# Weekly Papers on Quantum Foundations (42)

Characterizing quantum instruments: from non-demolition measurements to quantum error correction. (arXiv:2110.06954v1 [quant-ph])

In quantum information processing quantum operations are often processed alongside measurements which result in classical data. Due to the information gain of classical measurement outputs non-unitary dynamical processes can take place on the system, for which common quantum channel descriptions fail to describe the time evolution. Quantum measurements are correctly treated by means of so-called quantum instruments capturing both classical outputs and post-measurement quantum states. Here we present a general recipe to characterize quantum instruments alongside its experimental implementation and analysis. Thereby, the full dynamics of a quantum instrument can be captured, exhibiting details of the quantum dynamics that would be overlooked with common tomography techniques. For illustration, we apply our characterization technique to a quantum instrument used for the detection of qubit loss and leakage, which was recently implemented as a building block in a quantum error correction (QEC) experiment (Nature 585, 207-210 (2020)). Our analysis reveals unexpected and in-depth information about the failure modes of the implementation of the quantum instrument. We then numerically study the implications of these experimental failure modes on QEC performance, when the instrument is employed as a building block in QEC protocols on a logical qubit. Our results highlight the importance of careful characterization and modelling of failure modes in quantum instruments, as compared to simplistic hardware-agnostic phenomenological noise models, which fail to predict the undesired behavior of faulty quantum instruments. The presented methods and results are directly applicable to generic quantum instruments.

Coherent energy fluctuation theorems: theory and experiment. (arXiv:2110.07061v1 [quant-ph])

Heat, work and entropy production: the statistical distribution of such quantities are constrained by the fluctuation theorems (FT), which reveal crucial properties about the nature of non-equilibrium dynamics. In this paper we report theoretical and experimental results regarding two FT for a new quantity, named coherent energy, which is an energy form directly associated with the coherences of the quantum state. We also demonstrate that this quantity behaves as a thermodynamic arrow of time for unitary evolutions, that is, in the absence of entropy production. The experiment is implemented in an all-optical setup in which the system is encoded in the polarization of one photon of a pair. The FT are demonstrated using the two-point measurement protocol, executed using the other photon of the pair, allowing to assess the probability distributions directly from the outcomes of the experiment.

Finite-dimensional quantum observables are the special symmetric $\dagger$-Frobenius algebras of CP maps. (arXiv:2110.07074v1 [quant-ph])

We use purity, a principle borrowed from the foundations of quantum information, to show that all special symmetric $\dagger$-Frobenius algebras in $\operatorname{CPM}\left(\operatorname{fHilb}\right)$ — and, in particular, all classical structures — are canonical, i.e. that they arise by doubling of special symmetric $\dagger$-Frobenius algebras in $\operatorname{fHilb}$. This provides an exact classification of finite-dimensional quantum observables.

Physical mechanisms underpinning the vacuum permittivity. (arXiv:2110.07223v1 [quant-ph])

Debate about the emptiness of the space goes back to the prehistory of science and is epitomized by the Aristotelian \emph{horror vacui}, which can be seen as the precursor of the ether, whose modern version is the dynamical quantum vacuum. Here, we change our view to \emph{gaudium vacui} and discuss how the vacuum fluctuations fix the value of the permittivity $\varepsilon_{0}$ and permeability $\mu_{0}$.

Quantum state preparation, tomography, and entanglement of mechanical oscillators. (arXiv:2110.07561v1 [quant-ph])

Precisely engineered mechanical oscillators keep time, filter signals, and sense motion, making them an indispensable part of today’s technological landscape. These unique capabilities motivate bringing mechanical devices into the quantum domain by interfacing them with engineered quantum circuits. Proposals to combine microwave-frequency mechanical resonators with superconducting devices suggest the possibility of powerful quantum acoustic processors. Meanwhile, experiments in several mechanical systems have demonstrated quantum state control and readout, phonon number resolution, and phonon-mediated qubit-qubit interactions. Currently, these acoustic platforms lack processors capable of controlling multiple mechanical oscillators’ quantum states with a single qubit, and the rapid quantum non-demolition measurements of mechanical states needed for error correction. Here we use a superconducting qubit to control and read out the quantum state of a pair of nanomechanical resonators. Our device is capable of fast qubit-mechanics swap operations, which we use to deterministically manipulate the mechanical states. By placing the qubit into the strong dispersive regime with both mechanical resonators simultaneously, we determine the resonators’ phonon number distributions via Ramsey measurements. Finally, we present quantum tomography of the prepared nonclassical and entangled mechanical states. Our result represents a concrete step toward feedback-based operation of a quantum acoustic processor.

