Density HypercubesHigher Order Interference and Hyper-Decoherence: a Categorical Approach (original) (raw)

On the ongoing experiments looking for higher-order interference: What are they really testing?

arXiv: Quantum Physics, 2016

The existence of higher than pairwise quantum interference in the set-up, in which there are more than two slits, is currently under experimental investigation. However, it is still unclear what the confirmation of existence of such interference would mean for quantum theory -- whether that usual quantum mechanics is merely a limiting case of some more general theory or whether that some assumption of quantum theory taken as a fundamental one does not actually hold true. The present paper tries to understand why quantum theory is limited only to a certain kind of interference.

Quasi-Quantization: Classical Statistical Theories with an Epistemic Restriction

Fundamental Theories of Physics, 2015

A significant part of quantum theory can be obtained from a single innovation relative to classical theories, namely, that there is a fundamental restriction on the sorts of statistical distributions over physical states that can be prepared. This is termed an "epistemic restriction" because it implies a fundamental limit on the amount of knowledge that any observer can have about the physical state of a classical system. This article provides an overview of epistricted theories, that is, theories that start from a classical statistical theory and apply an epistemic restriction. We consider both continuous and discrete degrees of freedom, and show that a particular epistemic restriction called classical complementarity provides the beginning of a unification of all known epistricted theories. This restriction appeals to the symplectic structure of the underlying classical theory and consequently can be applied to an arbitrary classical degree of freedom. As such, it can be considered as a kind of quasi-quantization scheme; "quasi" because it generally only yields a theory describing a subset of the preparations, transformations and measurements allowed in the full quantum theory for that degree of freedom, and because in some cases, such as for binary variables, it yields a theory that is a distortion of such a subset. Finally, we propose to classify quantum phenomena as weakly or strongly nonclassical by whether or not they can arise in an epistricted theory. Contents A. Quadrature quantum subtheories and the Stabilizer formalism 32 References 33

Towards the demystificatiom of quantum interference

2009

It has been shown that velocity of propagation of wave front cannot coincide with observable velocity of quantum particles. It is additional argument leads to conclusion that phase wave of de Broglie cannot be associated with single "elementary" particle like electron. Therefore quantum interference under linear superposition cannot describe energy distribution in extended quantum particles. Essentially new approach is required in order to establish non-linear relativistic wave equations with soliton-like solutions.

Ruling out Higher-Order Interference from Purity Principles

Entropy, 2017

As first noted by Rafael Sorkin, there is a limit to quantum interference. The interference pattern formed in a multi-slit experiment is a function of the interference patterns formed between pairs of slits; there are no genuinely new features resulting from considering three slits instead of two. Sorkin has introduced a hierarchy of mathematically conceivable higher-order interference behaviours, where classical theory lies at the first level of this hierarchy and quantum theory theory at the second. Informally, the order in this hierarchy corresponds to the number of slits on which the interference pattern has an irreducible dependence. Many authors have wondered why quantum interference is limited to the second level of this hierarchy. Does the existence of higher-order interference violate some natural physical principle that we believe should be fundamental? In the current work we show that such principles can be found which limit interference behaviour to second-order, or "quantum-like", interference, but that do not restrict us to the entire quantum formalism. We work within the operational framework of generalised probabilistic theories, and prove that any theory satisfying Causality, Purity Preservation, Pure Sharpness, and Purification-four principles that formalise the fundamental character of purity in nature-exhibits at most second-order interference. Hence these theories are, at least conceptually, very "close" to quantum theory. Along the way we show that systems in such theories correspond to Euclidean Jordan algebras. Hence, they are self-dual and, moreover, multi-slit experiments in such theories are described by pure projectors.

Quartic quantum theory: an extension of the standard quantum mechanics

Journal of Physics A: Mathematical and Theoretical, 2008

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 .

Interference and entanglement: an intrinsic approach

Journal of Physics A: Mathematical and General, 2002

An addition rule of impure density operators, which provides a pure state density operator, is formulated. Quantum interference including visibility property is discussed in the context of the density operator formalism. A measure of entanglement is then introduced as the norm of the matrix equal to the difference between a bipartite density matrix and the tensor product of partial traces. Entanglement for arbitrary quantum observables for multipartite systems is discussed. Star-product kernels are used to map the formulation of the addition rule of density operators onto the addition rule of symbols of the operators. Entanglement and nonlocalization of the pure state projector and allied operators are discussed. Tomographic and Weyl symbols (tomograms and Wigner functions) are considered as examples. The squeezed-states and some spin-states (two qubits) are studied to illustrate the formalism.

Nonextensive approach to decoherence in quantum mechanics

Physics Letters A, 2001

We propose a nonextensive generalization (q parametrized) of the von Neumann equation for the density operator. Our model naturally leads to the phenomenon of decoherence, and unitary evolution is recovered in the limit of q → 1. The resulting evolution yields a nonexponential decay for quantum coherences, fact that might be attributed to nonextensivity. We discuss, as an example, the loss of coherence observed in trapped ions. 05.30.Ch, 03.65.Bz, 42.50.Lc In the past decade, there have been substantial advances regarding a nonextensive, q-parametrized generalization of Gibbs-Boltzmann statistical mechanics . The q parametrization is based on an approximate expression for the exponential, or the q-exponential

Why interference phenomena do not capture the essence of quantum theory

2021

Quantum interference phenomena are widely viewed as posing a challenge to the classical worldview. Feynman even went so far as to proclaim that they are the only mystery and the basic peculiarity of quantum mechanics. Many have also argued that such phenomena force us to accept a number of radical interpretational conclusions, including: that a photon is neither a particle nor a wave but rather a schizophrenic sort of entity that toggles between the two possibilities, that reality is observer-dependent, and that systems either do not have properties prior to measurements or else have properties that are subject to nonlocal or backwards-in-time causal influences. In this work, we show that such conclusions are not, in fact, forced on us by the phenomena. We do so by describing an alternative to quantum theory, a statistical theory of a classical discrete field (the ‘toy field theory’) that reproduces the relevant phenomenology of quantum interference while rejecting these radical int...

A Royal Road to Quantum Theory (or Thereabouts), Extended Abstract

Electronic Proceedings in Theoretical Computer Science, 2017

A representation of finite-dimensional probabilistic models in terms of formally real Jordan algebras is obtained, in a strikingly easy way, from simple assumptions. This provides a framework in which real, complex and quaternionic quantum mechanics can be treated on an equal footing, and allows some (but not too much) room for other alternatives. This is based on earlier work (arXiv:1206:2897), but the development here is further simplified, and also extended in several ways. I also discuss the possibilities for organizing probabilistic models, subject to the assumptions discussed here, into symmetric monoidal categories, showing that such a category will automatically have a dagger-compact structure. (Recent joint work with Howard Barnum and Matthew Graydon (arXiv:1507.06278) exhibits several categories of this kind.

A dynamical system model for interference effects and the two-slit experiment of quantum physics

Physics Letters A, 1992

Given two probability density functionsf~ and f2, a method is described for combining the densities in a physically meaningful way. The method involves the construction of underlying transformations r, and r2, and then forming a dynamical system from these two transformations referred to as a random transformation. The invariant (stationary) probability density function for the random transformation is the "combined" density off~ and f2. This method of combining probability density functions is used to model interference effects in physical systems. In particular, the dynamics of the two-slit experiment of quantum physics is modelled by an appropriate random transformation. Computer results are presented which qualitatively appear like experimental results. The notion of wave is not needed in the model.