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F. Herbut

Publications and source records attributed to F. Herbut.

9 recordsLinked to original sources
arXiv2004

On compatibility and improvement of different quantum state assignments

When Alice and Bob have different quantum knowledges or state assignments (density operators) for one and the same specific individual system, then the problems of compatibility and pooling arise. The so-called first Brun-Finkelstein-Mermin (BFM) condition for compatibility is reobtained in terms of possessed or sharp (i. e., probability one) properties. The second BFM condition is shown to be generally invalid in an infinite-dimensional state space. An argument leading to a procedure of improvement of one state assifnment on account of the other and vice versa is presented.

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arXiv2003

Chains of Quasi-Classical Informations for Bipartite Correlations and the Role of Twin Observables

Having the quantum correlations in a general bipartite state in mind, the information accessible by simultaneous measurement on both subsystems is shown never to exceed the information accessible by measurement on one subsystem, which, in turn is proved not to exceed the von Neumann mutual information. A particular pair of (opposite- subsystem) observables are shown to be responsible both for the amount of quasi-classical correlations and for that of the purely quantum entanglement in the pure-state case: the former via simultaneous subsystem measurements, and the latter through the entropy of coherence or of incompatibility, which is defined for the general case. The observables at issue are so-called twin observables. A general definition of the latter is given in terms of their detailed properties.

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arXiv2003

Hermitian Schmidt Decomposition and Twin Observables of Bipartite Mixed States

It is shown that for each mixed state there exists a Schmidt (super state vector) decomposition in terms of Hermitian operators. Its utilization for finding all twins is illustrated in full detail in the case of the two spin-one-half-particle states with maximally disordered subsystems (mixtures of Bell states).

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arXiv2001

A Theory of Quantum Preparation and the Corresponding Advantage of the Relative-Collapse Interpretation of Quantum Mechanics as Compared to the Conventional One

Analyzing two standard preparators, the Stern-Gerlach and the hole-in-the-screen ones, it is demonstrated that four entities are the basic ingredients of the theory: the composite-system preparator-plus-object state (coming about as a result of a suitable interaction between the subsystems), a suitable preparator observable, one of its characteristic projectors called the triggering event, and, finally, the conditional object state corresponding to the occurrence of the triggering event. The concepts of a conditional state and of retrospective apparent ideal occurrence are discussed in the conventional interpretation of quantum mechanics. In the general theory of a preparator in this interpretation first-kind and second-kind preparators are distinguished. They are described by the same entities in the same way, but in terms of different physical mechanisms. In this article the relative-collapse interpretation is extended to encompass also preparators (besides measuring apparatuses). In this interpretation also the mechanisms become the same and one has only one kind of preparators.

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arXiv2001

Is quantum decoherence reality or appearance?

It has been experimentally demonstrated that quantum coherence can persist in macroscopic phenomena [J.R. Friedman et al.,Nature, 406 (2000) 43]. To face the challenge of this new fact, in this article QM in its standard form is assumed to be extended by one beable (hidden variable), i. e., a quantum observable with always definite values in nature (but usually only statistically given in the quantum state). Localization is taken as the most plausible beable. The paradoxical aspects of conventional QM take now a different form. Suitably defining the notion of "subject" fully within the QM formalism, proving the quantum conditional subsystem-state theorem, and choosing the relative-decoherence interpretation of QM, the paradoxes formally disappear, leaving one with decoherence relative to the definite values of the beable; thus being only appearance, not absolute reality in QM. Relative to a different subject one has perseverance of coherence. Hence, in this approach it is claimed that decoherence and coherence, both exist in reality, but are not "seen" by the same subject, and "subject" is, in this interpretation, indispensable. The two mentioned, apparently contradictory phenomena, are in this way decoupled from each other, contradiction is avoided, and any one of the two can be treated in the way that is usual in QM.

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arXiv2001

Strong twin events in mixed-state entanglement

Continuing the study of mixed-state entanglement in terms of opposite-subsystem observables the measurement of one of which amounts to the same as that of the other (so-called twins), begun in a recent article, so-called strong twin events, which imply biorthogonal mixing of states, are defined and studied. It is shown that for each mixed state there exists a Schmidt canonical (super state vector) expansion in terms of Hermitian operators, and that it can be the continuation of the mentioned biorthogonal mixing due to strong twins. The case of weak twins and nonhermitian Schmidt canonical expansion is also investigated. A necessary and sufficient condition for the existence of nontrivial twins for separable states is derived.

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arXiv2001

On twin observables in entangled mixed states

It is pointed out that every mixed state statistical operator is, up to a normalization constant, a super state vector in the Hilbert space of linear Hilbert-Schmidt operators acting in the state space of the quantum system. Hence, the well understood Schmidt canonical expansion of ordinary state vectors can be carried over to mixed states. In particular, it can be utilized for evaluating all the twins, i. e., the opposite-subsystem observables the measurement of one of which is, on account of entanglement, ipso facto also a measurement of the other. This is illustrated in full detail in the case of the Horodecki two spin-one-half-particle states with maximally disordered subsystems.

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arXiv2000

Mixed-state twin observables

Twin observables, i.e. opposite subsystem observables A+ and A- that are indistinguishable in measurement in a given mixed or pure state W, are investigated in detail algebraicly and geometrically. It is shown that there is a far-reaching correspondence between the detectable (in W) spectral entities of the two operators. Twin observables are state-dependently quantum-logically equivalent, and direct subsystem measurement of one of them ipso facto gives rise to the indirect (i.e. distant) measurement of the other. Existence of nontrivial twins requires singularity of W. Systems in thermodynamic equilibrium do not admit subsystem twins. These observables may enable one to simplify the matrix representing W.

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