269 research outputs found
Degree of entanglement as a physically ill-posed problem: The case of entanglement with vacuum
We analyze an example of a photon in superposition of different modes, and
ask what is the degree of their entanglement with vacuum. The problem turns out
to be ill-posed since we do not know which representation of the algebra of
canonical commutation relations (CCR) to choose for field quantization. Once we
make a choice, we can solve the question of entanglement unambiguously. So the
difficulty is not with mathematics, but with physics of the problem. In order
to make the discussion explicit we analyze from this perspective a popular
argument based on a photon leaving a beam splitter and interacting with two
two-level atoms. We first solve the problem algebraically in Heisenberg
picture, without any assumption about the form of representation of CCR. Then
we take the -representation and show in two ways that in two-mode
states the modes are maximally entangled with vacuum, but single-mode states
are not entangled. Next we repeat the analysis in terms of the representation
of CCR taken from Berezin's book and show that two-mode states do not involve
the mode-vacuum entanglement. Finally, we switch to a family of reducible
representations of CCR recently investigated in the context of field
quantization, and show that the entanglement with vacuum is present even for
single-mode states. Still, the degree of entanglement is here difficult to
estimate, mainly because there are subsystems, with unspecified and
large.Comment: This paper is basically a reply to quant-ph/0507189 by S. J. van Enk
and to the remarks we got from L. Vaidman after our preliminary
quant-ph/0507151. Version accepted in Phys. Rev.
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
Revivals in the attractive BEC in a double-well potential and their decoherence
We study the dynamics of ultracold attractive atoms in a weakly linked two
potential wells. We consider an unbalanced initial state and monitor dynamics
of the population difference between the two wells. The average imbalance
between wells undergoes damped oscillations, like in a classical counterpart,
but then it revives almost to the initial value. We explain in details the
whole behavior using three different models of the system. Furthermore we
investigate the sensitivity of the revivals on the decoherence caused by one-
and three-body losses. We include the dissipative processes using appropriate
master equations and solve them using the stochastic wave approximation method
Entangled-state cryptographic protocol that remains secure even if nonlocal hidden variables exist and can be measured with arbitrary precision
Standard quantum cryptographic protocols are not secure if one assumes that
nonlocal hidden variables exist and can be measured with arbitrary precision.
The security can be restored if one of the communicating parties randomly
switches between two standard protocols.Comment: Shortened version, accepted in Phys. Rev.
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
The effects of the next-nearest-neighbour density-density interaction in the atomic limit of the extended Hubbard model
We have studied the extended Hubbard model in the atomic limit. The
Hamiltonian analyzed consists of the effective on-site interaction U and the
intersite density-density interactions Wij (both: nearest-neighbour and
next-nearest-neighbour). The model can be considered as a simple effective
model of charge ordered insulators. The phase diagrams and thermodynamic
properties of this system have been determined within the variational approach,
which treats the on-site interaction term exactly and the intersite
interactions within the mean-field approximation. Our investigation of the
general case taking into account for the first time the effects of
longer-ranged density-density interaction (repulsive and attractive) as well as
possible phase separations shows that, depending on the values of the
interaction parameters and the electron concentration, the system can exhibit
not only several homogeneous charge ordered (CO) phases, but also various phase
separated states (CO-CO and CO-nonordered). One finds that the model considered
exhibits very interesting multicritical behaviours and features, including
among others bicritical, tricritical, critical-end and isolated critical
points.Comment: 12 pages, 7 figures; final version, pdf-ReVTeX; corrected typos in
reference; submitted to Journal of Physics: Condensed Matte
On the connection between mutually unbiased bases and orthogonal Latin squares
We offer a piece of evidence that the problems of finding the number of
mutually unbiased bases (MUB) and mutually orthogonal Latin squares (MOLS)
might not be equivalent. We study a particular procedure which has been shown
to relate the two problems and generates complete sets of MUBs in
power-of-prime dimensions and three MUBs in dimension six. For these cases,
every square from an augmented set of MOLS has a corresponding MUB. We show
that this no longer holds for certain composite dimensions.Comment: 6 pages, submitted to Proceedings of CEWQO 200
A Unified Conformal Model for Fundamental Interactions without Dynamical Higgs Field
A Higgsless model for strong, electro-weak and gravitational interactions is
proposed. This model is based on the local symmetry group SU(3)xSU(2)xU(1)xC
where C is the local conformal symmetry group. The natural minimal conformally
invariant form of total lagrangian is postulated. It contains all Standard
Model fields and gravitational interaction. Using the unitary gauge and the
conformal scale fixing conditions we can eliminate all four real components of
the Higgs doublet in this model. However the masses of vector mesons, leptons
and quarks are automatically generated and are given by the same formulas as in
the conventional Standard Model. The gravitational sector is analyzed and it is
shown that the model admits in the classical limit the Einsteinian form of
gravitational interactions. No figures.Comment: 25 pages, preprin
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