605 research outputs found
Bell nonlocality, signal locality and unpredictability (or What Bohr could have told Einstein at Solvay had he known about Bell experiments)
The 1964 theorem of John Bell shows that no model that reproduces the
predictions of quantum mechanics can simultaneously satisfy the assumptions of
locality and determinism. On the other hand, the assumptions of \emph{signal
locality} plus \emph{predictability} are also sufficient to derive Bell
inequalities. This simple theorem, previously noted but published only
relatively recently by Masanes, Acin and Gisin, has fundamental implications
not entirely appreciated. Firstly, nothing can be concluded about the
ontological assumptions of locality or determinism independently of each other
-- it is possible to reproduce quantum mechanics with deterministic models that
violate locality as well as indeterministic models that satisfy locality. On
the other hand, the operational assumption of signal locality is an empirically
testable (and well-tested) consequence of relativity. Thus Bell inequality
violations imply that we can trust that some events are fundamentally
\emph{unpredictable}, even if we cannot trust that they are indeterministic.
This result grounds the quantum-mechanical prohibition of arbitrarily accurate
predictions on the assumption of no superluminal signalling, regardless of any
postulates of quantum mechanics. It also sheds a new light on an early stage of
the historical debate between Einstein and Bohr.Comment: Substantially modified version; added HMW as co-autho
PR-box correlations have no classical limit
One of Yakir Aharonov's endlessly captivating physics ideas is the conjecture
that two axioms, namely relativistic causality ("no superluminal signalling")
and nonlocality, so nearly contradict each other that a unique theory - quantum
mechanics - reconciles them. But superquantum (or "PR-box") correlations imply
that quantum mechanics is not the most nonlocal theory (in the sense of
nonlocal correlations) consistent with relativistic causality. Let us consider
supplementing these two axioms with a minimal third axiom: there exists a
classical limit in which macroscopic observables commute. That is, just as
quantum mechanics has a classical limit, so must any generalization of quantum
mechanics. In this classical limit, PR-box correlations violate relativistic
causality. Generalized to all stronger-than-quantum bipartite correlations,
this result is a derivation of Tsirelson's bound without assuming quantum
mechanics.Comment: for a video of this talk at the Aharonov-80 Conference in 2012 at
Chapman University, see quantum.chapman.edu/talk-10, published in Quantum
Theory: A Two-Time Success Story (Yakir Aharonov Festschrift), eds. D. C.
Struppa and J. M. Tollaksen (New York: Springer), 2013, pp. 205-21
Quantum correlations in Newtonian space and time: arbitrarily fast communication or nonlocality
We investigate possible explanations of quantum correlations that satisfy the
principle of continuity, which states that everything propagates gradually and
continuously through space and time. In particular, following [J.D. Bancal et
al, Nature Physics 2012], we show that any combination of local common causes
and direct causes satisfying this principle, i.e. propagating at any finite
speed, leads to signalling. This is true even if the common and direct causes
are allowed to propagate at a supraluminal-but-finite speed defined in a
Newtonian-like privileged universal reference frame. Consequently, either there
is supraluminal communication or the conclusion that Nature is nonlocal (i.e.
discontinuous) is unavoidable.Comment: It is an honor to dedicate this article to Yakir Aharonov, the master
of quantum paradoxes. Version 2 contains some more references and a clarified
conclusio
Violation of local realism vs detection efficiency
We put bounds on the minimum detection efficiency necessary to violate local
realism in Bell experiments. These bounds depends of simple parameters like the
number of measurement settings or the dimensionality of the entangled quantum
state. We derive them by constructing explicit local-hidden variable models
which reproduce the quantum correlations for sufficiently small detectors
efficiency.Comment: 6 pages, revtex. Modifications in the discussion for many parties in
section 3, small erros and typos corrected, conclusions unchange
Contextuality and nonlocality in 'no signaling' theories
We define a family of 'no signaling' bipartite boxes with arbitrary inputs
and binary outputs, and with a range of marginal probabilities. The defining
correlations are motivated by the Klyachko version of the Kochen-Specker
theorem, so we call these boxes Kochen-Specker-Klyachko boxes or, briefly,
KS-boxes. The marginals cover a variety of cases, from those that can be
simulated classically to the superquantum correlations that saturate the
Clauser-Horne-Shimony-Holt inequality, when the KS-box is a generalized PR-box
(hence a vertex of the `no signaling' polytope). We show that for certain
marginal probabilities a KS-box is classical with respect to nonlocality as
measured by the Clauser-Horne-Shimony-Holt correlation, i.e., no better than
shared randomness as a resource in simulating a PR-box, even though such
KS-boxes cannot be perfectly simulated by classical or quantum resources for
all inputs. We comment on the significance of these results for contextuality
and nonlocality in 'no signaling' theories.Comment: 22 pages. Changes to Introduction and final Commentary section. Added
two tables, one to Section 5, and some new reference
Parity proofs of the Kochen-Specker theorem based on the 24 rays of Peres
A diagrammatic representation is given of the 24 rays of Peres that makes it
easy to pick out all the 512 parity proofs of the Kochen-Specker theorem
contained in them. The origin of this representation in the four-dimensional
geometry of the rays is pointed out.Comment: 14 pages, 6 figures and 3 tables. Three references have been added.
