495 research outputs found
On the generalization of quantum state comparison
We investigate the unambiguous comparison of quantum states in a scenario
that is more general than the one that was originally suggested by Barnett et
al. First, we find the optimal solution for the comparison of two states taken
from a set of two pure states with arbitrary a priori probabilities. We show
that the optimal coherent measurement is always superior to the optimal
incoherent measurement. Second, we develop a strategy for the comparison of two
states from a set of N pure states, and find an optimal solution for some
parameter range when N=3. In both cases we use the reduction method for the
corresponding problem of mixed state discrimination, as introduced by Raynal et
al., which reduces the problem to the discrimination of two pure states only
for N=2. Finally, we provide a necessary and sufficient condition for
unambiguous comparison of mixed states to be possible.Comment: 8 pages, 4 figures, Proposition 1 corrected, appendix adde
Purifying and Reversible Physical Processes
Starting from the observation that reversible processes cannot increase the
purity of any input state, we study deterministic physical processes, which map
a set of states to a set of pure states. Such a process must map any state to
the same pure output, if purity is demanded for the input set of all states.
But otherwise, when the input set is restricted, it is possible to find
non-trivial purifying processes. For the most restricted case of only two input
states, we completely characterize the output of any such map. We furthermore
consider maps, which combine the property of purity and reversibility on a set
of states, and we derive necessary and sufficient conditions on sets, which
permit such processes.Comment: 5 pages, no figures, v2: only minimal change
Physical Purification of Quantum States
We introduce the concept of a physical process that purifies a mixed quantum
state, taken from a set of states, and investigate the conditions under which
such a purification map exists. Here, a purification of a mixed quantum state
is a pure state in a higher-dimensional Hilbert space, the reduced density
matrix of which is identical to the original state. We characterize all sets of
mixed quantum states, for which perfect purification is possible. Surprisingly,
some sets of two non-commuting states are among them. Furthermore, we
investigate the possibility of performing an imperfect purification.Comment: 5 pages, 1 figure; published versio
Finite key analysis for symmetric attacks in quantum key distribution
We introduce a constructive method to calculate the achievable secret key
rate for a generic class of quantum key distribution protocols, when only a
finite number n of signals is given. Our approach is applicable to all
scenarios in which the quantum state shared by Alice and Bob is known. In
particular, we consider the six state protocol with symmetric eavesdropping
attacks, and show that for a small number of signals, i.e. below the order of
10^4, the finite key rate differs significantly from the asymptotic value for n
approaching infinity. However, for larger n, a good approximation of the
asymptotic value is found. We also study secret key rates for protocols using
higher-dimensional quantum systems.Comment: 9 pages, 5 figure
Commutator Relations Reveal Solvable Structures in Unambiguous State Discrimination
We present a criterion, based on three commutator relations, that allows to
decide whether two self-adjoint matrices with non-overlapping support are
simultaneously unitarily similar to quasidiagonal matrices, i.e., whether they
can be simultaneously brought into a diagonal structure with 2x2-dimensional
blocks. Application of this criterion to unambiguous state discrimination
provides a systematic test whether the given problem is reducible to a solvable
structure. As an example, we discuss unambiguous state comparison.Comment: 5 pages, discussion of related work adde
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