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Fedor Herbut

Publications and source records attributed to Fedor Herbut.

At least 19 recordsLinked to original sources
arXiv2015

Derivation of quantum probability from measurement

To begin with, it is pointed out that the form of the quantum probabil- ity formula originates in the very initial state of the object system as seen when the state is expanded with the eigen-projectors of the measured ob- servable. Making use of the probability reproducibility condition, which is a key concept in unitary measurement theory, one obtains the relevant coher- ent distribution of the complete-measurement results in the final unitary- measurement state in agreement with the mentioned probability formula. Treating the transition from the final unitary, or premeasurement, state, where all possible results are present, to one complete-measurement result sketchily in the usual way, the well-known probability formula is derived. In conclusion it is pointed out that the entire argument is only formal unless one makes it physical assuming that the quantum probability law is valid in the extreme case of probability-one (certain) events (projectors).

quant-ph↗
arXiv2015

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.

quant-ph↗
arXiv2015

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.

quant-ph↗
arXiv2015

Does Unitary Measurement Theory Lead to an Everettian Interpretation?

Quantum-mechanical interpretation-related implications of the theory of unitary premeasurement [1] on complete measurement (objectification or collapse included) are investigated in the present article with a view to give an affirmative answer to the question in the title. It is argued that both Bohr's and von Neumann's ideas lead to those of Everett. Hence, the latter can be, in some sense, considered to be a continuation and elaboration of both former approaches. The importance of the idea of relativeness in Everett's theory is emphasized. To free the relative-state theory from its roots both of classicalness and of subjective observation in the argument of this study, the general or unfolded version of Everett's theory is sketched.

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arXiv2014

A Review of Unitary Quantum Premeasurement Theory An Algebraic Study of Basic Kinds of Premeasurements

A detailed theory of quantum premeasurement dynamics is presented in which a unitary composite-system operator that contains the relevant object-measuring-instrument interaction brings about the final premeasurement state. It does not include collapse, and it does not consider the environment. It is assumed that a discrete degenerate or non-degenerate observable is measured. Premeasurement is defined by the calibration condition, which requires that every initially statistically sharp value of the measured observable has to be detected with statistical certainty by the measuring instrument. The entire theory is derived as a logical consequence of this definition using the standard quantum formalism. The study has a comprehensive coverage, hence the article is actually a topical review. Connection is made with results of other authors, particularly with basic works on premeasurement. The article is a conceptual review, not a historical one. General exact premeasurement is defined in 7 equivalent ways. Nondemolition premeasurement, defined by requiring preservation of any sharp value of the measured observable, is characterized in 10 equivalent ways. Overmeasurement, i. e., a process in which the observable is measured on account of being a function of a finer observable that is actually measured, is discussed. Disentangled premeasurement, in which, by definition, to each result corresponds only one pointer-observable state in the final composite-system state, is investigated. Ideal premeasurement, a special case of both nondemolition premeasurement and disentangled premeasurement, is defined, and its most important properties are discussed. Finally, disentangled and entangled premeasurements, in conjunction with nondemolition or demolition premeasurements, are used for classification of all premeasurements.

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arXiv2014

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.

math-ph↗
arXiv2014

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.

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arXiv2013

Wavefunction reality, indeterminate properties and degrees of presence

The degree-of-presence (of the quantum system) concept, accompanying that of the wavefunction-reality postulate, is introduced and studied in two ways. To begin with, an incomplete exposition of the present author's views is given. Subsequently, a short historical and philosophical review of answers to the question about the meaning of indeterminate individual-system probabilities is presented from the literature. It is done in the form of a carefully selected collage of quotations mostly with polemic comments by the present author and with further elaboration of his point of view. The advocated notion of 'degree of presence' generalizes the intuitively most easily acceptable idea of 'delocalization' in (roughly called)wavelike behavior of a quantum system.

physics.hist-ph↗
arXiv2013

On the nucleon paradigm: the nucleons are closer to reality than the protons and neutrons

There is a widespread delusion that in theoretical nuclear physics protons and neutrons are the real thing, and nucleons are not more than a mathematically equivalent formality. It is shown that, on the contrary, nucleons are the real thing, because only a part of the theory is essentially identical to proton-and-neutron theory, whereas the remaining part is physically relevant. The approach is general. Thus, this is a paradigm of relation of a wider and a more narrow theory, so that the wider theory describes reality better. Also the relation of disjoint domains to the exclusion principle is clarified. A general fermion theory of how to distinguish identical particles is presented.

physics.gen-ph↗
arXiv2013

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.

quant-ph↗
arXiv2013

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.

quant-ph↗
arXiv2013

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.

quant-ph↗
arXiv2011

How Can the No-Collapse and the Collapse Interpretations of Quantum-Mechanics Give the Same Description?

