2,132 research outputs found
On Classical Teleportation and Classical Nonlocality
An interesting protocol for classical teleportation of an unknown classical
state was recently suggested by Cohen, and by Gour and Meyer. In that protocol,
Bob can sample from a probability distribution P that is given to Alice, even
if Alice has absolutely no knowledge about P. Pursuing a similar line of
thought, we suggest here a limited form of nonlocality - "classical
nonlocality". Our nonlocality is the (somewhat limited) classical analogue of
the Hughston-Jozsa-Wootters (HJW) quantum nonlocality. The HJW nonlocality
tells us how, for a given density matrix rho, Alice can generate any
rho-ensemble on the North Star. This is done using surprisingly few resources -
one shared entangled state (prepared in advance), one generalized quantum
measurement, and no communication. Similarly, our classical nonlocality
presents how, for a given probability distribution P, Alice can generate any
P-ensemble on the North Star, using only one correlated state (prepared in
advance), one (generalized) classical measurement, and no communication.
It is important to clarify that while the classical teleportation and the
classical non-locality protocols are probably rather insignificant from a
classical information processing point of view, they significantly contribute
to our understanding of what exactly is quantum in their well established and
highly famous quantum analogues.Comment: 8 pages, Version 2 is using the term "quantum remote steering" to
describe HJW idea, and "classical remote steering" is the main new result of
this current paper. Version 2 also has an additional citation (to Gisin's 89
paper
Implications of Teleportation for Nonlocality
Adopting an approach similar to that of Zukowski [Phys. Rev. A 62, 032101
(2000)], we investigate connections between teleportation and nonlocality. We
derive a Bell-type inequality pertaining to the teleportation scenario and show
that it is violated in the case of teleportation using a perfect singlet. We
also investigate teleportation using `Werner states' of the form x P + (1-x)
I/4, where P is the projector corresponding to a singlet state and I is the
identity. We find that our inequality is violated, implying nonlocality, if x >
1/sqrt(2). In addition, we extend Werner's local hidden variable model to
simulation of teleportation with the x = 1/2 Werner state. Thus teleportation
using this state does not involve nonlocality even though the fidelity achieved
is 3/4 which is greater than the `classical limit' of 2/3. Finally, we comment
on a result of Gisin's and offer some philosophical remarks on teleportation
and nonlocality generally.Comment: 10 pages, no figures. Title changed to accord with Phys. Rev. A
version. A note and an extra reference have been added. Journal reference
adde
Classical wave-optics analogy of quantum information processing
An analogous model system for quantum information processing is discussed,
based on classical wave optics. The model system is applied to three examples
that involve three qubits: ({\em i}) three-particle Greenberger-Horne-Zeilinger
entanglement, ({\em ii}) quantum teleportation, and ({\em iii}) a simple
quantum error correction network. It is found that the model system can
successfully simulate most features of entanglement, but fails to simulate
quantum nonlocality. Investigations of how far the classical simulation can be
pushed show that {\em quantum nonlocality} is the essential ingredient of a
quantum computer, even more so than entanglement. The well known problem of
exponential resources required for a classical simulation of a quantum
computer, is also linked to the nonlocal nature of entanglement, rather than to
the nonfactorizability of the state vector.Comment: 9 pages, 6 figure
Relations between entanglement, Bell-inequality violation and teleportation fidelity for the two-qubit X states
Based on the assumption that the receiver Bob can apply any unitary
transformation, Horodecki {\it et al.} [Phys. Lett. A {\bf 222}, 21 (1996)]
proved that any mixed two spin-1/2 state which violates the Bell-CHSH
inequality is useful for teleportation. Here, we further show that any X state
which violates the Bell-CHSH inequality can also be used for nonclassical
teleportation even if Bob can only perform the identity or the Pauli rotation
operations. Moreover, we showed that the maximal difference between the two
average fidelities achievable via Bob's arbitrary transformations and via the
sole identity or the Pauli rotation is 1/9.Comment: 5 pages, to be published in "Quantum Information Processing
On the Nonlocality of the Quantum Channel in the Standard Teleportation Protocol
By exhibiting a violation of a novel form of the Bell-CHSH inequality,
Zukowski has recently established that the quantum correlations exploited in
the standard perfect teleportation protocol cannot be recovered by any local
hidden variables model. Allowing the quantum channel state in the protocol to
be given by any density operator of two spin-1/2 particles, we show that a
violation of a generalized form of Zukowski's teleportation inequality can only
occur if the channel state, considered by itself, violates a Bell-CHSH
inequality. On the other hand, although it is sufficient for a teleportation
process to have a nonclassical fidelity-defined as a fidelity exceeding
2/3-that the channel state employed violate a Bell-CHSH inequality, we show
that such a violation does not imply a violation of Zukowski's teleportation
inequality or any of its generalizations. The implication does hold, however,
if the fidelity of the teleportation exceeds ,
suggesting the existence of a regime of nonclassical values of the fidelity,
less than .90, for which the standard teleportation protocol can be modelled by
local hidden variables.Comment: 9 pages, no figures, submitted to PR
Teleportation capability, distillability, and nonlocality on three-qubit states
In this paper, we consider teleportation capability, distillability, and
nonlocality on three-qubit states. In order to investigate some relations among
them, we first find the explicit formulas of the quantities about the maximal
teleportation fidelity on three-qubit states. We show that if any three-qubit
state is useful for three-qubit teleportation then the three-qubit state is
distillable into a Greenberger-Horne-Zeilinger state, and that if any
three-qubit state violates a specific form of Mermin inequality then the
three-qubit state is useful for three-qubit teleportation.Comment: 5 pages, 2 figures; The old version has been generalized into the
results on general 3-qubit state
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