733 research outputs found
Monogamy of Correlations vs. Monogamy of Entanglement
A fruitful way of studying physical theories is via the question whether the
possible physical states and different kinds of correlations in each theory can
be shared to different parties. Over the past few years it has become clear
that both quantum entanglement and non-locality (i.e., correlations that
violate Bell-type inequalities) have limited shareability properties and can
sometimes even be monogamous. We give a self-contained review of these results
as well as present new results on the shareability of different kinds of
correlations, including local, quantum and no-signalling correlations. This
includes an alternative simpler proof of the Toner-Verstraete monogamy
inequality for quantum correlations, as well as a strengthening thereof.
Further, the relationship between sharing non-local quantum correlations and
sharing mixed entangled states is investigated, and already for the simplest
case of bi-partite correlations and qubits this is shown to be non-trivial.
Also, a recently proposed new interpretation of Bell's theorem by Schumacher in
terms of shareability of correlations is critically assessed. Finally, the
relevance of monogamy of non-local correlations for secure quantum key
distribution is pointed out, although, and importantly, it is stressed that not
all non-local correlations are monogamous.Comment: 12 pages, 2 figures. Invited submission to a special issue of Quantum
Information Processing. v2: Published version. Open acces
General properties of Nonsignaling Theories
This article identifies a series of properties common to all theories that do
not allow for superluminal signaling and predict the violation of Bell
inequalities. Intrinsic randomness, uncertainty due to the incompatibility of
two observables, monogamy of correlations, impossibility of perfect cloning,
privacy of correlations, bounds in the shareability of some states; all these
phenomena are solely a consequence of the no-signaling principle and
nonlocality. In particular, it is shown that for any distribution, the
properties of (i) nonlocal, (ii) no arbitrarily shareable and (iii) positive
secrecy content are equivalent.Comment: 10 page
Constraint on teleportation over multipartite pure states
We first define a quantity exhibiting the usefulness of bipartite quantum
states for teleportation, called the quantum teleportation capability, and then
investigate its restricted shareability in multi-party quantum systems. In this
work, we verify that the quantum teleportation capability has a monogamous
property in its shareability for arbitrary three-qutrit pure states by
employing the monogamy inequality in terms of the negativity.Comment: 4 pages, 1 figur
Private quantum decoupling and secure disposal of information
Given a bipartite system, correlations between its subsystems can be
understood as information that each one carries about the other. In order to
give a model-independent description of secure information disposal, we propose
the paradigm of private quantum decoupling, corresponding to locally reducing
correlations in a given bipartite quantum state without transferring them to
the environment. In this framework, the concept of private local randomness
naturally arises as a resource, and total correlations get divided into
eliminable and ineliminable ones. We prove upper and lower bounds on the amount
of ineliminable correlations present in an arbitrary bipartite state, and show
that, in tripartite pure states, ineliminable correlations satisfy a monogamy
constraint, making apparent their quantum nature. A relation with entanglement
theory is provided by showing that ineliminable correlations constitute an
entanglement parameter. In the limit of infinitely many copies of the initial
state provided, we compute the regularized ineliminable correlations to be
measured by the coherent information, which is thus equipped with a new
operational interpretation. In particular, our results imply that two
subsystems can be privately decoupled if their joint state is separable.Comment: Child of 0807.3594 v2: minor changes v3: presentation improved, one
figure added v4: extended version with a lot of discussions and examples v5:
published versio
General polygamy inequality of multi-party quantum entanglement
Using entanglement of assistance, we establish a general polygamy inequality
of multi-party entanglement in arbitrary dimensional quantum systems. For
multi-party closed quantum systems, we relate our result with the monogamy of
entanglement to show that the entropy of entanglement is an universal
entanglement measure that bounds both monogamy and polygamy of multi-party
quantum entanglement.Comment: 4 pages, 1 figur
Conjectured Strong Complementary Information Tradeoff
We conjecture a new entropic uncertainty principle governing the entropy of
complementary observations made on a system given side information in the form
of quantum states, generalizing the entropic uncertainty relation of Maassen
and Uffink [Phys. Rev. Lett. 60, 1103 (1988)]. We prove a special case for
certain conjugate observables by adapting a similar result found by Christandl
and Winter pertaining to quantum channels [IEEE Trans. Inf. Theory 51, 3159
(2005)], and discuss possible applications of this result to the decoupling of
quantum systems and for security analysis in quantum cryptography.Comment: 4 page
Multipartite Einstein-Podolsky-Rosen steering and genuine tripartite entanglement with optical networks
The Einstein-Podolsky-Rosen (EPR) paradox established a link between
entanglement and nonlocality in quantum mechanics. EPR steering is the
nonlocality associated with the EPR paradox and has traditionally only been
investigated between two parties. Here, we present the first experimental
observations of multipartite EPR steering, and of the genuine tripartite
continuous variable entanglement of three mesoscopic optical systems. We
explore different linear optics networks - each one with optimised asymmetries
- that create multipartite steerable states containing different numbers of
quantised optical modes (qumodes). By introducing asymmetric loss on a 7-qumode
state, we characterize 8 regimes of directional steering, showing that N + 1
regimes exist for an N-qumode state. Further, we reveal the directional
monogamy of steering, and experimentally demonstrate continuous variable
one-sided semi device-independent quantum secret sharing. Our methods establish
principles for the development of multiparty quantum communication protocols
with asymmetric observers, and can be extended to qubits, whether photonic,
atomic, superconducting, or otherwise.Comment: 7 pages, 4 figures. Comments are most welcome. Edited version to
appear Jan 2015 in peer-reviewed journa
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