It is shown that no-collapse and collapse interpretations of quantum mechanics give equal object states (which predict everything that is observable) if one bases the relevant relations on the Von Neumann-Lüders 'projection'. This connection is elaborated in detail from simple to most general cases. Distinguishability of the two approaches, which exists in principle, is also discussed. In the very simple illustration of passing one slit physical-insight difficulties in the collapse approach are indicated. For the purpose of interference between the two wavefunction components also the Maxh-Zehnder interferometer is discussed.

quant-ph↗
arXiv2010

On EPR-type Entanglement in the Experiments of Scully et Al. II. Insight in the Real Random Delayed-choice Erasure Experiment

It was pointed out in the first part of this study that EPR-type entanglement is defined by the possibility of performing any of two mutually incompatible distant, i. e.,direct-interaction-free, measurements. They go together under the term 'EPR-type disentanglement'. In this second part, quantum-mechanical insight is gained in the real random delayed-choice erasure experiment of Kim et al. [Kim et al.: Phys. Rev. Lett. 84, 1-5 (2000)] by a relative-reality-of- unitarily-evolving-state (RRUES) approach (explained in the first part). Finally, it is shown that this remarkable experiment, which performs, by random choice, two incompatible measurements at the same time, is actually an EPR-type disentanglement experiment, closely related to the micromaser experiment discussed in the first part.

quant-ph↗
arXiv2010

A Theory of Quantum Preparation

Based on an analysis of two conventional preparators, the Stern-Gerlach and the hole-in-the-screen ones, it is argued that four entities can be taken as the basic ingredients of a rather general theory of a quantum preparator. These are the composite-system (object plus preparator) state coming about as a result of a suitable interaction between the subsystems, a suitable preparator projector called the triggering event, the conditional quantum state (density operator) of the quantum object coming about as a consequence of the occurrence of the triggering event on the preparator, and, finally, a unitary evolution operator of the object subsystem acting after preparation. The concepts of a general conditional state and of retrospective apparent ideal occurrence (which appears in the theory) are discussed in considerable detail. Ideal occurrence and the selective Lüders formula, which are made use of, are reviewed. Dynamical and geometrical preparators are distinguished in the general theory. They are described by the same entities in the same way, but in terms of different physical mechanisms from the point of view of standard interpretation with collapse.

quant-ph↗
arXiv2009

Critical Assessment of Wave-Particle Complementarity via Derivation from Quantum Mechanics

After introducing sketchily Bohr's wave-particle complementarity principle in his own words, a derivation of an extended form of the principle from standard quantum mechanics is performed. Reality-evaluation of each step is given. The derived theory is applied to simple examples and the extended entities are illustrated in a thought experiment. Assessment of the approach of Bohr and of this article is taken up again with a rather negative conclusion as far as reflecting reality is concerned. The paper ends with selected incisive opinions on Bohr's dogmatic attitude and with some comments by the present author.

quant-ph↗
arXiv2008

Quantum Correlations in Multipartite States. Study Based on the Wootters-Mermin Theorem

Decomposition of any N-partite state (density operator) into clusters (that do not overlap) is studied in detail with a view to learn as much as possible about the correlations implied by the state. The Wootters-Mermin theorem, stating that the totality of all strings of cluster events (projectors) determines the state in any finite- or infinite-dimensional state space, is a slightly sharpened and generalized form of the original results of Wootters and Mermin. It is applied to tensor factorization of the state into states of clusters (uncorrelated decomposition) and it is shown that a finest uncorrelated decomposition always exists, and that its coarsenings and only they are other possible uncorrelated cluster decompositions. Distant effects witin homogeneous cluster states, which are, by definition, the tensor factors in the finest uncorrelated decomposition, are discussed. The entire study is viewed by the author as a possible further elaboration of Mermin's Ithaca program.

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