643 research outputs found
Complementarity and the algebraic structure of 4-level quantum systems
The history of complementary observables and mutual unbiased bases is
reviewed. A characterization is given in terms of conditional entropy of
subalgebras. The concept of complementarity is extended to non-commutative
subalgebras. Complementary decompositions of a 4-level quantum system are
described and a characterization of the Bell basis is obtained.Comment: 19 page
Structure of sufficient quantum coarse-grainings
Let H and K be Hilbert spaces and T be a coarse-graining from B(H) to B(K).
Assume that density matrices D_1 and D_2 acting on H are given. In the paper
the consequences of the existence of a coarse-graining S from B(K) to B(H)
satisfying ST(D_1)=D_1 and ST(D_2)=D_2 are given. (This condition means the
sufficiency of T for D_1 and D_2.) Sufficiency implies a particular
decomposition of the density matrices. This decomposition allows to deduce the
exact condition for equality in the strong subadditivity of the von Neumann
entropy.Comment: 13 pages, LATE
Point Estimation of States of Finite Quantum Systems
The estimation of the density matrix of a -level quantum system is studied
when the parametrization is given by the real and imaginary part of the entries
and they are estimated by independent measurements. It is established that the
properties of the estimation procedure depend very much on the invertibility of
the true state. In particular, in case of a pure state the estimation is less
efficient. Moreover, several estimation schemes are compared for the unknown
state of a qubit when one copy is measured at a time. It is shown that the
average mean quadratic error matrix is the smallest if the applied observables
are complementary. The results are illustrated by computer simulations.Comment: 16 pages, 5 figure
What sexuality? : An exploratory study examining sexual activity and affectionate sexual expression in a Western Australian sample of older adults
Sexuality later in life has been receiving increased research interest, however, a large majority of research investigates a narrow range of sexual behaviours, primarily frequency of sexual intercourse. There is limited information regarding other forms of sexual expression, specifically affectionate sexual expression that are relevant to older adults. The present day study explores what affectionate sexual behaviours constitute affectionate sexual expression and compares sexual intercourse with affectionate expression. The sample consisted of 77 married men (n=35) and women (n=42) aged 60-89 years who came from various senior groups and organisations in the Perth metropolitan area. A survey was developed that investigated what constituted affectionate expression, and interest and changes in affectionate sexual expression and sexual intercourse
Covariance and Fisher information in quantum mechanics
Variance and Fisher information are ingredients of the Cramer-Rao inequality.
We regard Fisher information as a Riemannian metric on a quantum statistical
manifold and choose monotonicity under coarse graining as the fundamental
property of variance and Fisher information. In this approach we show that
there is a kind of dual one-to-one correspondence between the candidates of the
two concepts. We emphasis that Fisher informations are obtained from relative
entropies as contrast functions on the state space and argue that the scalar
curvature might be interpreted as an uncertainty density on a statistical
manifold.Comment: LATE
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.
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