Quantum Foundations

In spite of its immense importance in the present-day information technology, the foundational aspects of quantum theory (QT) remain still elusive. In particular, there is no such set of physically motivated axioms which can answer why Hilbert space formalism is the only natural choice to describe the microscopic world. Hence, to shed light on the unique formalism of QT, two different operational frameworks will be described in the primitive of various convex operational theories. The first one refers to a kinematical symmetry principle which would be proposed from the perspective of single copy state discrimination and it would be shown that this symmetry holds for both classical and QT – two successful descriptions of the physical world. On the other hand, studying a wide range of convex operational theories, namely the General Probabilistic Theories (GPTs) with polygonal state spaces, we observe the absence of such symmetry. Thus, the principle deserves its own importance to mark a sharp distinction between the physical and unphysical theories. Thereafter, a distributed computing scenario will be introduced for which the other convex theories except the QT turn out to be equivalent to the classical one even though the theories possess more exotic state and effect spaces. We have coined this particular operational framework as ‘Distributed computation with limited communication’ (DCLC). Furthermore, it will be shown that the distributed computational strength of quantum communication will be justified in terms of a stronger version of this task, namely the ‘Delayed choice distributed computation with limited communication’ (DC2LC). The proposed task thus provides a new approach to operationally single out quantum theory in the theory-space and hence promises a novel perspective towards the axiomatic derivation of Hilbert space quantum mechanics.

References:
Phys. Rev. A (Rapid)100, 060101 (2019)
Ann. Phys.(Berlin)2020,532, 2000334 (2020)
arXiv:2012.05781 [quant-ph](2020)

Zoom link:  https://pitp.zoom.us/j/92924188227?pwd=ODJYQXVoaUtzZmZIdFlmcUNIV3Rmdz09

In the context of irreversible dynamics, the meaning of the reverse of a physical evolution can be quite ambiguous. It is a standard choice to define the reverse process using Bayes' theorem, but, in general, this is not optimal with respect to the relative entropy of recovery. In this work we explore whether it is possible to characterise an optimal reverse map building from the concept of state retrieval maps. In doing so, we propose a set of  principles that state retrieval maps should satisfy. We find out that the Bayes inspired reverse is just one case in a whole class of possible choices, which can be optimised to give a map retrieving the initial state more precisely than the Bayes rule. Our analysis has the advantage of naturally extending to the quantum regime. In fact, we find a class of reverse transformations containing the Petz recovery map as a particular case, corroborating its interpretation as a quantum analogue of the Bayes retrieval.

Finally, we present numerical evidence showing that by adding a single extra axiom one can isolate for classical dynamics the usual reverse process derived from Bayes' theorem.

Zoom link:  https://pitp.zoom.us/j/93589286500?pwd=dkZuRzR0SlhVd1lPdGNOZWFYQWtRZz09

Non-normalizable quantum states are usually discarded as mathematical artefacts in quantum mechanics. However, such states naturally occur in quantum gravity as solutions to physical constraints. This suggests reconsidering the interpretation of such states. Some of the existing approaches to this question seek to redefine the inner product, but this arguably leads to further challenges. 

In this talk, I will propose an alternative interpretation of non-normalizable states using pilot-wave theory. First, I will argue that the basic conceptual structure of the theory contains a straightforward interpretation of these states. Second, to better understand such states, I will discuss non-normalizable states of the quantum harmonic oscillator from a pilot-wave perspective. I will show that, contrary to intuitions from orthodox quantum mechanics, the non-normalizable eigenstates and their superpositions are bound states in the sense that the pilot-wave velocity field vy→0 at large ±y. Third, I will introduce a new notion of equilibrium, named pilot-wave equilibrium, and use it to define physically-meaningful equilibrium densities for such states. I will show, via an H-theorem, that an arbitrary initial density with compact support relaxes to pilot-wave equilibrium at a coarse-grained level, under assumptions similar to those for relaxation to quantum equilibrium. I will conclude by discussing the implications for pilot-wave theory, quantum gravity and quantum foundations in general. 

Based on:

I. Sen. "Physical interpretation of non-normalizable harmonic oscillator states and relaxation to pilot-wave equilibrium" arXiv:2208.08945 (2022)

Zoom link:  https://pitp.zoom.us/j/93736627504?pwd=VGtxZE5rTFdnT1dqZlFRWTFvWlFQUT09

Quantum correlations in general and quantum entanglement in particular embody both our continued struggle towards a foundational understanding of quantum theory as well as the latter’s advantage over classical physics in various information processing tasks. Consequently, the problems of classifying (i) quantum states from more general (non-signalling) correlations, and (ii) entangled states within the set of all quantum states, are at the heart of the subject of quantum information theory.

In this talk I will present two recent results (from https://journals.aps.org/pra/abstract/10.1103/PhysRevA.106.062420 and https://arxiv.org/abs/2207.00024) that shed new light on these problems, by exploiting a surprising connection with time in quantum theory:

First, I will sketch a solution to problem (i) for the bipartite case, which identifies a key physical principle obeyed by quantum theory: quantum states preserve local time orientations—roughly, the unitary evolution in local subsystems.

