Weekly Papers on Quantum Foundations (1)

Intrinsic quantum coherence in particle oscillations. (arXiv:2012.14866v1 [hep-ph])

The quantum field theoretical description of coherence in the oscillations of particles, especially neutrinos, is a standing problem in particle physics. In this talk, several inconsistencies of the standard approach to particle oscillations will be explained, and how they are resolved in a process-independent manner, by a novel approach inspired by the Bardeen–Cooper–Schrieffer theory of superconductivity and the Nambu–Jona-Lasinio model. The formalism leads to corrections to the neutrino oscillation probability originally written by Pontecorvo and Gribov, however the standard probability is validated in the ultrarelativistic neutrino limit. The massive neutrino states are interpreted as quasiparticles on a vacuum condensate of “Cooper pairs” of massless flavour neutrinos. The newly defined oscillating particle states are for neutrino oscillations what the Klauder–Sudarshan–Glauber coherent states are for quantum optics.

A path integral formulation for particle detectors: the Unruh-DeWitt model as a line defect. (arXiv:2012.14912v1 [hep-th])

Particle detectors are an ubiquitous tool for probing quantum fields in the context of relativistic quantum information (RQI). We formulate the Unruh-DeWitt (UDW) particle detector model in terms of the path integral formalism. The formulation is able to recover the results of the model in general globally hyperbolic spacetimes and for arbitrary detector trajectories. Integrating out the detector’s degrees of freedom yields a line defect that allows one to express the transition probability in terms of Feynman diagrams. Inspired by the light-matter interaction, we propose a gauge invariant detector model whose associated line defect is related to the derivative of a Wilson line. This is another instance where nonlocal operators in gauge theories can be interpreted as physical probes for quantum fields.

Causal influence in operational probabilistic theories. (arXiv:2012.15213v1 [quant-ph])

We study the relation of causal influence between input systems of a reversible evolution and its output systems, in the context of operational probabilistic theories. We analyse two different definitions that are borrowed from the literature on quantum theory — where they are equivalent. One is the notion based on signalling, and the other one is the notion used to define the neighbourhood of a cell in a quantum cellular automaton. The latter definition, that we adopt in the general scenario, turns out to be strictly weaker than the former: it is possible for a system to have causal influence on another one without signalling to it. We stress that, according to our definition, it is impossible anyway to have causal influence in the absence of an interaction, e.g.~in a Bell-like scenario. We study various conditions for causal influence, and introduce the feature that we call {\em no interaction without disturbance}, under which we prove that signalling and causal influence coincide.

Zeroth Law in Quantum Thermodynamics at Strong Coupling: in Equilibrium’, not Equal Temperature’. (arXiv:2012.15607v1 [cond-mat.stat-mech])

The zeroth law of thermodynamics involves a transitivity relation (pairwise between three objects) expressed either in terms of equal temperature’ (ET), or in equilibrium’ (EQ) conditions. In conventional thermodynamics conditional on vanishingly weak system-bath coupling these two conditions are commonly regarded as equivalent. In this work we show that for thermodynamics at strong coupling they are inequivalent: namely, two systems can be in equilibrium and yet have different effective temperatures. A recent result \cite{NEqFE} for Gaussian quantum systems shows that an effective temperature $T^{*}$ can be defined at all times during a system’s nonequilibrium evolution, but because of the inclusion of interaction energy, after equilibration the system’s $T^*$ is slightly higher than the bath temperature $T_{\textsc{b}}$, with the deviation depending on the coupling. A second object coupled with a different strength with an identical bath at temperature $T_{\textsc{b}}$ will not have the same equilibrated temperature as the first object. Thus $ET \neq EQ$ for strong coupling thermodynamics. We then investigate the conditions for dynamical equilibration for two objects 1 and 2 strongly coupled with a common bath $B$, each with a different equilibrated effective temperature. We show this is possible, and prove the existence of a generalized fluctuation-dissipation relation under this configuration. This affirms that in equilibrium’ is a valid and perhaps more fundamental notion which the zeroth law for quantum thermodynamics at strong coupling should be based on. Only when the system-bath coupling becomes vanishingly weak that temperature’ appearing in thermodynamic relations becomes universally defined and makes better physical sense.

Quantum chaos challenges many-body localization. (arXiv:1905.06345v4 [cond-mat.str-el] UPDATED)

Characterizing states of matter through the lens of their ergodic properties is a fascinating new direction of research. In the quantum realm, the many-body localization (MBL) was proposed to be the paradigmatic ergodicity breaking phenomenon, which extends the concept of Anderson localization to interacting systems. At the same time, random matrix theory has established a powerful framework for characterizing the onset of quantum chaos and ergodicity (or the absence thereof) in quantum many-body systems. Here we numerically study the spectral statistics of disordered interacting spin chains, which represent prototype models expected to exhibit MBL. We study the ergodicity indicator $g=\log_{10}(t_{\rm H}/t_{\rm Th})$, which is defined through the ratio of two characteristic many-body time scales, the Thouless time $t_{\rm Th}$ and the Heisenberg time $t_{\rm H}$, and hence resembles the logarithm of the dimensionless conductance introduced in the context of Anderson localization. We argue that the ergodicity breaking transition in interacting spin chains occurs when both time scales are of the same order, $t_{\rm Th} \approx t_{\rm H}$, and $g$ becomes a system-size independent constant. Hence, the ergodicity breaking transition in many-body systems carries certain analogies with the Anderson localization transition. Intriguingly, using a Berezinskii-Kosterlitz-Thouless correlation length we observe a scaling solution of $g$ across the transition, which allows for detection of the crossing point in finite systems. We discuss the observation that scaled results in finite systems by increasing the system size exhibit a flow towards the quantum chaotic regime.

