513 research outputs found
Bell nonlocality and Bayesian game theory
We discuss a connection between Bell nonlocality and Bayesian games. This
link offers interesting perspectives for Bayesian games, namely to allow the
players to receive advice in the form of nonlocal correlations, for instance
using entangled quantum particles or more general no-signaling boxes. The
possibility of having such 'nonlocal advice' will lead to novel joint
strategies, impossible to achieve in the classical setting. This implies that
quantum resources, or more general no-signaling resources, offer a genuine
advantage over classical ones. Moreover, some of these strategies can represent
equilibrium points, leading to the notion of quantum/no-signaling Nash
equilibrium. Finally we describe new types of question in the study of
nonlocality, namely the consideration of non-local advantage when there is a
set of Bell expressions.Comment: 7 pages, 3 figure
Robustness of Measurement, discrimination games and accessible information
We introduce a way of quantifying how informative a quantum measurement is,
starting from a resource-theoretic perspective. This quantifier, which we call
the robustness of measurement, describes how much `noise' must be added to a
measurement before it becomes completely uninformative. We show that this
geometric quantifier has operational significance in terms of the advantage the
measurement provides over guessing at random in an suitably chosen state
discrimination game. We further show that it is the single-shot generalisation
of the accessible information of a certain quantum-to-classical channel. Using
this insight, we also show that the recently-introduced robustness of coherence
is the single-shot generalisation of the accessible information of an ensemble.
Finally we discuss more generally the connection between robustness-based
measures, discrimination problems and single-shot information theory.Comment: 10 pages, 1 figur
Path Intergals and Perturbative Expansions for Non-Compact Symmetric Spaces
We show how to construct path integrals for quantum mechanical systems where
the space of configurations is a general non-compact symmetric space.
Associated with this path integral is a perturbation theory which respects the
global structure of the system. This perturbation expansion is evaluated for a
simple example and leads to a new exactly soluble model. This work is a step
towards the construction of a strong coupling perturbation theory for quantum
gravity.Comment: 16 page
Measurement entropy in Generalized Non-Signalling Theory cannot detect bipartite non-locality
We consider entropy in Generalized Non-Signalling Theory (also known as box
world) where the most common definition of entropy is the measurement entropy.
In this setting, we completely characterize the set of allowed entropies for a
bipartite state. We find that the only inequalities amongst these entropies are
subadditivity and non-negativity. What is surprising is that non-locality does
not play a role - in fact any bipartite entropy vector can be achieved by
separable states of the theory. This is in stark contrast to the case of the
von Neumann entropy in quantum theory, where only entangled states satisfy
S(AB)<S(A).Comment: 14 pages, includes minor corrections from v
The non-local content of quantum operations
We show that quantum operations on multi-particle systems have a non-local
content; this mirrors the non-local content of quantum states. We introduce a
general framework for discussing the non-local content of quantum operations,
and give a number of examples. Quantitative relations between quantum actions
and the entanglement and classical communication resources needed to implement
these actions are also described. We also show how entanglement can catalyse
classical communication from a quantum action.Comment: 7 page
Optimal verification of entangled states with local measurements
Consider the task of verifying that a given quantum device, designed to
produce a particular entangled state, does indeed produce that state. One
natural approach would be to characterise the output state by quantum state
tomography; or alternatively to perform some kind of Bell test, tailored to the
state of interest. We show here that neither approach is optimal amongst local
verification strategies for two qubit states. We find the optimal strategy in
this case and show that quadratically fewer total measurements are needed to
verify to within a given fidelity than in published results for quantum state
tomography, Bell test, or fidelity estimation protocols. We also give efficient
verification protocols for any stabilizer state. Additionally, we show that
requiring that the strategy be constructed from local, non-adaptive and
non-collective measurements only incurs a constant-factor penalty over a
strategy without these restrictions.Comment: Document includes supplemental material. Main paper: 5 pages, 2 figs;
supplemental material: 16 pages, 2 fig
The structure of Renyi entropic inequalities
We investigate the universal inequalities relating the alpha-Renyi entropies
of the marginals of a multi-partite quantum state. This is in analogy to the
same question for the Shannon and von Neumann entropy (alpha=1) which are known
to satisfy several non-trivial inequalities such as strong subadditivity.
Somewhat surprisingly, we find for 0<alpha<1, that the only inequality is
non-negativity: In other words, any collection of non-negative numbers assigned
to the nonempty subsets of n parties can be arbitrarily well approximated by
the alpha-entropies of the 2^n-1 marginals of a quantum state.
For alpha>1 we show analogously that there are no non-trivial homogeneous (in
particular no linear) inequalities. On the other hand, it is known that there
are further, non-linear and indeed non-homogeneous, inequalities delimiting the
alpha-entropies of a general quantum state.
Finally, we also treat the case of Renyi entropies restricted to classical
states (i.e. probability distributions), which in addition to non-negativity
are also subject to monotonicity. For alpha different from 0 and 1 we show that
this is the only other homogeneous relation.Comment: 15 pages. v2: minor technical changes in Theorems 10 and 1
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