Why and whence the Hilbert space in quantum theory?. (arXiv:2110.05932v2 [physics.gen-ph] UPDATED)

We explain why and how the Hilbert space comes about in quantum theory. The axiomatic structures of a vector space, of scalar product, of orthogonality, and of the linear functional are derivable from the statistical description of quantum micro-events and from Hilbertian sum of squares $|\mathfrak{a}_1|^2+|\mathfrak{a}_2|^2+\cdots$. The latter leads (non-axiomatically) to the standard writing of the Born formula $\mathtt{f}=|\langle\psi|\varphi\rangle|^2$. As a corollary, the status of Pythagorean theorem, the concept of a length, and the 6-th Hilbert problem undergo a quantum revision’. An issue of deriving the normed topology is likely solvable in the affirmative and has been stated as a mathematical problem.

Bell’s theorem: A bridge between the measurement and the mind/body problems. (arXiv:2110.06927v1 [physics.hist-ph])

In this essay a quantum-dualistic, perspectival and synchronistic interpretation of quantum mechanics is further developed in which the classical world-from-decoherence which is perceived (decoherence) and the perceived world-in-consciousness which is classical (collapse) are not necessarily identified. Thus, Quantum Reality or “{\it unus mundus}” is seen as both i) a physical non-perspectival causal Reality where the quantum-to-classical transition is operated by decoherence, and as ii) a quantum linear superposition of all classical psycho-physical perspectival Realities which are governed by synchronicity as well as causality (corresponding to classical first-person observes who actually populate the world). This interpretation is termed the Nietzsche-Jung-Pauli interpretation and is a re-imagining of the Wigner-von Neumann interpretation which is also consistent with some reading of Bohr’s quantum philosophy.

“Mysteries” of Modern Physics and the Fundamental Constants $c$, $h$, and $G$. (arXiv:2110.06974v1 [quant-ph])

We review how the kinematic structures of special relativity and quantum mechanics both stem from the relativity principle, i.e., “no preferred reference frame” (NPRF). Essentially, NPRF applied to the measurement of the speed of light $c$ gives the light postulate and leads to the geometry of Minkowski spacetime, while NPRF applied to the measurement of Planck’s constant $h$ gives “average-only” projection and leads to the denumerable-dimensional Hilbert space of quantum mechanics. These kinematic structures contain the counterintuitive aspects (“mysteries”) of time dilation, length contraction, and quantum entanglement. In this essay, we extend the application of NPRF to the gravitational constant $G$ and show that it leads to the “mystery” of the contextuality of mass in general relativity. Thus, we see an underlying coherence and integrity in modern physics via its “mysteries” and the fundamental constants $c$, $h$, and $G$.

Same-diff? Part I: Conceptual similarities (and one difference) between gauge transformations and diffeomorphisms. (arXiv:2110.07203v1 [physics.hist-ph])

Authors: Henrique Gomes

The following questions are germane to our understanding of gauge-(in)variant quantities and physical possibility: in which ways are gauge transformations and spacetime diffeomorphisms similar, and in which are they different? To what extent are we justified in endorsing different attitudes — sophistication, quidditism/haecceitism, or full elimination — towards each? In a companion paper, I assess new and old contrasts between the two types of symmetries. In this one, I propose a new contrast: whether the symmetry changes pointwise the dynamical properties of a given field. This contrast distinguishes states that are related by a gauge-symmetry from states related by generic spacetime diffeomorphisms, as being pointwise dynamically indiscernible’. Only the rigid isometries of homogeneous spacetimes fall in the same category, but they are neither local nor modally robust, in the way that gauge transformations are. In spite of this difference, I argue that for both gauge transformations and spacetime diffeomorphisms, symmetry-related models are best understood through the doctrine of sophistication’.

Same Diff? Part II: A compendium of similarities between gauge transformations and diffeomorphisms. (arXiv:2110.07204v1 [physics.hist-ph])

Authors: Henrique Gomes

How should we understand gauge-(in)variant quantities and physical possibility? Does the redundancy present in gauge theory pose different interpretational issues than those present in general relativity? Here, I will assess new and old contrasts between general relativity and Yang-Mills theory, in particular, in relation to their symmetries. I will focus these comparisons on four topics: (i) non-locality, (ii) conserved charges, (iii) Aharonov-Bohm effect, and (iv) the choice of representational conventions of the field configuration. In a companion paper, I propose a new contrast and defend sophistication for both theories.

Noether charges: the link between empirical significance of symmetries and non-separability. (arXiv:2110.07208v1 [physics.hist-ph])

Authors: Henrique Gomes

A fundamental tenet of gauge theory is that physical quantities should be gauge-invariant. This prompts the question: can gauge symmetries have physical significance? On one hand, the Noether theorems relate conserved charges to symmetries, endowing the latter with physical significance, though this significance is sometimes taken as indirect. But for theories in spatially finite and bounded regions, the standard Noether charges are not gauge-invariant. I here argue that gauge-\emph{variance} of charges is tied to the nature of the non-locality within gauge theories. I will flesh out these links by providing a chain of (local) implications: local conservation laws’${\Rightarrow}$ conserved regional charges’ $\Leftrightarrow$ non-separability’ ${\Leftrightarrow}$ `direct empirical significance of symmetries’.

