695 research outputs found
Quantum Error Correction and One-Way LOCC State Distinguishability
We explore the intersection of studies in quantum error correction and
quantum local operations and classical communication (LOCC). We consider
one-way LOCC measurement protocols as quantum channels and investigate their
error correction properties, emphasizing an operator theory approach to the
subject, and we obtain new applications to one-way LOCC state
distinguishability as well as new derivations of some established results. We
also derive conditions on when states that arise through the stabilizer
formalism for quantum error correction are distinguishable under one-way LOCC.Comment: 20 page
Distinguishing Bipartitite Orthogonal States using LOCC: Best and Worst Cases
Two types of results are presented for distinguishing pure bipartite quantum
states using Local Operations and Classical Communications. We examine sets of
states that can be perfectly distinguished, in particular showing that any
three orthogonal maximally entangled states in C^3 tensor C^3 form such a set.
In cases where orthogonal states cannot be distinguished, we obtain upper
bounds for the probability of error using LOCC taken over all sets of k
orthogonal states in C^n tensor C^m. In the process of proving these bounds, we
identify some sets of orthogonal states for which perfect distinguishability is
not possible.Comment: 22 pages, published version. Some proofs rewritten for clarit
Tight bounds on the distinguishability of quantum states under separable measurements
One of the many interesting features of quantum nonlocality is that the
states of a multipartite quantum system cannot always be distinguished as well
by local measurements as they can when all quantum measurements are allowed. In
this work, we characterize the distinguishability of sets of multipartite
quantum states when restricted to separable measurements -- those which contain
the class of local measurements but nevertheless are free of entanglement
between the component systems. We consider two quantities: The separable
fidelity -- a truly quantum quantity -- which measures how well we can "clone"
the input state, and the classical probability of success, which simply gives
the optimal probability of identifying the state correctly.
We obtain lower and upper bounds on the separable fidelity and give several
examples in the bipartite and multipartite settings where these bounds are
optimal. Moreover the optimal values in these cases can be attained by local
measurements. We further show that for distinguishing orthogonal states under
separable measurements, a strategy that maximizes the probability of success is
also optimal for separable fidelity. We point out that the equality of fidelity
and success probability does not depend on an using optimal strategy, only on
the orthogonality of the states. To illustrate this, we present an example
where two sets (one consisting of orthogonal states, and the other
non-orthogonal states) are shown to have the same separable fidelity even
though the success probabilities are different.Comment: 19 pages; published versio
Optimal estimation of one parameter quantum channels
We explore the task of optimal quantum channel identification, and in
particular the estimation of a general one parameter quantum process. We derive
new characterizations of optimality and apply the results to several examples
including the qubit depolarizing channel and the harmonic oscillator damping
channel. We also discuss the geometry of the problem and illustrate the
usefulness of using entanglement in process estimation.Comment: 23 pages, 4 figures. Published versio
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