Minor typos have been correcte
Information Invariance and Quantum Probabilities
We consider probabilistic theories in which the most elementary system, a
two-dimensional system, contains one bit of information. The bit is assumed to
be contained in any complete set of mutually complementary measurements. The
requirement of invariance of the information under a continuous change of the
set of mutually complementary measurements uniquely singles out a measure of
information, which is quadratic in probabilities. The assumption which gives
the same scaling of the number of degrees of freedom with the dimension as in
quantum theory follows essentially from the assumption that all physical states
of a higher dimensional system are those and only those from which one can
post-select physical states of two-dimensional systems. The requirement that no
more than one bit of information (as quantified by the quadratic measure) is
contained in all possible post-selected two-dimensional systems is equivalent
to the positivity of density operator in quantum theory.Comment: 8 pages, 1 figure. This article is dedicated to Pekka Lahti on the
occasion of his 60th birthday. Found. Phys. (2009
Hamiltonian Light-Front Field Theory: Recent Progress and Tantalizing Prospects
Fundamental theories, such as Quantum Electrodynamics (QED) and Quantum
Chromodynamics (QCD) promise great predictive power addressing phenomena over
vast scales from the microscopic to cosmic scales. However, new
non-perturbative tools are required for physics to span from one scale to the
next. I outline recent theoretical and computational progress to build these
bridges and provide illustrative results for Hamiltonian Light Front Field
Theory. One key area is our development of basis function approaches that cast
the theory as a Hamiltonian matrix problem while preserving a maximal set of
symmetries. Regulating the theory with an external field that can be removed to
obtain the continuum limit offers additional possibilities as seen in an
application to the anomalous magnetic moment of the electron. Recent progress
capitalizes on algorithm and computer developments for setting up and solving
very large sparse matrix eigenvalue problems. Matrices with dimensions of 20
billion basis states are now solved on leadership-class computers for their
low-lying eigenstates and eigenfunctions.Comment: 8 pages with 2 figure
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
The communication complexity of non-signaling distributions
We study a model of communication complexity that encompasses many
well-studied problems, including classical and quantum communication
complexity, the complexity of simulating distributions arising from bipartite
measurements of shared quantum states, and XOR games. In this model, Alice gets
an input x, Bob gets an input y, and their goal is to each produce an output
a,b distributed according to some pre-specified joint distribution p(a,b|x,y).
We introduce a new technique based on affine combinations of lower-complexity
distributions. Specifically, we introduce two complexity measures, one which
gives lower bounds on classical communication, and one for quantum
communication. These measures can be expressed as convex optimization problems.
We show that the dual formulations have a striking interpretation, since they
coincide with maximum violations of Bell and Tsirelson inequalities. The dual
expressions are closely related to the winning probability of XOR games. These
lower bounds subsume many known communication complexity lower bound methods,
most notably the recent lower bounds of Linial and Shraibman for the special
case of Boolean functions.
We show that the gap between the quantum and classical lower bounds is at
most linear in the size of the support of the distribution, and does not depend
on the size of the inputs. This translates into a bound on the gap between
maximal Bell and Tsirelson inequality violations, which was previously known
only for the case of distributions with Boolean outcomes and uniform marginals.
Finally, we give an exponential upper bound on quantum and classical
communication complexity in the simultaneous messages model, for any
non-signaling distribution. One consequence is a simple proof that any quantum
distribution can be approximated with a constant number of bits of
communication.Comment: 23 pages. V2: major modifications, extensions and additions compared
to V1. V3 (21 pages): proofs have been updated and simplified, particularly
Theorem 10 and Theorem 22. V4 (23 pages): Section 3.1 has been rewritten (in
particular Lemma 10 and its proof), and various minor modifications have been
made. V5 (24 pages): various modifications in the presentatio
- …