229 research outputs found
Keyring models: an approach to steerability
If a measurement is made on one half of a bipartite system, then, conditioned
on the outcome, the other half has a new reduced state. If these reduced states
defy classical explanation -- that is, if shared randomness cannot produce
these reduced states for all possible measurements -- the bipartite state is
said to be steerable. Determining which states are steerable is a challenging
problem even for low dimensions. In the case of two-qubit systems a criterion
is known for T-states (that is, those with maximally mixed marginals) under
projective measurements. In the current work we introduce the concept of
keyring models -- a special class of local hidden state models. When the
measurements made correspond to real projectors, these allow us to study
steerability beyond T-states.
Using keyring models, we completely solve the steering problem for real
projective measurements when the state arises from mixing a pure two-qubit
state with uniform noise. We also give a partial solution in the case when the
uniform noise is replaced by independent depolarizing channels.Comment: 15(+4) pages, 5 figures. v2: references added, v3: minor change
Causality - Complexity - Consistency: Can Space-Time Be Based on Logic and Computation?
The difficulty of explaining non-local correlations in a fixed causal
structure sheds new light on the old debate on whether space and time are to be
seen as fundamental. Refraining from assuming space-time as given a priori has
a number of consequences. First, the usual definitions of randomness depend on
a causal structure and turn meaningless. So motivated, we propose an intrinsic,
physically motivated measure for the randomness of a string of bits: its length
minus its normalized work value, a quantity we closely relate to its Kolmogorov
complexity (the length of the shortest program making a universal Turing
machine output this string). We test this alternative concept of randomness for
the example of non-local correlations, and we end up with a reasoning that
leads to similar conclusions as in, but is conceptually more direct than, the
probabilistic view since only the outcomes of measurements that can actually
all be carried out together are put into relation to each other. In the same
context-free spirit, we connect the logical reversibility of an evolution to
the second law of thermodynamics and the arrow of time. Refining this, we end
up with a speculation on the emergence of a space-time structure on bit strings
in terms of data-compressibility relations. Finally, we show that logical
consistency, by which we replace the abandoned causality, it strictly weaker a
constraint than the latter in the multi-party case.Comment: 17 pages, 16 figures, small correction
Entropic uncertainty relations for extremal unravelings of super-operators
A way to pose the entropic uncertainty principle for trace-preserving
super-operators is presented. It is based on the notion of extremal unraveling
of a super-operator. For given input state, different effects of each
unraveling result in some probability distribution at the output. As it is
shown, all Tsallis' entropies of positive order as well as some of Renyi's
entropies of this distribution are minimized by the same unraveling of a
super-operator. Entropic relations between a state ensemble and the generated
density matrix are revisited in terms of both the adopted measures. Using
Riesz's theorem, we obtain two uncertainty relations for any pair of
generalized resolutions of the identity in terms of the Renyi and Tsallis
entropies. The inequality with Renyi's entropies is an improvement of the
previous one, whereas the inequality with Tsallis' entropies is a new relation
of a general form. The latter formulation is explicitly shown for a pair of
complementary observables in a -level system and for the angle and the
angular momentum. The derived general relations are immediately applied to
extremal unravelings of two super-operators.Comment: 8 pages, one figure. More explanations are given for Eq. (2.19) and
Example III.5. One reference is adde
Bell inequalities from no-signaling distributions
A Bell inequality is a constraint on a set of correlations whose violation
can be used to certify non-locality. They are instrumental for
device-independent tasks such as key distribution or randomness expansion. In
this work we consider bipartite Bell inequalities where two parties have
and possible inputs and give and possible outputs, referring
to this as the scenario. By exploiting knowledge of the
set of extremal no-signalling distributions, we find all 175 Bell inequality
classes in the (4, 4, 2, 2) scenario, as well as providing a partial list of
18277 classes in the (4, 5, 2, 2) scenario. We also use a probabilistic
algorithm to obtain 5 classes of inequality in the (2, 3, 3, 2) scenario, which
we confirmed to be complete, 25 classes in the (3, 3, 2, 3) scenario, and a
partial list of 21170 classes in the (3, 3, 3, 3) scenario. Our inequalities
are given in supplementary files. Finally, we discuss the application of these
inequalities to the detection loophole problem, and provide new lower bounds on
the detection efficiency threshold for small numbers of inputs and outputs.Comment: 15 + 7 pages. v2: more scenarios are covered and more analysis has
been done. v3: shorter title and a few additional updates, including summary
table
The Intrinsic Quantum Nature of Nash Equilibrium Mixtures
Every undergraduate textbook in game theory has a chapter discussing the difficulty to interpret the mixed Nash equilibrium strategies. Unlike the usual suggested interpretations made in those textbooks, here we prove that these randomised strategies neither imply that players use some coin flips to make their decisions, nor that the mixtures represent the uncertainty of each player about the others' actions.Instead, the paper demonstrates a fundamental connection between the Nash equilibrium 'randomised' or 'mixed' strategies of classical game theory and the pure quantum states of quantum theory in physics. This link has some key consequences for the meaning of randomised strategies:In the main theorem, I prove that in every mixed Nash equilibrium, each player state of knowledge about his/her own future rational choices is represented by a pure quantum state. This indicates that prior making his/her actual choice, each player must be in a quantum superposition over her/his possible rational choices (in the support of his probability measure). This result notably permits to show that the famous 'indifference condition' that must be satisfied by each player in an equilibrium is actually the condition that ensures each player is in a 'rational epistemic state of ignorance' about her/his own future choice of an action
Quantum Tasks in Minkowski Space
The fundamental properties of quantum information and its applications to
computing and cryptography have been greatly illuminated by considering
information-theoretic tasks that are provably possible or impossible within
non-relativistic quantum mechanics. I describe here a general framework for
defining tasks within (special) relativistic quantum theory and illustrate it
with examples from relativistic quantum cryptography and relativistic
distributed quantum computation. The framework gives a unified description of
all tasks previously considered and also defines a large class of new questions
about the properties of quantum information in relation to Minkowski causality.
