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