303 research outputs found
Quantum-mechanical machinery for rational decision-making in classical guessing game
In quantum game theory, one of the most intriguing and important questions
is, "Is it possible to get quantum advantages without any modification of the
classical game?" The answer to this question so far has largely been negative.
So far, it has usually been thought that a change of the classical game setting
appears to be unavoidable for getting the quantum advantages. However, we give
an affirmative answer here, focusing on the decision-making process (we call
'reasoning') to generate the best strategy, which may occur internally, e.g.,
in the player's brain. To show this, we consider a classical guessing game. We
then define a one-player reasoning problem in the context of the
decision-making theory, where the machinery processes are designed to simulate
classical and quantum reasoning. In such settings, we present a scenario where
a rational player is able to make better use of his/her weak preferences due to
quantum reasoning, without any altering or resetting of the classically defined
game. We also argue in further analysis that the quantum reasoning may make the
player fail, and even make the situation worse, due to any inappropriate
preferences.Comment: 9 pages, 10 figures, The scenario is more improve
Quantum constraints, Dirac observables and evolution: group averaging versus Schroedinger picture in LQC
A general quantum constraint of the form (realized in particular in Loop Quantum Cosmology models) is
studied. Group Averaging is applied to define the Hilbert space of solutions
and the relational Dirac observables. Two cases are considered. In the first
case, the spectrum of the operator is assumed to be
discrete. The quantum theory defined by the constraint takes the form of a
Schroedinger-like quantum mechanics with a generalized Hamiltonian
. In the second case, the spectrum is absolutely continuous
and some peculiar asymptotic properties of the eigenfunctions are assumed. The
resulting Hilbert space and the dynamics are characterized by a continuous
family of the Schroedinger-like quantum theories. However, the relational
observables mix different members of the family. Our assumptions are motivated
by new Loop Quantum Cosmology models of quantum FRW spacetime. The two cases
considered in the paper correspond to the negative and, respectively, positive
cosmological constant. Our results should be also applicable in many other
general relativistic contexts.Comment: RevTex4, 32 page
Certifying an irreducible 1024-dimensional photonic state using refined dimension witnesses
We report on a new class of dimension witnesses, based on quantum random
access codes, which are a function of the recorded statistics and that have
different bounds for all possible decompositions of a high-dimensional physical
system. Thus, it certifies the dimension of the system and has the new distinct
feature of identifying whether the high-dimensional system is decomposable in
terms of lower dimensional subsystems. To demonstrate the practicability of
this technique we used it to experimentally certify the generation of an
irreducible 1024-dimensional photonic quantum state. Therefore, certifying that
the state is not multipartite or encoded using non-coupled different degrees of
freedom of a single photon. Our protocol should find applications in a broad
class of modern quantum information experiments addressing the generation of
high-dimensional quantum systems, where quantum tomography may become
intractable.Comment: Journal version (except for small editorial modifications), 4+12
pages, 7 figure
Real space inhomogeneities in high temperature superconductors: the perspective of two-component model
The two-component model of high temperature superconductors in its real space
version has been solved using Bogoliubov-de Gennes equations. The disorder in
the electron and boson subsystem has been taken into account. It strongly
modifies the superconducting properties and leads to local variations of the
gap parameter and density of states. The assumption that the impurities mainly
modify boson energies offers natural explanation of the puzzling positive
correlation between the positions of impurities and the values of the order
parameter found in the scanning tunnelling microscopy experiments.Comment: 19 pages, IOPP style include
Generalised Compositional Theories and Diagrammatic Reasoning
This chapter provides an introduction to the use of diagrammatic language, or
perhaps more accurately, diagrammatic calculus, in quantum information and
quantum foundations. We illustrate the use of diagrammatic calculus in one
particular case, namely the study of complementarity and non-locality, two
fundamental concepts of quantum theory whose relationship we explore in later
part of this chapter.
The diagrammatic calculus that we are concerned with here is not merely an
illustrative tool, but it has both (i) a conceptual physical backbone, which
allows it to act as a foundation for diverse physical theories, and (ii) a
genuine mathematical underpinning, permitting one to relate it to standard
mathematical structures.Comment: To appear as a Springer book chapter chapter, edited by G.
Chirabella, R. Spekken
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