Quantum/Classical Interface: A Geometric Approach from the Classical Side

Baylis, W. E.

doi:10.1007/1-4020-2307-3_6

Cited by 11 publications

(12 citation statements)

References 8 publications

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“…The APS interpretation, when combined with the use of amplitudes such as eigenspinors as discussed above, is quite consistent with quantum phenomena such as violations of Bell's inequalities that originate from interference of amplitudes in the computation of probabilities. [47] We have concentrated here on single-particle systems and have not discussed the important statistical properties of fermions and only touched on the classical view of entanglement. Much more work is needed.…”

Section: Discussionmentioning

confidence: 99%

“…To substantiate the ability of APS to make quantum predictions for spin distributions, we demonstrate here that the use of probability amplitudes, even locally on single beams, is sufficient to violate the Bell inequalities. [47] Nonlocal correlations or the use of Clifford-valued functions for the probabilities [48] are not necessary. Consider a beam of silver atoms passing through a sequence of Stern-Gerlach magnets aligned to split the beam into spins polarized in opposite directions specified by unit vectors ±a, ±b, ±c.…”

Section: Bell Inequalitiesmentioning

confidence: 99%

See 1 more Smart Citation

Quantum/Classical Interface: Classical Geometric Origin of Fermion Spin

Baylis

Cabrera

Keselica

2010

Adv. Appl. Clifford Algebras

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Although intrinsic spin is usually viewed as a purely quantum property with no classical analog, we present evidence that fermion spin has a classical origin rooted in the geometry of three-dimensional physical space. Our approach to the quantum/classical interface is based on a formulation of relativistic classical mechanics that uses spinors. Spinors and projectors arise naturally in the Clifford's geometric algebra of physical space and not only provide powerful tools in classical electrodynamics, but also reproduce a number of quantum results. We show in particular that many properties of elementary fermions, as spin-1/2 particles, are obtained classically and relate spin, the associated g-factor, its coupling to an external magnetic field, Zitterbewegung, and de Broglie waves. Spinors are also amplitudes that can undergo quantum-like interference. The relationship of spin and geometry is further strengthened by the fact that physical space and its geometric algebra can be derived from fermion annihilation and creation operators. The approach is important because of the insights it provides about spin and quantum phenomena more generally. Mathematics Subject Classification (2000). 15A66, 81P15, 81R25, 83A05.

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Section: Discussionmentioning

confidence: 99%

Section: Bell Inequalitiesmentioning

confidence: 99%

Quantum/Classical Interface: Classical Geometric Origin of Fermion Spin

Baylis

Cabrera

Keselica

2010

Adv. Appl. Clifford Algebras

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“…How to implement them physically and really? See [51][52][53][54][55][56][57]. -What returns a real quantum computer (non-adiabatic), in the general case?…”

Section: Quantum Image Processing and Its Implementation Problemsmentioning

confidence: 99%

“…Equations (50) and (52) tell us that when we measure  (in each of its projections, see Equations 27 and 28), we are introducing a noise measurement, which is inherent to the type of measurement, however, always exists and it cannot be overlooked, and this noise will disappear only when we measure CBS   01 ,…”

Section: What Is the Quantum Measurement Equivalent In Quip And Qusp?mentioning

confidence: 99%

Quantum image processing?

Mastriani¹

2016

Quantum Inf Process

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This paper presents a number of problems concerning the practical (real) implementation of the techniques known as Quantum Image Processing. The most serious problem is the recovery of the outcomes after the quantum measurement, which will be demonstrated in this work that is equivalent to a noise measurement, and it is not considered in the literature on the subject. It is noteworthy that this is due to several factors: 1) a classical algorithm that uses Dirac's notation and then it is coded in MATLAB does not constitute a quantum algorithm, 2) the literature emphasizes the internal representation of the image but says nothing about the classical-to-quantum and quantum-to-classical interfaces and how these are affected by decoherence, 3) the literature does not mention how to implement in a practical way (at the laboratory) these proposals internal representations, 4) given that Quantum Image Processing works with generic qubits this requires measurements in all axes of the Bloch sphere, logically, and 5) among others. In return, the technique known as Quantum Boolean Image Processing is mentioned, which works with computational basis states (CBS), exclusively. This methodology allows us to avoid the problem of quantum measurement, which alters the results of the measured except in the case of CBS. Said so far is extended to quantum algorithms outside image processing too.Quantum computation and quantum information is the study of the information processing tasks that can be accomplished using quantum mechanical systems. Like many simple but profound ideas it was a long time before anybody thought of doing information processing using quantum mechanical systems [1].Quantum computation is the field that investigates the computational power and other properties of computers based on quantum-mechanical principles. An important objective is to find quantum algorithms that are significantly faster than any classical algorithm solving the same problem. The field started in the early 1980s with suggestions for analog quantum computers by Paul Benioff [2] and Richard Feynman [3,4], and reached more digital ground when in 1985 David Deutsch defined the universal quantum Turing machine [5]. The following years saw only sparse activity, notably the development of the first algorithms by Deutsch and Jozsa [6] and by Simon [7], and the development of quantum complexity theory by Bernstein and Vazirani [8]. However, interest in the field increased tremendously after Peter Shor's very surprising discovery of efficient quantum algorithms (or simulations on a quantum computer) for the problems of integer factorization and discrete logarithms in 1994 [9]. Quantum Information Processing (QuIn) -The main concepts related to Quantum InformationProcessing may be grouped in the next topics: quantum bit (qubit, which is the elemental quantum information unity), Bloch's Sphere (geometric environment for qubit representation), Hilbert's Space (which generalizes the notion of Euclidean space), Schrödinger's Equation (which is a partial d...

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“…Many authors have been investigating the applications of Clifford algebras to describe entanglement and the numerous aspects related to this subject [2,14,24]. For many reasons, algebraic and geometric approaches to quantum mechanics and its peculiar features have always been appealing.…”

Section: Introductionmentioning

confidence: 99%

Algebraic Criteria for Entanglement in Multipartite Systems

2007

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Quantum computing depends heavily on quantum entanglement. It has been known that geometric models for correlated two-state quantum systems (qubits) can be developed using geometric algebra. This suggests that entanglement may be given a purely algebraic description without resort to any particular representation on Hilbert spaces. In the case of the Clifford algebra, for example, the states are not simply operands in a Hilbert space representation of the algebra but they are considered as embedded within the Clifford algebra itself. In other words the space of states sits inside the algebra. This Cliffordalgebraic substructure is a minimal left ideal of the algebra. This fact naturally poses the question of whether or not the description of entanglement in multipartite systems can be generalized to algebras possessing one-sided ideal structure. By making tensor products of algebras and their minimal one-sided ideals we propose an algebraic criteria for characterizing entanglement in multipartite systems without resort to any representation on Hilbert spaces.

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Quantum/Classical Interface: A Geometric Approach from the Classical Side

Cited by 11 publications

References 8 publications

Quantum/Classical Interface: Classical Geometric Origin of Fermion Spin

Quantum/Classical Interface: Classical Geometric Origin of Fermion Spin

Quantum image processing?

Algebraic Criteria for Entanglement in Multipartite Systems

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