162 research outputs found
LOCC distinguishability of unilaterally transformable quantum states
We consider the question of perfect local distinguishability of mutually
orthogonal bipartite quantum states, with the property that every state can be
specified by a unitary operator acting on the local Hilbert space of Bob. We
show that if the states can be exactly discriminated by one-way LOCC where
Alice goes first, then the unitary operators can also be perfectly
distinguished by an orthogonal measurement on Bob's Hilbert space. We give
examples of sets of N<=d maximally entangled states in for
d=4,5,6 that are not perfectly distinguishable by one-way LOCC. Interestingly
for d=5,6 our examples consist of four and five states respectively. We
conjecture that these states cannot be perfectly discriminated by two-way LOCC.Comment: Revised version, new proofs added; to appear in New Journal of
Physic
Twist-teleportation based local discrimination of maximally entangled states
In this work, we study the local distinguishability of maximally entangled
states (MESs). In particular, we are concerned with whether any fixed number of
MESs can be locally distinguishable for sufficiently large dimensions. Fan and
Tian \emph{et al.} have already obtained two satisfactory results for the
generalized Bell states (GBSs) and the qudit lattice states when applied to
prime or prime power dimensions. We construct a general twist-teleportation
scheme for any orthonormal basis with MESs that is inspired by the method used
in [Phys. Rev. A \textbf{70}, 022304 (2004)]. Using this teleportation scheme,
we obtain a sufficient and necessary condition for one-way distinguishable sets
of MESs, which include the GBSs and the qudit lattice states as special cases.
Moreover, we present a generalized version of the results in [Phys. Rev. A
\textbf{92}, 042320 (2015)] for the arbitrary dimensional case.Comment: 7 pages, 2 figure
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
Relativistic quantum coin tossing
A relativistic quantum information exchange protocol is proposed allowing two
distant users to realize ``coin tossing'' procedure. The protocol is based on
the point that in relativistic quantum theory reliable distinguishing between
the two orthogonal states generally requires a finite time depending on the
structure of these states.Comment: 6 pages, no figure
Distinguishability-based genuine nonlocality with genuine multipartite entanglement
A set of orthogonal multipartite quantum states is said to be
distinguishability-based genuinely nonlocal (also genuinely nonlocal, for
abbreviation) if the states are locally indistinguishable across any
bipartition of the subsystems. This form of multipartite nonlocality, although
more naturally arising than the recently popular "strong nonlocality" in the
context of local distinguishability, receives much less attention. In this
work, we study the distinguishability-based genuine nonlocality of a special
type of genuinely multipartite entangled states -- the
Greenberger-Horne-Zeilinger (GHZ)-like states. We first show that any 5 states
of the three-qubit GHZ basis are genuinely nonlocal, while any 4 states of them
are not. Then for more general tripartite systems, we present a universal bound
about the cardinality for an arbitrary set of GHZ-like states to be genuinely
nonlocal. Although not necessary, entanglement is believed to raise difficulty
in state discrimination in many situations. In the literature, there has been
lots of studies in favor of this perspective, including the efforts seeking for
small nonlocal sets consisting of maximally entangled states in bipartite
systems. Here in the tripartite case, where GHZ-like states are studied, we
also find the existence of some small genuinely nonlocal sets: we show that the
cardinality can scale down to linear in the local dimension d. This result not
only substantiates the aforemention perspective in multipartite scenario, but
also suggests that there might exist substantial difference between strong
nonlocality and the normal distinguishability-based multipartite nonlocality.Comment: 13 pages, 1 figure, submitted to "New journal of physics" in Sep,
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