An Algebraic Approach to Physical Fields. (arXiv:2108.07184v2 [physics.hist-ph] UPDATED)

Authors: Lu ChenTobias Fritz

According to the algebraic approach to spacetime, a thoroughgoing dynamicism, physical fields exist without an underlying manifold. This view is usually implemented by postulating an algebraic structure (e.g., commutative ring) of scalar-valued functions, which can be interpreted as representing a scalar field, and deriving other structures from it. In this work, we point out that this leads to the unjustified primacy of an undetermined scalar field. Instead, we propose to consider algebraic structures in which all (and only) physical fields are primitive. We explain how the theory of \emph{natural operations} in differential geometry — the modern formalism behind classifying diffeomorphism-invariant constructions — can be used to obtain concrete implementations of this idea for any given collection of fields.

For concrete examples, we illustrate how our approach applies to a number of particular physical fields, including electrodynamics coupled to a Weyl spinor.

Publication date: Available online 12 October 2021

Source: Physics Reports

Author(s): Suvrat Raju

Light, delayed: The Shapiro Effect and the Newtonian Limit. (arXiv:2110.07016v1 [gr-qc])

Authors: Markus Pössel

The Shapiro effect, also known as the gravitational time delay, is close kin to the gravitational deflection of light that was the central topic of our Summer School. It is also an interesting test bed for exploring a topic that provides the foundations for most of the calculations we have done in this school, yet is highly complex when treated more rigorously: the question of the Newtonian limit, and of the post-Newtonian corrections that must be applied to include the leading-order effects of general relativity. This contribution discusses simplified derivations for the gravitational redshift and the Shapiro effect, as well as astrophysical situations in which the Shapiro effect can be measured.

Edge modes as reference frames and boundary actions from post-selection. (arXiv:2109.06184v3 [hep-th] UPDATED)

Authors: Sylvain CarrozzaPhilipp A. Hoehn

We introduce a general framework realizing edge modes in (classical) gauge field theory as dynamical reference frames, an often suggested interpretation that we make entirely explicit. We focus on a bounded region $M$ with a co-dimension one time-like boundary $\Gamma$, which we embed in a global spacetime. Taking as input a variational principle at the global level, we develop a systematic formalism inducing consistent variational principles (and in particular, boundary actions) for the subregion $M$. This relies on a post-selection procedure on $\Gamma$, which isolates the subsector of the global theory compatible with a general choice of gauge-invariant boundary conditions for the dynamics in $M$. Crucially, the latter relate the configuration fields on $\Gamma$ to a dynamical frame field carrying information about the spacetime complement of $M$; as such, they may be equivalently interpreted as frame-dressed or relational observables. Generically, the external frame field keeps an imprint on the ensuing dynamics for subregion $M$, where it materializes itself as a local field on the time-like boundary $\Gamma$; in other words, an edge mode. We identify boundary symmetries as frame reorientations and show that they divide into three types, depending on the boundary conditions, that affect the physical status of the edge modes. Our construction relies on the covariant phase space formalism, and is in principle applicable to any gauge (field) theory. We illustrate it on three standard examples: Maxwell, Abelian Chern-Simons and non-Abelian Yang-Mills theories. In complement, we also analyze a mechanical toy-model to connect our work with recent efforts on (quantum) reference frames.

Fundamentality

French, Steven (2021) Fundamentality. [Preprint]

Cosmological Realism

Merritt, David (2020) Cosmological Realism. [Preprint]

Neither Contextuality nor Nonlocality Admits Catalysts

Author(s): Martti Karvonen

We show that the resource theory of contextuality does not admit catalysts, i.e., there are no correlations that can enable an otherwise impossible resource conversion and still be recovered afterward. As a corollary, we observe that the same holds for nonlocality. As entanglement allows for catalys…

[Phys. Rev. Lett. 127, 160402] Published Wed Oct 13, 2021

Anderson Localization of Composite Particles

Author(s): Fumika Suzuki, Mikhail Lemeshko, Wojciech H. Zurek, and Roman V. Krems

We investigate the effect of coupling between translational and internal degrees of freedom of composite quantum particles on their localization in a random potential. We show that entanglement between the two degrees of freedom weakens localization due to the upper bound imposed on the inverse part…

[Phys. Rev. Lett. 127, 160602] Published Tue Oct 12, 2021

Thermodynamic Uncertainty Relation and Thermodynamic Speed Limit in Deterministic Chemical Reaction Networks

Author(s): Kohei Yoshimura and Sosuke Ito

The thermodynamic uncertainty relation and speed limit provide fundamental bounds relating basic properties of chemical reaction networks and their diffusion coefficients.

[Phys. Rev. Lett. 127, 160601] Published Mon Oct 11, 2021

On the alleged extra-structures of quantum mechanics

Romano, Davide (2021) On the alleged extra-structures of quantum mechanics. [Preprint]