# Weekly Papers on Quantum Foundations (12)

On Two Recent Approaches to the Born Rule. (arXiv:2103.09910v1 [quant-ph])

I comment briefly on derivations of the Born rule presented by Masanes et al. and by Hossenfelder.

Experimental SWAP test of infinite dimensional quantum states. (arXiv:2103.10219v1 [quant-ph])

Efficient overlap estimation of high-dimensional quantum states is an important task in quantum information and a core element in computational speedups of quantum machine learning. Here we experimentally demonstrate the SWAP test that measures the overlap of two motional states in a system of trapped $^{171}\mathrm{Yb}^+$ ions. To illustrate the versatility of our implementation, we report the overlap measurement of a variety of quantum states: Fock states, coherent states, squeezed vacuum states, and cat states. We highlight applications of the SWAP test by measuring the purity of mixed states. Our results enable quantum information processing with high dimensional quantum states.

Classical causal models cannot faithfully explain Bell nonlocality or Kochen-Specker contextuality in arbitrary scenarios. (arXiv:1909.05434v3 [quant-ph] UPDATED)

In a recent work, it was shown by one of us (EGC) that Bell-Kochen-Specker inequality violations in phenomena satisfying the no-disturbance condition (a generalisation of the no-signalling condition) cannot in general be explained with a faithful classical causal model — that is, a classical causal model that satisfies the assumption of no fine-tuning. The proof of that claim however was restricted to Bell scenarios involving 2 parties or Kochen-Specker-contextuality scenarios involving 2 measurements per context. Here we show that the result holds in the general case of arbitrary numbers of parties or measurements per context; it is not an artefact of the simplest scenarios. This result unifies, in full generality, Bell nonlocality and Kochen-Specker contextuality as violations of a fundamental principle of classical causality. We identify, however, an implicit assumption in the former proof, making it explicit here: that certain operational symmetries of the phenomenon are reflected in the model, rather than requiring fine-tuned choices of model parameters. This clarifies a subtle but important distinction between Bell nonlocality and Kochen-Specker contextuality.

3D-Space and the preferred basis cannot uniquely emerge from the quantum structure. (arXiv:2102.08620v3 [quant-ph] UPDATED)

Authors: Ovidiu Cristinel Stoica

Is it possible that only the state vector exists, and the 3D-space, a preferred basis, a preferred factorization of the Hilbert space, and everything else, emerge uniquely from the Hamiltonian and the state vector?

In this article no-go theorems are given, showing that whenever such a candidate preferred structure exists and can distinguish among physically distinct states, infinitely many physically distinct structures of the same kind exist. The idea of the proof is very simple: it is always possible to make a unitary transformation of the candidate structure into another one of the same kind, but with respect to which the state of the system at a given time appears identical to its (physically distinct) state at any other time, or even to states from “alternative realities”.

Therefore, such minimalist approaches lead to strange consequences like “passive” travel in time and in alternative realities, realized simply by passive transformations of the Hilbert space.

These theorems affect all minimalist theories in which the only fundamental structures are the state vector and the Hamiltonian, whether they assume branching or state vector reduction, in particular, the version of Everett’s Interpretation coined by Carroll and Singh “Mad-dog Everettianism”, various proposals based on decoherence, proposals that aim to describe everything by the quantum structure, and proposals that spacetime emerges from a purely quantum theory of gravity.

The Stable Marriage Problem: An interdisciplinary review from the physicist’s perspective

Publication date: Available online 16 March 2021

Source: Physics Reports

Author(s): Enrico Maria Fenoaltea, Izat B. Baybusinov, Jianyang Zhao, Lei Zhou, Yi-Cheng Zhang

Schr\”odinger’s cat for de Sitter spacetime. (arXiv:2012.10025v2 [gr-qc] UPDATED)

Authors: Joshua FooRobert B. MannMagdalena Zych

Quantum gravity is expected to contain descriptions of semiclassical spacetime geometries in quantum superpositions. To date, no framework for modelling such superpositions has been devised. Here, we provide a new phenomenological description for the response of quantum probes (i.e. Unruh-deWitt detectors) on a spacetime manifold in quantum superposition. By introducing an additional control degree of freedom, one can assign a Hilbert space to the spacetime, allowing it to exist in a superposition of spatial or curvature states. Applying this approach to static de Sitter space, we discover scenarios in which the effects produced by the quantum spacetime are operationally indistinguishable from those induced by superpositions of Rindler trajectories in Minkowski spacetime. The distinguishability of such quantum spacetimes from superpositions of trajectories in flat space reduces to the equivalence or non-equivalence of the field correlations between the superposed amplitudes.

Typicality of Dynamics and Laws of Nature

Filomeno, Aldo (2021) Typicality of Dynamics and Laws of Nature. [Preprint]

The Philosophy of Quantum Computing

Cuffaro, Michael E. (2021) The Philosophy of Quantum Computing. [Preprint]

Does the No Alternatives Argument need Gerrymandering to Be Significant?

Dawid, Richard (2021) Does the No Alternatives Argument need Gerrymandering to Be Significant? [Preprint]

Four Postulates of Quantum Mechanics Are Three

Author(s): Gabriele Carcassi, Lorenzo Maccone, and Christine A. Aidala

The tensor product postulate of quantum mechanics states that the Hilbert space of a composite system is the tensor product of the components’ Hilbert spaces. All current formalizations of quantum mechanics that do not contain this postulate contain some equivalent postulate or assumption (sometimes…

[Phys. Rev. Lett. 126, 110402] Published Tue Mar 16, 2021

Gauge-underdetermination and shades of locality in the Aharonov-Bohm effect

Mulder, Ruward A. (2021) Gauge-underdetermination and shades of locality in the Aharonov-Bohm effect. [Preprint]