56,998 research outputs found
Device-independent tests of classical and quantum dimensions
We address the problem of testing the dimensionality of classical and quantum
systems in a `black-box' scenario. We develop a general formalism for tackling
this problem. This allows us to derive lower bounds on the classical dimension
necessary to reproduce given measurement data. Furthermore, we generalise the
concept of quantum dimension witnesses to arbitrary quantum systems, allowing
one to place a lower bound on the Hilbert space dimension necessary to
reproduce certain data. Illustrating these ideas, we provide simple examples of
classical and quantum dimension witnesses.Comment: To appear in PR
Separability criteria and bounds for entanglement measures
Employing a recently proposed separability criterion we develop analytical
lower bounds for the concurrence and for the entanglement of formation of
bipartite quantum systems. The separability criterion is based on a
nondecomposable positive map which operates on state spaces with even dimension
N >= 4, and leads to a class of nondecomposable optimal entanglement witnesses.
It is shown that the bounds derived here complement and improve the existing
bounds obtained from the criterion of positive partial transposition and from
the realignment criterion.Comment: 8 pages, 2 figure
Certifying an irreducible 1024-dimensional photonic state using refined dimension witnesses
We report on a new class of dimension witnesses, based on quantum random
access codes, which are a function of the recorded statistics and that have
different bounds for all possible decompositions of a high-dimensional physical
system. Thus, it certifies the dimension of the system and has the new distinct
feature of identifying whether the high-dimensional system is decomposable in
terms of lower dimensional subsystems. To demonstrate the practicability of
this technique we used it to experimentally certify the generation of an
irreducible 1024-dimensional photonic quantum state. Therefore, certifying that
the state is not multipartite or encoded using non-coupled different degrees of
freedom of a single photon. Our protocol should find applications in a broad
class of modern quantum information experiments addressing the generation of
high-dimensional quantum systems, where quantum tomography may become
intractable.Comment: Journal version (except for small editorial modifications), 4+12
pages, 7 figure
Witnessing Irreducible Dimension
The Hilbert space dimension of a quantum system is the most basic quantifier of its information content. Lower bounds on the dimension can be certified in a device-independent way, based only on observed statistics. We highlight that some such “dimension witnesses” capture only the presence of systems of some dimension, which in a sense is trivial, not the capacity of performing information processing on them, which is the point of experimental efforts to control high-dimensional systems. In order to capture this aspect, we introduce the notion of irreducible dimension of a quantum behavior. This dimension can be certified, and we provide a witness for irreducible dimension four
Monogamy of nonlocal quantum correlations
We describe a new technique for obtaining Tsirelson bounds, or upper bounds
on the quantum value of a Bell inequality. Since quantum correlations do not
allow signaling, we obtain a Tsirelson bound by maximizing over all
no-signaling probability distributions. This maximization can be cast as a
linear program. In a setting where three parties, A, B, and C, share an
entangled quantum state of arbitrary dimension, we: (i) bound the trade-off
between AB's and AC's violation of the CHSH inequality, and (ii) demonstrate
that forcing B and C to be classically correlated prevents A and B from
violating certain Bell inequalities, relevant for interactive proof systems and
cryptography.Comment: This is the submitted version. The refereed version, which contains
an additional result about strong parallel repetition and corrects some
typos, is available on my personal web site at
http://bentoner.com/papers/monogamyrs.pdf [PDF
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