A density tensor hierarchy for open system dynamics: retrieving the noise

Adler, Stephen L.

doi:10.1088/1751-8113/40/30/020

Cited by 5 publications

(3 citation statements)

References 32 publications

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“…It is worth to emphasize that our approach differs from the theory of Adler based on higher order correlation tensors [17], the 'two-state vector formalism' of Aharonov and Vaidman [18], the 'time-symmetric quantum mechanics' of Wharton [19], and the quaternionic version of quantum theory [20,21,22], which is not consistent with the power like scaling, K = N r , in analogy to the quantum theory of real density matrices.…”

Section: Introductionmentioning

confidence: 83%

Quartic quantum theory: an extension of the standard quantum mechanics

Życzkowski¹

2008

J. Phys. A: Math. Theor.

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We propose an extended quantum theory, in which the number K of parameters necessary to characterize a quantum state behaves as fourth power of the number N of distinguishable states. As the simplex of classical N -point probability distributions can be embedded inside a higher dimensional convex body M Q N of mixed quantum states, one can further increase the dimensionality constructing the set of extended quantum states. The embedding proposed corresponds to an assumption that the physical system described in N dimensional Hilbert space is coupled with an auxiliary subsystem of the same dimensionality. The extended theory works for simple quantum systems and is shown to be a non-trivial generalisation of the standard quantum theory for which K = N 2 . Imposing certain restrictions on initial conditions and dynamics allowed in the quartic theory one obtains quadratic theory as a special case. By imposing even stronger constraints one arrives at the classical theory, for which K = N .

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Section: Introductionmentioning

confidence: 83%

Quartic quantum theory: an extension of the standard quantum mechanics

Życzkowski¹

2008

J. Phys. A: Math. Theor.

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“…which satisfies various identities derived by contracting pairs of indices [26]. The hierarchy of all such tensors captures the properties of the noise acting on the system; in particular, the expectation E[V ] of the variance V = TrρA 2 − (TrρA) 2 of an operator A can be rewritten as…”

Section: Reductionmentioning

confidence: 99%

Gravitation and the Noise Needed in Objective Reduction Models

Adler¹

2016

Quantum Nonlocality and Reality

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I briefly recall intersections of my research interests with those of John Bell. I then argue that the noise needed in theories of objective state vector reduction most likely comes from a fluctuating complex part in the classical spacetime metric, that is, state vector reduction is driven by complex number valued "spacetime foam". I. INTRODUCTIONMy research interests have intersected those of John Bell three times. The first was when I found the forward lepton theorem for high energy neutrino reactions, showing that for forward lepton kinematics, a conserved vector current (CVC) and partially conserved axial vector current (PCAC) imply that the neutrino cross section can be related to a pion scattering cross section [1]. This led to an exchange of letters and discussions with Bell during 1964-1965, which are described in the Commentaries for my selected papers [2]. The second was in the course of my work on the axial-vector anomaly [3], when I had further correspondence with John Bell, as described in both the Commentaries [4] and in the volume of essays on Yang-Mills theories assembled by 't Hooft [5]. The third time was a few years after Bell's death in 1990, when I became interested in the foundations of quantum theory and the quantum measurement problem, in the course of writing my book on quaternionic quantum mechanics [6]. Foundational issues in standard, complex quantum theory had preoccupied Bell for much of his career, and led to his best known work. However, my correspondence with Bell in the 1960s never touched on quantum foundations, and I only read his seminal writings on the subject much later on. In this article I focus on this third area of shared interests. II. OBJECTIVE REDUCTION MODELSThere is now a well-defined phenomenology of state vector reduction, pioneered by the work of Ghirardi, Rimini, and Weber (GRW) and of Philip Pearle, and worked on by many others. John

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“…In this section, we discuss possible experiments proposed to test collapse models against the standard quantum theory. For a more detailed analysis on this topic, we refer to [ 11 , 12 , 13 , 14 , 15 ].…”

Section: Experimental Tests Of Collapse Modelsmentioning

confidence: 99%

Collapse Models: A Theoretical, Experimental and Philosophical Review

Bassi

Dorato

2023

Entropy

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In this paper, we review and connect the three essential conditions needed by the collapse model to achieve a complete and exact formulation, namely the theoretical, the experimental, and the ontological ones. These features correspond to the three parts of the paper. In any empirical science, the first two features are obviously connected but, as is well known, among the different formulations and interpretations of non-relativistic quantum mechanics, only collapse models, as the paper well illustrates with a richness of details, have experimental consequences. Finally, we show that a clarification of the ontological intimations of collapse models is needed for at least three reasons: (1) to respond to the indispensable task of answering the question ’what are collapse models (and in general any physical theory) about?’; (2) to achieve a deeper understanding of their different formulations; (3) to enlarge the panorama of possible readings of a theory, which historically has often played a fundamental heuristic role.

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A density tensor hierarchy for open system dynamics: retrieving the noise

Cited by 5 publications

References 32 publications

Quartic quantum theory: an extension of the standard quantum mechanics

Quartic quantum theory: an extension of the standard quantum mechanics

Gravitation and the Noise Needed in Objective Reduction Models

Collapse Models: A Theoretical, Experimental and Philosophical Review

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