scholarly journals Qubit state vector in probability representation of quantum mechanics

2021 ◽  
Author(s):  
Vladimir N. Chernega ◽  
Olga V. Man’ko ◽  
Vladimir I. Man’ko
Keyword(s):  
Quantum Mechanics ◽  
State Vector ◽  
Qubit State ◽  
Probability Representation

scholarly journals The measure problem in no-collapse (many worlds) quantum mechanics

2017 ◽  
Vol 26 (03) ◽  
pp. 1730008 ◽  
Author(s):  
Stephen D. H. Hsu
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Probability Measure ◽  
Ab Initio ◽  
Subjective Probability ◽  
State Vector ◽  
A Priori ◽  
Born Rule ◽  
Many Worlds ◽  
Measure Problem

We explain the measure problem (cf. origin of the Born probability rule) in no-collapse quantum mechanics. Everett defined maverick branches of the state vector as those on which the usual Born probability rule fails to hold — these branches exhibit highly improbable behaviors, including possibly the breakdown of decoherence or even the absence of an emergent semi-classical reality. Derivations of the Born rule which originate in decision theory or subjective probability (i.e. the reasoning of individual observers) do not resolve this problem, because they are circular: they assume, a priori, that the observer occupies a non-maverick branch. An ab initio probability measure is sometimes assumed to explain why we do not occupy a maverick branch. This measure is constrained by, e.g. Gleason’s theorem or envariance to be the usual Hilbert measure. However, this ab initio measure ultimately governs the allocation of a self or a consciousness to a particular branch of the wave function, and hence invokes primitives which lie beyond the Everett wave function and beyond what we usually think of as physics. The significance of this leap has been largely overlooked, but requires serious scrutiny.

Remarks on Some Basic Issues in Quantum Mechanics

1999 ◽  
Vol 54 (1) ◽  
pp. 11-32 ◽  
Author(s):  
Berthold-Georg Englert
Keyword(s):  
Quantum Mechanics ◽  
Physical Meaning ◽  
State Vector ◽  
Undergraduate Teaching ◽  
Teaching Device ◽  
Physical Research ◽  
Wave Particle Duality ◽  
Einstein Podolsky Rosen ◽  
Quantum Erasure ◽  
As If

Abstract Two-way interferometers with which-way detectors are not only of importance in physical research, they are also a useful teaching device. A number of basic issues can be illustrated and discussed, even at the level of undergraduate teaching. Among these issues are: the physical meaning of a state vector; entangled systems; Einstein-Podolsky-Rosen correlations; statistical operators and the as-if realities associated with them; quantum erasure; Schrödinger's cat; and, finally, wave-particle duality.

scholarly journals Superposition Principle and Born’s Rule in the Probability Representation of Quantum States

2019 ◽  
Vol 1 (2) ◽  
pp. 130-150 ◽  
Author(s):  
Igor Ya. Doskoch ◽  
Margarita A. Man’ko
Keyword(s):  
Quantum Mechanics ◽  
Probability Distribution ◽  
Particle System ◽  
Superposition Principle ◽  
Quantum States ◽  
Particle State ◽  
Probability Representation ◽  
Tomographic Probability ◽  
Born’S Rule ◽  
System States

The basic notion of physical system states is different in classical statistical mechanics and in quantum mechanics. In classical mechanics, the particle system state is determined by its position and momentum; in the case of fluctuations, due to the motion in environment, it is determined by the probability density in the particle phase space. In quantum mechanics, the particle state is determined either by the wave function (state vector in the Hilbert space) or by the density operator. Recently, the tomographic-probability representation of quantum states was proposed, where the quantum system states were identified with fair probability distributions (tomograms). In view of the probability-distribution formalism of quantum mechanics, we formulate the superposition principle of wave functions as interference of qubit states expressed in terms of the nonlinear addition rule for the probabilities identified with the states. Additionally, we formulate the probability given by Born’s rule in terms of symplectic tomographic probability distribution determining the photon states.

Quantenmechanik und Objektivierbarkeit/ Quantum Mechanics and Objective Reality

1970 ◽  
Vol 25 (12) ◽  
pp. 1954-1957 ◽  
Author(s):  
K. Baumann
Keyword(s):  
Quantum Mechanics ◽  
Density Matrix ◽  
State Vector ◽  
The State ◽  
Measuring Apparatus ◽  
Measuring Process ◽  
Objective Reality ◽  
Objective Description ◽  
The Universe

Abstract Quantum Mechanics and Objective Reality A Schrödinger function (or a density matrix) can he ascribed only to an object whose isolation time is larger than its time of revolution. This condition can never be satisfied for macroscopic bodies. Consequently, the "cut" between object and observer must not separate a macroscopic body (measuring apparatus) from the rest of the universe. Hence in an analysis of the measuring process, the state vector of the universe must be introduced. An interpretation of this state vector is given which provides an objective description of nature.

scholarly journals Can small quantum systems learn

2017 ◽  
Vol 17 (7&8) ◽  
pp. 568-594
Author(s):  
Nathan Wiebe ◽  
Christopher Grandade
Keyword(s):  
Quantum Mechanics ◽  
Fault Tolerance ◽  
Bayesian Inference ◽  
Quantum System ◽  
Lower Bounds ◽  
State Vector ◽  
Quantum Systems ◽  
Posterior Distributions ◽  
Quantum Devices ◽  
Small Quantum

We examine the question of whether quantum mechanics places limitations on the ability of small quantum devices to learn. We specifically examine the question in the context of Bayesian inference, wherein the prior and posterior distributions are encoded in the quantum state vector. We conclude based on lower bounds from Grover’s search that an efficient blackbox method for updating the distribution is impossible. We then address this by providing a new adaptive form of approximate quantum Bayesian inference that is polynomially faster than its classical anolog and tractable if the quantum system is augmented with classical memory or if the low–order moments of the distribution are protected through redundant preparation. This work suggests that there may be a connection between fault tolerance and the capacity of a quantum system to learn from its surroundings.

scholarly journals Probability, preclusion and biological evolution in Heisenberg-picture Everett quantum mechanics

2021 ◽  
pp. 2150117
Author(s):  
Mark A. Rubin
Keyword(s):  
Quantum Mechanics ◽  
State Vector ◽  
Biological Evolution ◽  
Second Law Of Thermodynamics ◽  
Quantum Mechanical ◽  
Second Law ◽  
Subjective Experiences ◽  
Everett Interpretation ◽  
Heisenberg Picture ◽  
Physical Laws

The fact that certain “extraordinary” probabilistic phenomena — in particular, macroscopic violations of the second law of thermodynamics — have never been observed to occur can be accounted for by taking hard preclusion as a basic physical law, i.e. precluding from existence events corresponding to very small but nonzero values of quantum-mechanical weight. This approach is not consistent with the usual ontology of the Everett interpretation, in which outcomes correspond to branches of the state vector, but can be successfully implemented using a Heisenberg-picture-based ontology in which outcomes are encoded in transformations of operators. Hard preclusion can provide an explanation for biological evolution, which can in turn explain our subjective experiences of, and reactions to, “ordinary” probabilistic phenomena, and the compatibility of those experiences and reactions with what we conventionally take to be objective probabilities arising from physical laws.

scholarly journals Probability representation of quantum mechanics and star product quantization

2019 ◽  
Vol 1348 ◽  
pp. 012101 ◽  
Author(s):  
V N Chernega ◽  
S N Belolipetskiy ◽  
O V Man’ko ◽  
V I Man’ko
Keyword(s):  
Quantum Mechanics ◽  
Star Product ◽  
Probability Representation ◽  
Product Quantization
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