# Weekly Papers on Quantum Foundations (46)

To know the quantum mechanical state of a system implies not only statistical restrictions on the results of measurements. (arXiv:2111.06221v1 [quant-ph])

Using the one-dimensional Schr\”{o}dinger equation as an example, it is shown that for any self-adjoint operator it is possible to uniquely predict the value of the corresponding observable (including momentum, kinetic and total energy of the particle) at that spatial point where the particle will be accidentally detected at a given instant of time. It is shown that the Schr\”{o}dinger formalism ensures the fulfillment of the relations of wave-particle duality, which connect the energy and momentum of a particle with the frequency and wave number of the wave function, for any spatial point and any instant of time.

Quantum Correlations in the Minimal Scenario. (arXiv:2111.06270v1 [quant-ph])

In the minimal scenario of quantum correlations, two parties can choose from two observables with two possible outcomes each. Probabilities are specified by four marginals and four correlations. The resulting four-dimensional convex body of correlations, denoted $\mathcal{Q}$, is fundamental for quantum information theory. It is here studied through the lens of convex algebraic geometry. We review and systematize what is known and add many details, visualizations, and complete proofs. A new result is that $\mathcal{Q}$ is isomorphic to its polar dual. The boundary of $\mathcal{Q}$ consists of three-dimensional faces isomorphic to elliptopes and sextic algebraic manifolds of exposed extreme points. These share all basic properties with the usual maximally CHSH-violating correlations. These patches are separated by cubic surfaces of non-exposed extreme points. We provide a trigonometric parametrization of all extreme points, along with their exposing Tsirelson inequalities and quantum models. All non-classical extreme points (exposed or not) are self-testing, i.e., realized by an essentially unique quantum model.

Two principles, which are specific to the minimal scenario, allow a quick and complete overview: The first is the pushout transformation, the application of the sine function to each coordinate. This transforms the classical polytope exactly into the correlation body $\mathcal{Q}$, also identifying the boundary structures. The second principle, self-duality, reveals the polar dual, i.e., the set of all Tsirelson inequalities satisfied by all quantum correlations. The convex body $\mathcal{Q}$ includes the classical correlations, a cross polytope, and is contained in the no-signaling body, a 4-cube. These polytopes are dual to each other, and the linear transformation realizing this duality also identifies $\mathcal{Q}$ with its dual.

Insights on Entanglement Entropy in $1+1$ Dimensional Causal Sets. (arXiv:2111.05879v1 [hep-th])

Entanglement entropy in causal sets offers a fundamentally covariant characterisation of quantum field degrees of freedom. A known result in this context is that the degrees of freedom consist of a number of contributions that have continuum-like analogues, in addition to a number of contributions that do not. The latter exhibit features below the discreteness scale and are excluded from the entanglement entropy using a “truncation scheme”. This truncation is necessary to recover the standard spatial area law of entanglement entropy. In this paper we build on previous work on the entanglement entropy of a massless scalar field on a causal set approximated by a 1+1D causal diamond in Minkowski spacetime. We present new insights into the truncated contributions, including evidence that they behave as fluctuations and encode features specific to a particular causal set sprinkling. We extend previous results in the massless theory to include R\’enyi entropies and include new results for the massive theory. We also discuss the implications of our work for the treatment of entanglement entropy in causal sets in more general settings.

Stochastic Quantization of Relativistic Theories. (arXiv:2103.02501v3 [gr-qc] UPDATED)

Authors: Folkert Kuipers

It was shown recently that stochastic quantization can be made into a well defined quantization scheme on (pseudo-)Riemannian manifolds using second order differential geometry, which is an extension of the commonly used first order differential geometry. In this letter, we show that restrictions to relativistic theories can be obtained from this theory by imposing a stochastic energy-momentum relation. In the process, we derive non-perturbative quantum corrections to the line element as measured by scalar particles. Furthermore, we extend the framework of stochastic quantization to massless scalar particles.

Cyclic Cosmology and Geodesic Completeness. (arXiv:2110.15380v2 [gr-qc] UPDATED)

Authors: William H. KinneyNina K. Stein (Univ. at Buffalo, SUNY)

We consider recently proposed bouncing cosmological models for which the Hubble parameter is periodic in time, but the scale factor grows from one cycle to the next as a mechanism for shedding entropy. Since the scale factor for a flat universe is equivalent to an overall conformal factor, it has been argued that this growth corresponds to a physically irrelevant rescaling, and such bouncing universes can be made perfectly cyclic, extending infinitely into the past and future. We show that any bouncing universe which uses growth of the scale factor to dissipate entropy must necessarily be geodesically past-incomplete, and therefore cannot be truly cyclic in time.

Viewing quantum charge from the classical vantage point

GIlton, Marian J. R. (2021) Viewing quantum charge from the classical vantage point. In: UNSPECIFIED.

Irreversible (One-hit) and Reversible (Sustaining) Causation

Ross, Lauren N. and Woodward, James (2021) Irreversible (One-hit) and Reversible (Sustaining) Causation. In: UNSPECIFIED.

Geometrization vs. Unification. The Reichenbach-Einstein Quarrel about the Fernparallelismus Field Theory

Giovanelli, Marco (2021) Geometrization vs. Unification. The Reichenbach-Einstein Quarrel about the Fernparallelismus Field Theory. [Preprint]

Pseudorandomness in Simulations and Nature

Abrams, Marshall (2021) Pseudorandomness in Simulations and Nature. In: UNSPECIFIED.

One world is (probably) just as good as many

Steeger, Jeremy (2021) One world is (probably) just as good as many. [Preprint]

Laws beyond spacetime

Lam, Vincent and Wuthrich, Christian (2021) Laws beyond spacetime. [Preprint]

On the (Im)possibility of Scalable Quantum Computing

Knight, Andrew (2021) On the (Im)possibility of Scalable Quantum Computing. [Preprint]

Spacetime: Function and Approximation

Baron, Sam (2021) Spacetime: Function and Approximation. [Preprint]

How to Make Presentism Consistent with Special Relativity

Balaguer, Mark (2021) How to Make Presentism Consistent with Special Relativity. In: UNSPECIFIED.