It offers a way of exploring interesting new fundamental tasks and
applications, and also highlights the scope for a more systematic understanding
of the fundamental information-theoretic properties of relativistic quantum
theory
A channel-based framework for steering, non-locality and beyond
Non-locality and steering are both non-classical phenomena witnessed in nature as a result of quantum entanglement. It is now well-established that one can study non-locality independently of the formalism of quantum mechanics, in the so-called device-independent framework. With regards to steering, although one cannot study it completely independently of the quantum formalism, 'post-quantum steering' has been described, which is steering that cannot be reproduced by measurements on entangled states but does not lead to superluminal signalling. In this work we present a framework based on the study of quantum channels in which one can study steering (and non-locality) in quantum theory and beyond. In this framework, we show that kinds of steering, whether quantum or post-quantum, are directly related to particular families of quantum channels that have been previously introduced by Beckman et al (2001 Phys. Rev. A 64 052309). Utilizing this connection we also demonstrate new analytical examples of post-quantum steering, give a quantum channel interpretation of almost quantum non-locality and steering, easily recover and generalize the celebrated Gisin–Hughston–Jozsa–Wootters theorem, and initiate the study of post-quantum Buscemi non-locality and non-classical teleportation. In this way, we see post-quantum non-locality and steering as just two aspects of a more general phenomenon
Simulations of quantum double models
We demonstrate how to build a simulation of two dimensional physical theories
describing topologically ordered systems whose excitations are in one to one
correspondence with irreducible representations of a Hopf algebra, D(G), the
quantum double of a finite group G. Our simulation uses a digital sequence of
operations on a spin lattice to prepare a ground "vacuum" state and to create,
braid and fuse anyonic excitations. The simulation works with or without the
presence of a background Hamiltonian though only in the latter case is the
system topologically protected. We describe a physical realization of a
simulation of the simplest non-Abelian model, D(S_3), using trapped neutral
atoms in a two dimensional optical lattice and provide a sequence of steps to
perform universal quantum computation with anyons. The use of ancillary spin
degrees of freedom figures prominently in our construction and provides a novel
technique to prepare and probe these systems.Comment: 24 pages, 2 figure
Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km
For more than 80 years, the counterintuitive predictions of quantum theory
have stimulated debate about the nature of reality. In his seminal work, John
Bell proved that no theory of nature that obeys locality and realism can
reproduce all the predictions of quantum theory. Bell showed that in any local
realist theory the correlations between distant measurements satisfy an
inequality and, moreover, that this inequality can be violated according to
quantum theory. This provided a recipe for experimental tests of the
fundamental principles underlying the laws of nature. In the past decades,
numerous ingenious Bell inequality tests have been reported. However, because
of experimental limitations, all experiments to date required additional
assumptions to obtain a contradiction with local realism, resulting in
loopholes. Here we report on a Bell experiment that is free of any such
additional assumption and thus directly tests the principles underlying Bell's
inequality. We employ an event-ready scheme that enables the generation of
high-fidelity entanglement between distant electron spins. Efficient spin
readout avoids the fair sampling assumption (detection loophole), while the use
of fast random basis selection and readout combined with a spatial separation
of 1.3 km ensure the required locality conditions. We perform 245 trials
testing the CHSH-Bell inequality and find . A
null hypothesis test yields a probability of that a local-realist
model for space-like separated sites produces data with a violation at least as
large as observed, even when allowing for memory in the devices. This result
rules out large classes of local realist theories, and paves the way for
implementing device-independent quantum-secure communication and randomness
certification.Comment: Raw data will be made available after publicatio
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