This is a list of this week’s papers on quantum foundations published in various journals or uploaded to preprint servers such as arxiv.org and PhilSci Archive.

# Bell’s Universe: A Personal Recollection. (arXiv:1605.08081v1 [physics.hist-ph])

## physics.hist-ph updates on arXiv.org

Authors: Reinhold A. Bertlmann

My collaboration and friendship with John Bell is recollected. I will explain his outstanding contributions in particle physics, in accelerator physics, and his joint work with Mary Bell. Mary’s work in accelerator physics is also summarized. I recall our quantum debates, mention some personal reminiscences, and give my personal view on Bell’s fundamental work on quantum theory, in particular, on the concept of contextuality and nonlocality of quantum physics. Finally, I describe the huge influence Bell had on my own work, in particular on entanglement and Bell inequalities in particle physics and their experimental verification, and on mathematical physics, where some geometric aspects of the quantum states are illustrated.

# A Local and Discrete Model Simulating Nonrelativistic Quantum Mechanical Systems. (arXiv:1605.08232v1 [quant-ph])

## quant-ph updates on arXiv.org

Authors: Antonio Sciarretta

This paper presents a simple model that mimics quantum mechanics (QM) results without using complex wavefunctions or non-localities. The proposed model only uses integer-valued quantities and arithmetic operations, in particular assuming a discrete spacetime under the form of a Euclidean lattice. The proposed approach describes individual particle trajectories as random walks. Transition probabilities are simple functions of a few quantities that are either randomly associated to the particles during their preparation, or stored in the lattice nodes they visit during the walk. Non-relativistic QM predictions are retrieved as probability distributions of similarly-prepared ensembles of particles. The scenarios considered to assess the model comprise of free particle, constant external force, harmonic oscillator, particle in a box, and the Delta potential.

Authors: Alessio Benavoli, Alessandro Facchini, Marco Zaffalon

We consider the problem of gambling on a quantum experiment and enforce rational behaviour by a few rules. These rules yield, in the classical case, the Bayesian theory of probability via duality theorems. In our quantum setting, they yield the Bayesian theory generalised to the space of Hermitian matrices. This very theory is quantum mechanics: in fact, we derive all its four postulates from the generalised Bayesian theory. This implies that quantum mechanics is self-consistent. It also leads us to reinterpret the main operations in quantum mechanics as probability rules: Bayes’ rule (measurement), marginalisation (partial tracing), independence (tensor product). To say it with a slogan, we obtain that quantum mechanics is the Bayesian theory in the complex numbers.

# Products of weak values: Uncertainty relations, complementarity, and incompatibility

## PRA: Fundamental concepts

Author(s): Michael J. W. Hall, Arun Kumar Pati, and Junde Wu

The products of weak values of quantum observables are shown to be of value in deriving quantum uncertainty and complementarity relations, for both weak and strong measurement statistics. First, a “product representation formula” allows the standard Heisenberg uncertainty relation to be derived from…

[Phys. Rev. A 93, 052118] Published Fri May 27, 2016

# Quantum Gravity signatures in the Unruh effect. (arXiv:1605.08015v1 [gr-qc])

## hep-th updates on arXiv.org

Authors: Natalia Alkofer, Giulio D’Odorico, Frank Saueressig, Fleur Versteegen

We study quantum gravity signatures emerging from phenomenologically motivated multiscale models, spectral actions, and Causal Set Theory within the detector approach to the Unruh effect. We show that while the Unruh temperature is unaffected, Lorentz-invariant corrections to the two-point function leave a characteristic fingerprint in the induced emission rate of the accelerated detector. Generically, quantum gravity models exhibiting dynamical dimensional reduction exhibit a suppression of the Unruh rate at high energy while the rate is enhanced in Kaluza-Klein theories with compact extra dimensions. We quantify this behavior by introducing the “Unruh dimension” as the effective spacetime dimension seen by the Unruh effect and show that it is related, though not identical, to the spectral dimension used to characterize spacetime in quantum gravity. We comment on the physical origins of these effects and their relevance for black hole evaporation.

# Holographic fluctuations and the principle of minimal complexity. (arXiv:1605.07768v1 [hep-th])

## quant-ph updates on arXiv.org

Authors: Wissam Chemissany, Tobias J. Osborne

We discuss, from a quantum information perspective, recent proposals of Maldacena, Ryu, Takayanagi, van Raamsdonk, Swingle, and Susskind that spacetime is an emergent property of the quantum entanglement of an associated boundary quantum system. We review the idea that the informational principle of minimal complexity determines a dual holographic bulk spacetime from a minimal quantum circuit U preparing a given boundary state from a trivial reference state. We describe how this idea may be extended to determine the relationship between the fluctuations of the bulk holographic geometry and the fluctuations of the boundary low-energy subspace. In this way we obtain, for every quantum system, an Einstein-like equation of motion for what might be interpreted as a bulk gravity theory dual to the boundary system.

# What are the observable effects of the physical properties of a quantum system?. (arXiv:1605.07744v1 [quant-ph])

## quant-ph updates on arXiv.org

Authors: Holger F. Hofmann, Taiki Nii, Masataka Iinuma

In recent work (Nii et al., arXiv:1603.06291; Iinuma et al., Phys. Rev. A 93, 032104 (2016)(arXiv:1510.03958)) we have studied the relation between experimental outcomes and the physical properties represented by Hilbert space operators of a quantum system. We find that the values of physical properties are determined by the combination of initial and final conditions, which means that eigenstates and eigenvalues should not be misinterpreted as an exclusive set of possible realities. Here, we discuss the practical implications of these results and point out the importance of quantitative relations for a proper understanding of physical effects.

# Gleason-Type Theorem for Projective Measurements, Including Qubits: The Born Rule Beyond Quantum Physics

## Latest Results for Foundations of Physics

### Abstract

Born’s quantum probability rule is traditionally included among the quantum postulates as being given by the squared amplitude projection of a measured state over a prepared state, or else as a trace formula for density operators. Both Gleason’s theorem and Busch’s theorem derive the quantum probability rule starting from very general assumptions about probability measures. Remarkably, Gleason’s theorem holds only under the physically unsound restriction that the dimension of the underlying Hilbert space \(\mathcal {H}\) must be larger than two. Busch’s theorem lifted this restriction, thereby including qubits in its domain of validity. However, while Gleason assumed that observables are given by complete sets of orthogonal projectors, Busch made the mathematically stronger assumption that observables are given by positive operator-valued measures. The theorem we present here applies, similarly to the quantum postulate, without restricting the dimension of \(\mathcal {H}\) and for observables given by complete sets of orthogonal projectors. We also show that the Born rule applies beyond the quantum domain, thereby exhibiting the common root shared by some quantum and classical phenomena.

# On the Fatal Mistake Made by John S. Bell in the Proof of His Famous Theorem

## PhilSci-Archive: No conditions. Results ordered -Date Deposited.

Author(s): Marco Túlio Quintino, Joseph Bowles, Flavien Hirsch, and Nicolas Brunner

The relation between the incompatibility of general quantum measurements and quantum nonlocality is investigated, where it is shown that measurement incompatibility does not imply Bell nonlocality.

[Phys. Rev. A 93, 052115] Published Mon May 23, 2016