Second, I will show that time orientations are intimately connected with quantum entanglement: a bipartite quantum state is separable if and only if it preserves arbitrary local time orientations. As a variant of Peres's well-known entanglement criterion, this provides a solution to problem (ii).

Zoom link:  https://pitp.zoom.us/j/97607837999?pwd=cXBYUmFVaDRpeFJSZ0JzVmhSajdwQT09

Superdeterminism has received a recent surge of attention in the foundations community. A particular superdeterministic proposal, named Invariant-set theory, appears to bring ideas from several diverse fields (eg. number theory, chaos theory etc.) to quantum foundations and provides a novel justification for the choice of initial conditions in terms of state-space geometry. However, the lack of a concrete hidden-variable model makes it difficult to evaluate the proposal from a foundational perspective. 

In this talk, I will critically analyse this superdeterministic proposal in three steps. First, I will show how to build a hidden-variable model based on the proposal's ideas. Second, I will analyse the properties of the model and show that several arguments that appear to work in the proposal (on counter-factual measurements, non-commutativity etc.) fail when considered in the model. Further, the model is not only superdeterministic but also nonlocal, $\psi$-ontic and contains redundant information in its bit-string. Third, I will discuss the accuracy of the model in representing the proposal. I will consider the arguments put forward to claim inaccuracy and show that they are incorrect. My results lend further support to the view that superdeterminism is unlikely to solve the puzzle posed by the Bell correlations.

Based on the papers: 

1. I. Sen. "Analysis of the superdeterministic Invariant-set theory in a hidden-variable setting." Proc. R. Soc. A 478.2259 (2022): 20210667.

2. I. Sen. "Reply to superdeterminists on the hidden-variable formulation of Invariant-set theory." arXiv:2109.11109 (2021).

Zoom link:  https://pitp.zoom.us/j/99415427245?pwd=T3NOWUxKTENnMThRVEd3ZTRzU3ZKZz09

Central to many of the paradoxes arising in quantum theory is that the act of measurement cannot be understood as merely revealing the pre-existing values of some hidden variables, a phenomenon known as contextuality. In the past few years quantum contextuality has been formalized in a variety of ways; operation-theoretic, sheaf-theoretic, (hyper)graph-theoretic, and cohomological. In this seminar we will discuss the simplicial approach to contextuality introduced in arXiv:2204.06648, which builds off the earlier sheaf-theoretic approach of Abramsky-Brandenberger (arXiv:1102.0264) and the cohomological approach of Okay, et al. (arXiv:1701.01888). In the simplicial approach measurement scenarios and their statistics can be modeled topologically as simplicies using the theory of simplicial sets. The connection to topology provides an additional analytical handle, allowing for a rigorous study of both state-dependent and state-independent contextuality. Using this formalism we present a novel topological proof of Fine's theorem for characterizing noncontextuality in Bell scenarios.

Zoom link:  https://pitp.zoom.us/j/93748699892?pwd=SVhVaTdoRmlwaGdCZVdIWVlKTktjQT09

In the new wave of quantum foundations activity with its indirect approach to problems of fundamental ontology, individual explicit positions of informational immaterialism are replaced by a shared "soft informatic realism" that governs research practice, encouraging conflation of theories of information processes and theories of physical processes, and disregard for the microphysical dynamics effecting a given information process.  This kind of abstraction, indispensable in the formulation of enlightening no-go theorems, can become problematic when imported to certain other projects, including recently popular investigations of quantum causal structure.  I shall provide examples, describe ramifications for the efficiency of knowledge production in quantum foundations, and consider when features of quantum information processing can legitimately be called informatic features of quantum physics.

Zoom link:  https://pitp.zoom.us/j/93415836509?pwd=MXJLZVVzMnZjcWFQSWM0dmg5czE3dz09

We consider two interacting systems when one is treated classically while the other remains quantum. Despite several famous no-go arguments, consistent dynamics of this coupling exist, and its most general form can be derived. We discuss the application of these dynamics to the foundations of quantum theory, and to the problem of understanding gravity when space-time is treated classically while matter has a quantum nature.

The talk will be informal and I'll review and follow on from joint work with Isaac Layton, Andrea Russo, Carlo Sparaciari, Barbara Šoda & Zachary Weller-Davies

https://arxiv.org/abs/2208.11722
https://arxiv.org/abs/2203.01982
https://arxiv.org/abs/1811.03116

Zoom link:  https://pitp.zoom.us/j/92520708199?pwd=WUowdnd4Z0k3dlU2YjVmVlAva3Q0UT09

The usual quantum mechanical description of measurements, unitary kicks, and other local operations has the potential to produce pathological causality violations in the relativistic setting of quantum field theory (QFT). While there are some operations that do not violate causality, those that do cannot be physically realisable. For local observables in QFT it is an open question whether the projection postulate, or more specifically the associated ideal measurement operation, is consistent with causality, and hence whether it is physically realisable in principle.

