139 research outputs found
Secure quantum signatures using insecure quantum channels
Digital signatures are widely used in modern communication to guarantee authenticity and transferability of messages. The security of currently used classical schemes relies on computational assumptions. We present a quantum signature scheme that does not require trusted quantum channels. We prove that it is unconditionally secure against the most general coherent attacks, and show that it requires the transmission of significantly fewer quantum states than previous schemes. We also show that the quantum channel noise threshold for our scheme is less strict than for distilling a secure key using quantum key distribution. This shows that “direct” quantum signature schemes can be preferable to signature schemes relying on secret shared keys generated using quantum key distribution.This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) under EP/G009821/1 and EP/K022717/1. P.W. gratefully acknowledges support from the COST Action MP1006. A.K. was partially supported by a grant from FQXi and by Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation.This is the author accepted manuscript. The final version is available from the American Physical Society via http://dx.doi.org/10.1103/PhysRevA.93.03232
Decomposition of pure states of quantum register
The generalization of Schmidt decomposition due to
Cartelet-Higuchi-Sudbery applied to quantum register (a system of N
qubits) is shown to acquire direct geometrical meaning: any pure
state is canonically associated with a chain of a simplicial
complex. A leading vector method is presented to calculate the
values of the coefficients of appropriate chain
Dynamics & Predictions in the Co-Event Interpretation
Sorkin has introduced a new, observer independent, interpretation of quantum
mechanics that can give a successful realist account of the 'quantum
microworld' as well as explaining how classicality emerges at the level of
observable events for a range of systems including single time 'Copenhagen
measurements'. This 'co-event interpretation' presents us with a new ontology,
in which a single 'co-event' is real. A new ontology necessitates a review of
the dynamical & predictive mechanism of a theory, and in this paper we begin
the process by exploring means of expressing the dynamical and predictive
content of histories theories in terms of co-events.Comment: 35 pages. Revised after refereein
Spacetime Coarse Grainings in the Decoherent Histories Approach to Quantum Theory
We investigate the possibility of assigning consistent probabilities to sets
of histories characterized by whether they enter a particular subspace of the
Hilbert space of a closed system during a given time interval. In particular we
investigate the case that this subspace is a region of the configuration space.
This corresponds to a particular class of coarse grainings of spacetime
regions. We consider the arrival time problem and the problem of time in
reparametrization invariant theories as for example in canonical quantum
gravity. Decoherence conditions and probabilities for those application are
derived. The resulting decoherence condition does not depend on the explicit
form of the restricted propagator that was problematic for generalizations such
as application in quantum cosmology. Closely related is the problem of
tunnelling time as well as the quantum Zeno effect. Some interpretational
comments conclude, and we discuss the applicability of this formalism to deal
with the arrival time problem.Comment: 23 pages, Few changes and added references in v
Distinguishing Initial State-Vectors from Each Other in Histories Formulations and the PBR Argument
Following the argument of Pusey, Barrett and Rudolph (Nature Phys. 8:476,
2012), new interest has been raised on whether one can interpret state-vectors
(pure states) in a statistical way (-epistemic theories), or if each of
them corresponds to a different ontological entity. Each interpretation of
quantum theory assumes different ontology and one could ask if the PBR argument
carries over. Here we examine this question for histories formulations in
general with particular attention to the co-event formulation. State-vectors
appear as the initial state that enters into the quantum measure. While the PBR
argument goes through up to a point, the failure to meet some of the
assumptions they made does not allow one to reach their conclusion. However,
the author believes that the "statistical interpretation" is still impossible
for co-events even if this is not proven by the PBR argument.Comment: 25 pages, v2 published versio
The coevent formulation of quantum theory
Understanding quantum theory has been a subject of debate from its birth.
