45 research outputs found
Generic local distinguishability and completely entangled subspaces
A subspace of a multipartite Hilbert space is completely entangled if it
contains no product states. Such subspaces can be large with a known maximum
size, S, approaching the full dimension of the system, D. We show that almost
all subspaces with dimension less than or equal to S are completely entangled,
and then use this fact to prove that n random pure quantum states are
unambiguously locally distinguishable if and only if n does not exceed D-S.
This condition holds for almost all sets of states of all multipartite systems,
and reveals something surprising. The criterion is identical for separable and
for nonseparable states: entanglement makes no difference.Comment: 12 page
Distinguishing two-qubit states using local measurements and restricted classical communication
The problem of unambiguous state discrimination consists of determining which
of a set of known quantum states a particular system is in. One is allowed to
fail, but not to make a mistake. The optimal procedure is the one with the
lowest failure probability. This procedure has been extended to bipartite
states where the two parties, Alice and Bob, are allowed to manipulate their
particles locally and communicate classically in order to determine which of
two possible two-particle states they have been given. The failure probability
of this local procedure has been shown to be the same as if the particles were
together in the same location. Here we examine the effect of restricting the
classical communication between the parties, either allowing none or
eliminating the possibility that one party's measurement depends on the result
of the other party's. These issues are studied for two-qubit states, and
optimal procedures are found. In some cases the restrictions cause increases in
the failure probability, but in other cases they do not. Applications of these
procedures, in particular to secret sharing, are discussed.Comment: 18 pages, two figure
A framework for bounding nonlocality of state discrimination
We consider the class of protocols that can be implemented by local quantum
operations and classical communication (LOCC) between two parties. In
particular, we focus on the task of discriminating a known set of quantum
states by LOCC. Building on the work in the paper "Quantum nonlocality without
entanglement" [BDF+99], we provide a framework for bounding the amount of
nonlocality in a given set of bipartite quantum states in terms of a lower
bound on the probability of error in any LOCC discrimination protocol. We apply
our framework to an orthonormal product basis known as the domino states and
obtain an alternative and simplified proof that quantifies its nonlocality. We
generalize this result for similar bases in larger dimensions, as well as the
"rotated" domino states, resolving a long-standing open question [BDF+99].Comment: 33 pages, 7 figures, 1 tabl
Hiding bits in Bell states
We present a scheme for hiding bits in Bell states that is secure even when
the sharers Alice and Bob are allowed to carry out local quantum operations and
classical communication. We prove that the information that Alice and Bob can
gain about a hidden bit is exponentially small in , the number of qubits in
each share, and can be made arbitrarily small for hiding multiple bits. We
indicate an alternative efficient low-entanglement method for preparing the
shared quantum states. We discuss how our scheme can be implemented using
present-day quantum optics.Comment: 4 pages RevTex, 1 figure, various small changes and additional
paragraph on optics implementatio
Experimentally obtaining the Likeness of Two Unknown Quantum States on an NMR Quantum Information Processor
Recently quantum states discrimination has been frequently studied. In this
paper we study them from the other way round, the likeness of two quantum
states. The fidelity is used to describe the likeness of two quantum states.
Then we presented a scheme to obtain the fidelity of two unknown qubits
directly from the integral area of the spectra of the assistant qubit(spin) on
an NMR Quantum Information Processor. Finally we demonstrated the scheme on a
three-qubit quantum information processor. The experimental data are consistent
with the theoretical expectation with an average error of 0.05, which confirms
the scheme.Comment: 3 pages, 4 figure
Greenberger-Horne-Zeilinger-like proof of Bell's theorem involving observers who do not share a reference frame
Vaidman described how a team of three players, each of them isolated in a
remote booth, could use a three-qubit Greenberger-Horne-Zeilinger state to
always win a game which would be impossible to always win without quantum
resources. However, Vaidman's method requires all three players to share a
common reference frame; it does not work if the adversary is allowed to
disorientate one player. Here we show how to always win the game, even if the
players do not share any reference frame. The introduced method uses a 12-qubit
state which is invariant under any transformation
(where , where is a
unitary operation on a single qubit) and requires only single-qubit
measurements. A number of further applications of this 12-qubit state are
described.Comment: REVTeX4, 6 pages, 1 figur
Random repeated quantum interactions and random invariant states
We consider a generalized model of repeated quantum interactions, where a
system is interacting in a random way with a sequence of
independent quantum systems . Two types of randomness
are studied in detail. One is provided by considering Haar-distributed
unitaries to describe each interaction between and
. The other involves random quantum states describing each copy
. In the limit of a large number of interactions, we present
convergence results for the asymptotic state of . This is achieved
by studying spectral properties of (random) quantum channels which guarantee
the existence of unique invariant states. Finally this allows to introduce a
new physically motivated ensemble of random density matrices called the
\emph{asymptotic induced ensemble}
On local indistinguishability of orthogonal pure states by using a bound on distillable entanglement
We show that the four states a|00>+b|11>, b^*|00>-a^*|11>, c|01>+d|10> and
d^*|01>-c^*|10> cannot be discriminated with certainty if only local operations
and classical communication (LOCC) are allowed and if only a single copy is
provided, except in the case when they are simply |00>, |11>, |01> and |10> (in
which case they are trivially distinguishable with LOCC). We go on to show that
there exists a continuous range of values of a, b, c and d such that even three
states among the above four are not locally distinguishable, if only a single
copy is provided. The proof follows from the fact that logarithmic negativity
is an upper bound of distillable entanglement.Comment: 6 pages latex, no figure