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arXiv:quant-ph/0409094

Quantum Register Physics

George Jaroszkiewicz

Published Sep 15, 2004• 11 citations
arXivHTMLPDF

Abstract

Motivated by Feynman's 1983 paper on the simulation of physics by computers, we present a general approach to the description of quantum experiments which uses quantum bit registers to represent the spatio-temporal changes occurring in apparatus-systems during the course of such experiments. To illustrate our ideas, we discuss the Stern-Gerlach experiment, Wollaston prisms, beam splitters, Mach-Zender interferometers, von Neumann (PVM) tests, the more general POVM formalism, and a variety of modern quantum experiments, such as two-particle interferometry and the EPR scenario.

DOI
10.48550/arxiv.quant-ph/0409094

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Motivated by Feynman's 1983 paper on the simulation of physics by computers, we present a general approach to the description of quantum experiments which uses quantum bit registers to represent the spatio-temporal changes occurring in apparatus-systems during the course of such experiments. To illustrate our ideas, we discuss the Stern-Gerlach experiment, Wollaston prisms, beam splitters, Mach-Zender interferometers, von Neumann (PVM) tests, the more general POVM formalism, and a variety of modern quantum experiments, such as two-particle interferometry and the EPR scenario.
Quantum experiments are described in terms of time-dependent networks of quantum bits, each qubit representing an elementary information gateway. The emphasis is on the signal properties of apparatus rather than on systems under observation (SUOs), with the quantum states of the theory (the labstates) representing the observer's information about the state of their apparatus, rather than of any SUO. The formalism gives an efficient quantum register description related to the formalism of quantum computation. Experiments conventionally described by the PVM and POVM formalisms are treated in identical terms, the formalism providing an efficient modular approach to quantum optics experiments of arbitrary complexity.
Following the approach to quantum measurement, proposed in an earlier paper, in which the apparatus is treated as a purely classical instrument to be described by the laws of classical mechanics we examine some simple experiments for the purpose of illustration. The Stern-Gerlach experiment is examined in detail, within our approach, and we see explicitly how the relevant information is transferred to the apparatus variables. We also examine a magnetic interferometer arrangement and a crossed-field arrangement. Consideration of these experiments leads us to the inclusion of an extra procedural step in our approach. This extra step is necessary so that an observer may measure the classical apparatus variables at will after the interaction is completed.
Modules ModulesIn this chapter, we discuss important modules such as Wollaston prisms, Newtonian prisms, beam splitters, phase shifters, mirrors, and null modules.Modules are pieces of apparatus placed at various strategic positions in the information void and are designed to influence labstate amplitudes at signal detectors.Modules are therefore a critical component in the quantized detector network (QDN) approach to quantum mechanics (QM).Modules are not classified as either real or virtual detectors, because no information is extracted from them.Their function is solely to influence quantum amplitude propagation between stages in specific ways.Even empty space (the vacuum) can be regarded as a module, for the propagation of signals through nominally "empty" space is a fundamental subject in its own right.A particularly important example illustrating how nontrivial that can be is the Hubble-Doppler red shift of light from distant galaxies.In the QDN description of the double-slit (DS) experiment, shown in Figure 10.2, the stage Σ 1 detectors labeled 1 1 and 2 1 may be considered as on the V 2 side of the wall W , where V 2 is the information void between stages Σ 1 and Σ 2 .Viewed in this way, the wall may be interpreted as a part of the apparatus that is positioned in the information void region V 1 so as to influence the signals obtained at detectors 1 1 and 2 1 .Virtually all experiments have similar components of apparatus in the information void.We shall call any such piece of apparatus a module.Modules are necessary to the architecture of the experiment, are situated in the information void, and therefore are not detectors.Examples of modules are Stern-Gerlach (SG) inhomogeneous field magnets, Wollaston prisms, mirrors, phase changers, and so on.Even empty space, otherwise known as the vacuum, should be regarded as a module.Each module has its own physical properties.These include the number of detectors feeding amplitudes into that module and the number of detectors that
Multiport beam splitters are shown to be applicable in feasible optical realizations of higher-dimensional EPR correlations, and of tests of local realism involving measurements of nondichotomic variables. These multiports permit optical realizations of any unitary operator in Hilbert spaces of arbitrary finite dimension. Thus it is shown that one is by no means constrained to entangled spin systems, and to Stern-Gerlach apparatuses. In the analysis the concept of generalized Bell numbers is employed, which is more suitable than the standard set of spin eigenvalues. The results presented here move the discussion on entangled higher-than- spin systems from the realm of gedanken experiments to real experiments.
Quantum computing is a process that incorporates interacting physical systems that represent quantum bits and quantum gates. We present the quantum bit (qubit), the quantum register and the quantum gates. The qubit is described as a vector in a two-dimensional Hilbert space and the quantum register, which comprises a number of qubits, as a vector in a multidimensional Hilbert space. Quantum gates are Hilbert space operators that rotate the qubit or the quantum register vectors. Quantum computations are modeled and described using a quantum circuit model. We also present a quantum computer simulator based on the circuit model of quantum computation. In this model quantum computations and quantum algorithms are represented by circuits, which comprise quantum gates and quantum registers. The well-known Deutsch's algorithm is described and the corresponding quantum circuit is presented. Possible applications of quantum computers are be presented and discussed.