Quantum Information for Particle Theorists. (arXiv:2010.02931v2 [quant-ph] UPDATED)

Lectures given at the Theoretical Advanced Study Institute (TASI 2020), 1-26 June 2020. The topics covered include quantum circuits, entanglement, quantum teleportation, Bell inequalities, quantum entropy and decoherence, classical versus quantum measurement, the area law for entanglement entropy in quantum field theory, and simulating quantum field theory on a quantum computer. Along the way we confront the fundamental sloppiness of how we all learned (and some of us taught) quantum mechanics in college. Links to a Python notebook and Mathematica notebooks will allow the reader to reproduce and extend the calculations, as well as perform five experiments on a quantum simulator.

Noether Theorems and Reality of Motion. (arXiv:1601.02847v3 [physics.hist-ph] UPDATED)

Authors: M. PaleseE. Winterroth

We will read, through the Emmy Noether paper and the two concepts of proper’ and improper’ conservation laws, the problem, posed by Hilbert, of the nature of the law of conservation of energy in the theory of General Relativity. Epistemological issues involved with the two kind of conservation laws will be enucleate.

Black holes and other clues to the quantum structure of gravity. (arXiv:2012.14434v1 [gr-qc])

Authors: Steven B. Giddings

Bringing gravity into a quantum-mechanical framework is likely the most profound remaining problem in fundamental physics. The “unitarity crisis” for black hole evolution appears to be a key facet of this problem, whose resolution will provide important clues. Investigating this raises the important structural question of how to think about subsystems and localization of information in quantum gravity. Paralleling field theory, the answer to this is expected to be an important ingredient in the mathematical structure of the theory. Perturbative gravity results indicate a structure different from that of quantum field theory, but suggest an avenue to defining subsystems. If black holes do behave similarly to familiar subsystems, unitarity demands new interactions that transfer entanglement from them. Such interactions can be parameterized in an effective approach, without directly addressing the question of the fundamental dynamics, whether that is associated with quantum spacetime, wormholes, or something else. Since such interactions need to extend outside the horizon, that raises the question of whether they can be constrained, or might be observed, by new electromagnetic or gravitational wave observations of strong gravity regions. This note overviews and provides connections between these developments.

Consistency of quantum computation and the equivalence principle. (arXiv:2012.14990v1 [quant-ph])

Authors: Marcin Nowakowski

The equivalence principle, being one of the building blocks of general relativity, seems to be also crucial for analysis of quantum effects in gravity. In this paper we consider the question if the equivalence principle has to hold for consistency of performing quantum computation in gravitational field. We propose an analysis with a looped evolution consisting of steps both in the gravitational field and in the accelerated reference frame. We show that without the equivalence principle the looped quantum evolution cannot be unitary and looses its consistency. For this reasoning the equivalence principle is formulated in terms of the gauge transformations and is analyzed for particles acquiring an appropriate phases associated with the actions over the looped path. In consequence, to keep consistency of quantum operations in gravitational field, it is required to keep some quantum variant of the equivalence principle. This proves importance of the quantized versions of this fundamental gravitational principle for quantum information processing.

Quantum nonlocality in extended theories of gravity. (arXiv:2012.15331v1 [gr-qc])

We investigate how pure-state Einstein-Podolsky-Rosen correlations in the internal degrees of freedom of massive particles are affected by a curved spacetime background described by extended theories of gravity. We consider models for which the corrections to the Einstein-Hilbert action are quadratic in the curvature invariants and we focus on the weak-field limit. We quantify nonlocal quantum correlations by means of the violation of the Clauser-Horne-Shimony-Holt inequality, and show how a curved background suppresses the violation by a leading term due to general relativity and a further contribution due to the corrections to Einstein gravity. Our results can be generalized to massless particles such as photon pairs and can thus be suitably exploited to devise precise experimental tests of extended models of gravity.

Collapse models and cosmology. (arXiv:1912.07429v3 [quant-ph] UPDATED)

Authors: Jerome MartinVincent Vennin

Attempts to apply quantum collapse theories to Cosmology and cosmic inflation are reviewed. These attempts are motivated by the fact that the theory of cosmological perturbations of quantum-mechanical origin suffers from the single outcome problem, which is a modern incarnation of the quantum measurement problem, and that collapse models can provide a solution to these issues. Since inflationary predictions can be very accurately tested by cosmological data, this also leads to constraints on collapse models. These constraints are derived in the case of Continuous Spontaneous Localization (CSL) and are shown to be of unprecedented efficiency.

Reviving Frequentism

Hubert, Mario (2021) Reviving Frequentism. [Preprint]

Philosophy of Probability and Statistical Modeling

Suárez, Mauricio (2020) Philosophy of Probability and Statistical Modeling. Elements in the Philosophy of Science series. ISSN 9781108985826

The End of a Classical Ontology for Quantum Mechanics?

Evans, Peter W (2020) The End of a Classical Ontology for Quantum Mechanics? Entropy, 23 (1). p. 12. ISSN 1099-4300

Abduction – the Context of Discovery + Underdetermination = Inference to the Best Explanation

Mohammadian, Mousa (2019) Abduction – the Context of Discovery + Underdetermination = Inference to the Best Explanation. Synthese. ISSN 1573-0964

The explanatory nature of constraints: Law-based, mathematical, and causal

Ross, Lauren N. (2020) The explanatory nature of constraints: Law-based, mathematical, and causal. [Preprint]