30 research outputs found
Jamming non-local quantum correlations
We present a possible scheme to tamper with non-local quantum correlations in
a way that is consistent with relativistic causality, but goes beyond quantum
mechanics. A non-local ``jamming" mechanism, operating within a certain
space-time window, would not violate relativistic causality and would not lead
to contradictory causal loops. The results presented in this Letter do not
depend on any model of how quantum correlations arise and apply to any jamming
mechanism.Comment: 10 pp, LaTe
Entropy in general physical theories
Information plays an important role in our understanding of the physical
world. We hence propose an entropic measure of information for any physical
theory that admits systems, states and measurements. In the quantum and
classical world, our measure reduces to the von Neumann and Shannon entropy
respectively. It can even be used in a quantum or classical setting where we
are only allowed to perform a limited set of operations. In a world that admits
superstrong correlations in the form of non-local boxes, our measure can be
used to analyze protocols such as superstrong random access encodings and the
violation of `information causality'. However, we also show that in such a
world no entropic measure can exhibit all properties we commonly accept in a
quantum setting. For example, there exists no`reasonable' measure of
conditional entropy that is subadditive. Finally, we prove a coding theorem for
some theories that is analogous to the quantum and classical setting, providing
us with an appealing operational interpretation.Comment: 20 pages, revtex, 7 figures, v2: Coding theorem revised, published
versio
A Bell Inequality Analog in Quantum Measure Theory
One obtains Bell's inequalities if one posits a hypothetical joint
probability distribution, or {\it measure}, whose marginals yield the
probabilities produced by the spin measurements in question. The existence of a
joint measure is in turn equivalent to a certain causality condition known as
``screening off''. We show that if one assumes, more generally, a joint {\it
quantal measure}, or ``decoherence functional'', one obtains instead an
analogous inequality weaker by a factor of . The proof of this
``Tsirel'son inequality'' is geometrical and rests on the possibility of
associating a Hilbert space to any strongly positive quantal measure. These
results lead both to a {\it question}: ``Does a joint measure follow from some
quantal analog of `screening off'?'', and to the {\it observation} that
non-contextual hidden variables are viable in histories-based quantum
mechanics, even if they are excluded classically.Comment: 38 pages, TeX. Several changes and added comments to bring out the
meaning more clearly. Minor rewording and extra acknowledgements, now closer
to published versio
A derivation of quantum theory from physical requirements
Quantum theory is usually formulated in terms of abstract mathematical
postulates, involving Hilbert spaces, state vectors, and unitary operators. In
this work, we show that the full formalism of quantum theory can instead be
derived from five simple physical requirements, based on elementary assumptions
about preparation, transformations and measurements. This is more similar to
the usual formulation of special relativity, where two simple physical
requirements -- the principles of relativity and light speed invariance -- are
used to derive the mathematical structure of Minkowski space-time. Our
derivation provides insights into the physical origin of the structure of
quantum state spaces (including a group-theoretic explanation of the Bloch ball
and its three-dimensionality), and it suggests several natural possibilities to
construct consistent modifications of quantum theory.Comment: 16 pages, 2 figures. V3: added alternative formulation of Requirement
5, extended abstract, some minor modification
The states of W-class as shared resources for perfect teleportation and superdense coding
As we know, the states of triqubit systems have two important classes:
GHZ-class and W-class.
In this paper, the states of W-class are considered for teleportation and
superdense coding, and are generalized to multi-particle systems. First we
describe two transformations of the shared resources for teleportation and
superdense coding, which allow many new protocols from some known ones for
that. As an application of these transformations, we obtain a sufficient and
necessary condition for a state of W-class being suitable for perfect
teleportation and superdense coding. As another application, we find that state
can be used to
transmit three classical bits by sending two qubits, which was considered to be
impossible by P. Agrawal and A. Pati [Phys. Rev. A to be published]. We
generalize the states of W-class to multi-qubit systems and multi-particle
systems with higher dimension. We propose two protocols for teleportation and
superdense coding by using W-states of multi-qubit systems that generalize the
protocols by using proposed by P. Agrawal and A. Pati. We obtain an
optimal way to partition some W-states of multi-qubit systems into two
subsystems, such that the entanglement between them achieves maximum value.Comment: 10 pages, critical comments and suggestions are welcom