30 research outputs found
Quantum counter erasure
Interference comes from coherent mixing. It can be suppressed by
entanglement, and the latter can be erased so as to revive interference. If the
entanglement is a mimal-term one (with minimal-term mixing), as is the case in
most thought and real experiments reported, there appears the possibility of
counter erasure and counter interference. This peculiar phenomenon of
minimal-term mixing and minimal-term entanglement is investigated in detail. In
particular, all two-term mixings of an (arbitrary) given minimal-term mixed
state are explicitly exhibited. And so are their possible laboratory
realizations in terms of distant ensemble decomposition.Comment: 9 page
Bipartite Entanglement Review of Subsystem-Basis Expansions and Correlation Operators in It
The present review presents the authors previous results on the topic from
the title in a new light. Most of the previous results were obtained using the
techniques of antilinear Hilbert-Schmidt mappings of one Hilbert pace into
another, which is unknown and unused in the literature. This, naturally,
diminished the impact of the results. In this article the results are derived
anew with standard techniques. The topics listed at the end of the
Introduction, are expounded in 9 theorems, 5 propositions etc. Partial scalar
product and partial trace methods are used throughout. Further relevant
research articles that are not reproduced in this review, are sketched in the
Concluding remarks.Comment: 37 pages, no figues or table
Indeterminate Probabilities and the Weak Quantum Law of Large Numbers
The quantum probabilistic convergence in measurement, distinct from
mathematical convergence, is derived for indeterminate probabilities from the
weak quantum law of large numbers. This is presented in three theorems. The
first establishes the necessary bridge between ensemble theory and experiment.
The second analyzes the most important theoretical ensemble entity: the
eigen-projector of the relative frequency operator. Its physical meaning is the
experimental relative frequency. The third theorem formulates the quantum
probabilistic convergence, which is the final result of this investigation.Comment: 19 pages, no figure
General Theory of Overmeasurement of Discrete Quantum Observables and Application to Simultaneous Measurement
A complete theory of overmeasurement by measuring refinements of observables
is presented. It encompasses a wider set of functions of observ- ables
(coarsenings) . Thus the theory has a broad potential application.It is applied
to a thorough investigation of simultaneous measurements. In partic- ular, the
set of all simultaneous measurements for a given pair of compatible observables
is determined.Comment: 14 page
Delayed Twin Observables Are They a Fundamental Concept in Quantum Mechanics?
Opposite-subsystem twin events and twin observables, studied previously in
the context of distant correlations, are first generalized to pure states of
not-necessarily-composite systems, and afterwards they are further generalized
to delayed twins that are due to unitary evolution of the quantum system. The
versatile aspects of delayed twin observables are studied in terms of necessary
and sufficient conditions to make possible various applications. Three of these
are sketched: Preparation of some quantum experiments, easy solution of a
puzzle in an important Scully et al. real experiment, and, finally, it is shown
that exact measurement in quantum mechanics is an example of opposite-subsystem
delayed twins in bipartite pure states.Comment: 29 pages, no Figure
On quantum subsystem measurement
It is assumed that an arbitrary composite bipartite pure state in which the
two subsystems are entangled is given, and it is investigated how the
entanglement transmits the influence of measurement on only one of the
subsystems to the state of the opposite subsystem. It is shown that any exact
subsystem measurement has the same influence as ideal measurement on the
opposite subsystem. In particular, the distant effect of subsystem measurement
of a twin observable, i. e., so-called 'distant measurement', is always ideal
measurement on the distant subsystem no matter how intricate the direct exact
measurement on the opposite subsystem is.Comment: 12 page
Fleeting Critical Review of the Recent Ontic Breakthrough in Quantum Mechanics
The ontic breakthrough in quantum foundations, consisting of three theo-
rems, that of Pusey, Barrett, and Rudolph (PBR), the Colbeck-Renner one, and
Hardy's one, is shortly presented, together with various reactions. Some of the
ideas involved are explained and/or commented upon. Thus, the wave- function is
proved real in three independent ways. Each of the theorems rests on more or
less plausible assumptions, but they require more in-depth anal- yses.Comment: 24 pages, Latex2
On Historical Background to the Ontic Breakthrough.I Polemic Defense of Quantum Reality
After stating the author's ontic position, a collage of relevant thoughts of
some distinguished foundationally-minded physicists are quoted and polemically
commented upon. Thus, a kind of historical background of the recent ontic
breakthrough is given. The brealthrough itself is presented in Part II
Mixing Property of Quantum Relative Entropy
An analogue of the mixing property of quantum entropy is derived for quantum
relative entropy.It is applied to the final state of ideal measurement and to
the spectral form of the second density operator. Three cases of states on a
directed straight line of relative entropy are discussed.Comment: 4 pages, Latex2e and Revtex
Zurek's envariance derivation of Born's rule and measurement
Zurek's derivation of Born's rule using envariance (invariance due to
entanglement) is considered to capture the probability in full generality, but
only as applied to measurement of a quantum observable. Contrariwise, textbook
formulations of Born's rule begin with a pure state of a closed, undivided
system. The task of this study is to show that a rearrangement of the Zurek
approach is possible in which the latter is viewed as giving the probabilities
for Schmidt states of an arbitrary composite state vector, and afterwards it is
extended to probabilities in a closed, undivided system. This is achieved by
determining simultaneously probability and measurement based on the fact that
the physical meaning of probability and that of measurement are inextricably
dependent on each other.Comment: 14 pages, no figure