiguous discrimination among all standard
oracle operators corresponding to integer functions with fixed domain and range
is impossible. However, we find that it is possible to unambiguously
discriminate among the Grover oracle operators corresponding to an arbitrarily
large unsorted database. The unambiguous distinguishability of standard oracle
operators corresponding to totally indistinguishable functions, which possess a
strong form of classical indistinguishability, is analysed. We prove that these
operators are not unambiguously distinguishable for any finite set of totally
indistinguishable functions on a Boolean domain and with arbitrary fixed range.
Sets of such functions on a larger domain can have unambiguously
distinguishable standard oracle operators and we provide a complete analysis of
the simplest case, that of four functions. We also examine the possibility of
unambiguous oracle operator discrimination with multiple parallel calls and
investigate an intriguing unitary superoperator transformation between standard
and entanglement-assisted minimal oracle operators.Comment: 35 pages. Final version. To appear in J. Phys. A: Math. & Theo
Probing the quantumness of channels with mixed states
We present an alternative approach to the derivation of benchmarks for
quantum channels, such as memory or teleportation channels. Using the concept
of effective entanglement and the verification thereof, a testing procedure is
derived which demands very few experimental resources. The procedure is
generalized by allowing for mixed test states. By constructing optimized
measure & re-prepare channels, the benchmarks are found to be very tight in the
considered experimental regimes.Comment: 11 Pages, 9 Figures, published versio
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