In this talk I will recap a criteria that distinguishes causal and acausal operations in real scalar QFT. I will then focus on operations constructed from smeared field operators - the basic local observables of the theory. For this simple class of operations we can write down a more practical causality criteria. With this we find that, under certain assumptions - such as there being a continuum spacetime - ideal measurements of smeared fields are acausal, despite prior heuristic arguments to the contrary. For a discrete spacetime (e.g. a causal set), however, one can evade this result in a ‘natural’ way, and thus uphold causality while retaining the projection postulate.

Zoom link:  https://pitp.zoom.us/j/94464896161?pwd=UkhPQnJONmlxYy9pQXJINThpY3l4QT09

Generalized noncontextuality is a well-studied notion of classicality that is applicable to a single system, as opposed to Bell locality. It relies on representing operationally indistinguishable procedures identically in an ontological model. However, operational indistinguishability depends on the set of operations that one may use to distinguish two procedures: we refer to this set as the reference of indistinguishability. Thus, whether or not a given experiment is noncontextual depends on the choice of reference. The choices of references appearing in the literature are seldom discussed, but typically relate to a notion of system underlying the experiment. This shift in perspective then begs the question: how should one define the extent of the system underlying an experiment? Our paper primarily aims at exposing this question rather than providing a definitive answer to it. We start by formulating a notion of relative noncontextuality for prepare-and-measure scenarios, which is simply noncontextuality with respect to an explicit reference of indistinguishability. We investigate how verdicts of relative noncontextuality depend on this choice of reference, and in the process introduce the concept of the noncontextuality graph of a prepare-and-measure scenario. We then discuss several proposals that one may appeal to in order to fix the reference to a specific choice, and relate these proposals to different conceptions of what a system really is.

arXiv link:  https://arxiv.org/abs/2209.04469

Zoom link:  https://pitp.zoom.us/j/97393198973?pwd=dWhCOUJQLytxeXVIVmEvOHRnRHc1QT09

Joint work (in progress) with Ladina Hausmann, Nuriya Nurgalieva and Renato Renner

We can classify contemporary approaches to thermodynamics in roughly four camps:

(1) Top-down microscopic approaches. These are for example resource-theoretical approaches to quantum thermodynamics: they have a microscopic model of states and systems, and which microscopic restrictions implement macroscopic properties. For instance, in the resource theory of quantum thermodynamics, states are represented by density operators, thermal states in particular have a specific micro-canonical form, and constraints like energy preservation are enforced by forcing quantum transformations to commute with a global Hamiltonian. These approaches success at deriving thermodynamic laws in general settings that satisfy the microscopic model (like non-relativistic quantum systems.

(2) Bottom-up microscopic approaches. These also start from a microscopic model, but rather than looking for universal restrictions, they search for explicit thermodynamics protocols: this is the case of recent proposals for quantum work extraction or nano quantum heat engines.

(3) Top-down phenomenological approaches. These try to derive thermodynamic laws from first principles independently of a microscopic model. In principle the results derived in this framework can be applied to a wider variety of explicit systems, and the challenge is then to find the right implementations.  The first derivations of thermodynamics were naturally phenomenological, and some modern information-inspired derivations follow this approach.

(4) Bottom-up phenomenological approaches. These approaches try to find explicit thermodynamic protocols independently of the microscopic model, based only on operational properties of the systems at hand. It was the case for Carnot's original engines and more recently for some approaches to deriving black hole thermodynamics, or thermodynamics of new materials; some experimental results also fit in this camp.

In this work we generalize top-down phenomenological approaches to the case of multiple conserved quantities. Note that multiple conserved quantities have been studied in top-down and bottom-up microscopic approaches to quantum thermodynamics. We argue that our framework is more general, in that it can be applied to systems for which we don't have an explicit microscopic model; in particular we will apply the results of this framework to black hole thermodynamics. Moreover, having a phenomenological axiomatic approach to thermodynamics allows us to identify which properties are specific to a microscopic model like quantum physics, and which hold in any physical theory: our results can be applied to study the thermodynamics of generalized process theories, and other generalizations and foils of quantum mechanics. This generalization makes us reconsider the second law of thermodynamics, adapting for an exchange of different conserved quantities, for example, energy and angular momentum, or energy and spin. Our guiding principle here is to use information as a universal token of exchange to convert between different quantities via Landauer's principle.

Zoom Link: https://pitp.zoom.us/j/96001094153?pwd=YTArTGpPdEJ1NFBMcnFqV1dIRTVyZz09

Information is physical, and for a physical theory to be universal, it
should model observers as physical systems, with concrete memories where
they store the information acquired through experiments and reasoning.
Here we address these issues in Spekkens' toy theory, a non-contextual
epistemically restricted model that partially mimics the behaviour of
quantum mechanics. We propose a way to model physical implementations of
agents, memories, measurements, conditional actions and information
processing. We find that the actions of toy agents are severely limited:
although there are non-orthogonal states in the theory, there is no way
for physical agents to consciously prepare them. Their memories are also
constrained: agents cannot forget in which of two arbitrary states a
system is. Finally, we formalize the process of making inferences about
other agents' experiments and model multi-agent experiments like
Wigner's friend. Unlike quantum theory or box world, in the toy theory
there are no inconsistencies when physical agents reason about each
other's knowledge.

Zoom Link: TBD