767 research outputs found
All quantum states useful for teleportation are nonlocal resources
Understanding the relation between the different forms of inseparability in
quantum mechanics is a longstanding problem in the foundations of quantum
theory and has implications for quantum information processing. Here we make
progress in this direction by establishing a direct link between quantum
teleportation and Bell nonlocality. In particular, we show that all entangled
states which are useful for teleportation are nonlocal resources, i.e. lead to
deterministic violation of Bell's inequality. Our result exploits the
phenomenon of super-activation of quantum nonlocality, recently proved by
Palazuelos, and suggests that the latter might in fact be generic.Comment: 4 pages. v2: Title and abstract changed, presentation improved,
references updated, same result
Quantum incompatibility in collective measurements
We study the compatibility (or joint measurability) of quantum observables in
a setting where the experimenter has access to multiple copies of a given
quantum system, rather than performing the experiments on each individual copy
separately. We introduce the index of incompatibility as a quantifier of
incompatibility in this multi-copy setting, as well as the notion of
compatibility stack representing the various compatibility relations present in
a given set of observables. We then prove a general structure theorem for
multi-copy joint observables, and use it to prove that all abstract
compatibility stacks with three vertices have realizations in terms of quantum
observables.Comment: 22 pages, 13 figure
Efficient Quantum Tensor Product Expanders and k-designs
Quantum expanders are a quantum analogue of expanders, and k-tensor product
expanders are a generalisation to graphs that randomise k correlated walkers.
Here we give an efficient construction of constant-degree, constant-gap quantum
k-tensor product expanders. The key ingredients are an efficient classical
tensor product expander and the quantum Fourier transform. Our construction
works whenever k=O(n/log n), where n is the number of qubits. An immediate
corollary of this result is an efficient construction of an approximate unitary
k-design, which is a quantum analogue of an approximate k-wise independent
function, on n qubits for any k=O(n/log n). Previously, no efficient
constructions were known for k>2, while state designs, of which unitary designs
are a generalisation, were constructed efficiently in [Ambainis, Emerson 2007].Comment: 16 pages, typo in references fixe
Concurrence in arbitrary dimensions
We argue that a complete characterisation of quantum correlations in
bipartite systems of many dimensions may require a quantity which, even for
pure states, does not reduce to a single number. Subsequently, we introduce
multi-dimensional generalizations of concurrence and find evidence that they
may provide useful tools for the analysis of quantum correlations in mixed
bipartite states. We also introudce {\it biconcurrence} that leads to a
necessary and sufficient condition for separability.Comment: RevTeX 7 page
A Tractable Extension of Linear Indexed Grammars
It has been shown that Linear Indexed Grammars can be processed in polynomial
time by exploiting constraints which make possible the extensive use of
structure-sharing. This paper describes a formalism that is more powerful than
Linear Indexed Grammar, but which can also be processed in polynomial time
using similar techniques. The formalism, which we refer to as Partially Linear
PATR manipulates feature structures rather than stacks.Comment: 8 pages LaTeX, uses eaclap.sty, to appear in EACL-9
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