Many different formulations and interpretations have been proposed. Here we
examine a recent novel formulation, namely the coevents formulation. It is a
histories formulation and has as starting point the Feynman path integral and
the decoherence functional. The new ontology turns out to be that of a
coarse-grained history. We start with a quantum measure defined on the space of
histories, and the existence of zero covers rules out single-history as
potential reality (the Kochen Specker theorem casted in histories form is a
special case of a zero cover). We see that allowing coarse-grained histories as
potential realities avoids the previous paradoxes, maintains deductive
non-contextual logic (alas non-Boolean) and gives rise to a unique classical
domain. Moreover, we can recover the probabilistic predictions of quantum
theory with the use of the Cournot's principle. This formulation, being both a
realist formulation and based on histories, is well suited conceptually for the
purposes of quantum gravity and cosmology.Comment: 19 pages, 1 figure. In v2 equation 7 corrected, figure added and
references modifie
Twistor form of massive 6D superparticle
The massive six-dimensional (6D) superparticle with manifest (n, 0) supersymmetry is shown to have a supertwistor formulation in which its “hidden” (0, n) supersymmetry is also manifest. The mass-shell constraint is replaced by Spin(5) spin-shell constraints which imply that the quantum superparticle has zero superspin; for n = 1 it propagates the 6D Proca supermultiplet.PKT acknowledges support from the UK Science and Technology Facilities Council (grant ST/L000385/1). AJR is supported by a grant from the London Mathematical Society.This is the final version of the article. It was first available from IOP Science via http://dx.doi.org/10.1088/1751-8113/49/2/02540
The Generalized Second Law implies a Quantum Singularity Theorem
The generalized second law can be used to prove a singularity theorem, by
generalizing the notion of a trapped surface to quantum situations. Like
Penrose's original singularity theorem, it implies that spacetime is null
geodesically incomplete inside black holes, and to the past of spatially
infinite Friedmann--Robertson--Walker cosmologies. If space is finite instead,
the generalized second law requires that there only be a finite amount of
entropy producing processes in the past, unless there is a reversal of the
arrow of time. In asymptotically flat spacetime, the generalized second law
also rules out traversable wormholes, negative masses, and other forms of
faster-than-light travel between asymptotic regions, as well as closed timelike
curves. Furthermore it is impossible to form baby universes which eventually
become independent of the mother universe, or to restart inflation. Since the
semiclassical approximation is used only in regions with low curvature, it is
argued that the results may hold in full quantum gravity. An introductory
section describes the second law and its time-reverse, in ordinary and
generalized thermodynamics, using either the fine-grained or the coarse-grained
entropy. (The fine-grained version is used in all results except those relating
to the arrow of time.) A proof of the coarse-grained ordinary second law is
given.Comment: 46 pages, 8 figures. v2: discussion of global hyperbolicity revised
(4.1, 5.2), more comments on AdS. v3: major revisions including change of
title. v4: similar to published version, but with corrections to plan of
paper (1) and definition of global hyperbolicity (3.2). v5: fixed proof of
Thm. 1, changed wording of Thm. 3 & proof of Thm. 4, revised Sec. 5.2, new
footnote
Spacelike distance from discrete causal order
Any discrete approach to quantum gravity must provide some prescription as to
how to deduce continuum properties from the discrete substructure. In the
causal set approach it is straightforward to deduce timelike distances, but
surprisingly difficult to extract spacelike distances, because of the unique
combination of discreteness with local Lorentz invariance in that approach. We
propose a number of methods to overcome this difficulty, one of which
reproduces the spatial distance between two points in a finite region of
Minkowski space. We provide numerical evidence that this definition can be used
to define a `spatial nearest neighbor' relation on a causal set, and conjecture
that this can be exploited to define the length of `continuous curves' in
causal sets which are approximated by curved spacetime. This provides evidence
in support of the ``Hauptvermutung'' of causal sets.Comment: 32 pages, 16 figures, revtex4; journal versio
Emergence of spatial structure from causal sets
There are numerous indications that a discrete substratum underlies continuum
spacetime. Any fundamentally discrete approach to quantum gravity must provide
some prescription for how continuum properties emerge from the underlying
discreteness. The causal set approach, in which the fundamental relation is
based upon causality, finds it easy to reproduce timelike distances, but has a
more difficult time with spatial distance, due to the unique combination of
Lorentz invariance and discreteness within that approach. We describe a method
to deduce spatial distances from a causal set. In addition, we sketch how one
might use an important ingredient in deducing spatial distance, the `-link',
to deduce whether a given causal set is likely to faithfully embed into a
continuum spacetime.Comment: 21 pages, 21 figures; proceedings contribution for DICE 2008, to
appear in Journal of Physics: Conference Serie
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