537 research outputs found
Three maximally entangled states can require two-way LOCC for local discrimination
We show that there exist sets of three mutually orthogonal -dimensional
maximally entangled states which cannot be perfectly distinguished using
one-way local operations and classical communication (LOCC) for arbitrarily
large values of . This contrasts with several well-known families of
maximally entangled states, for which any three states can be perfectly
distinguished. We then show that two-way LOCC is sufficient to distinguish
these examples. We also show that any three mutually orthogonal -dimensional
maximally entangled states can be perfectly distinguished using measurements
with a positive partial transpose (PPT) and can be distinguished with one-way
LOCC with high probability. These results circle around the question of whether
there exist three maximally entangled states which cannot be distinguished
using the full power of LOCC; we discuss possible approaches to answer this
question.Comment: 23 pages, 1 figure, 1 table. (Published version
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
Multiplicativity properties of entrywise positive maps
Multiplicativity of certain maximal p -> q norms of a tensor product of
linear maps on matrix algebras is proved in situations in which the condition
of complete positivity (CP) is either augmented by, or replaced by, the
requirement that the entries of a matrix representative of the map are
non-negative (EP). In particular, for integer t, multiplicativity holds for the
maximal 2 -> 2t norm of a product of two maps, whenever one of the pair is EP;
for the maximal 1 -> t norm for pairs of CP maps when one of them is also EP;
and for the maximal 1 -> 2t norm for the product of an EP and a 2-positive map.
Similar results are shown in the infinite-dimensional setting of convolution
operators on L^2(R), with the pointwise positivity of an integral kernel
replacing entrywise positivity of a matrix. These results apply in particular
to Gaussian bosonic channels.Comment: results extended to some infinite dimensional cases, including the
Gaussian bosonic channe
Testing for a pure state with local operations and classical communication
We examine the problem of using local operations and classical communication
(LOCC) to distinguish a known pure state from an unknown (possibly mixed)
state, bounding the error probability from above and below. We study the
asymptotic rate of detecting multiple copies of the pure state and show that,
if the overlap of the two states is great enough, then they can be
distinguished asymptotically as well with LOCC as with global measurements;
otherwise, the maximal Schmidt coefficient of the pure state is sufficient to
determine the asymptotic error rate.Comment: 11 pages, 2 figures. Published version with small revisions and
expanded title
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
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