Quantum Foundations

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

I will discuss a recent result on an intimate link between two a priori distinct phenomena: quantum nonlocality without entanglement and classically-achievable indefinite causal order. The first phenomenon refers to a multipartite scenario where the parties are unable to perfectly discriminate orthogonal product states drawn from an ensemble of quantum states by using local operations and classical communication (LOCC). The second (hypothetical) phenomenon refers to a multipartite scenario where the parties can communicate classically but the local operations of each party are in the future of the other parties, i.e., they cannot be ordered causally. Specifically, I will show how three separated parties with access to a classical process exhibiting indefinite causal order---the AF/BW process---can perfectly discriminate the states in an ensemble---the SHIFT ensemble---that exhibits quantum nonlocality without entanglement. Time permitting, I will discuss the generalization of this result beyond the tripartite case and comment on its connection with separable operations that are outside LOCC. 

Based on joint work with Ämin Baumeler, arXiv:2202.00440.

Zoom Link: https://pitp.zoom.us/j/93727212623?pwd=cjVRL3cvMmhicDRic3lXRFBkNi9xZz09

 It is unknown how the Einstein Equivalence Principle (EEP) should be modified to account for quantum features. A possibility introduced in arXiv:2012.13754 is that the EEP holds in a generalized form for particles having an arbitrary quantum state. The core of this proposal is the ability to transform to a Quantum Reference Frame (QRF) associated to an arbitrary quantum state of a physical system, in which the metric is locally inertial. I will show that this extended EEP, initially formulated in terms of the local expression of the metric field in a QRF, can be verified in an interferometric setup via tests on the proper time of entangled clocks (arXiv:2112.03303). Moreover, the same setup can be analyzed with quantum sensing techniques (arXiv:2204.03006): I will talk about how gravitational time dilation may be used as a resource in quantum information theory, showing that it may enhance the precision in estimating the gravitational acceleration for long interferometric times.

The current theories of quantum physics and general relativity on their own do not allow us to study situations in which spacetime is in a quantum superposition. In this talk, I propose a general strategy to determine the dynamics of objects on an indefinite spacetime metric, using an extended notion of quantum reference frame transformations. First, we study the situation of the gravitational source mass being in a spatial superposition state and, using a generalized principle of covariance, show how to transform to a frame in which the standard theories of GR and QFT allow to determine the dynamics. In the second part, we consider superpositions of conformally equivalent metrics inhabited by a massive quantized Klein-Gordon field. By requiring invariance of the KG equation under quantum conformal transformations, we find that the superposition is transferred to the quantum field in the form of an effective, spacetime dependent mass term. Overall, the proposed strategy allows to construct the respective explicit quantum frame change operators, and to study physical phenomena such as time dilation and cosmological particle production in different quantum frames.

Zoom Link: https://pitp.zoom.us/j/96903859307?pwd=aEtLUy9tME5GL25nTjBVNXVmb2N3Zz09

Certifying quantum properties with minimal assumptions is a fundamental problem in quantum information science. Self-testing is a method to infer the underlying physics of a quantum experiment only from the measured statistics. While all bipartite pure entangled states can be self-tested, little is known about how to self-test quantum states of an arbitrary number of systems. Here, we introduce a framework for network-assisted self-testing and use it to self-test any pure entangled quantum state of an arbitrary number of systems. The scheme requires the preparation of a number of singlets that scales linearly with the number of systems, and the implementation of standard projective and Bell measurements, all feasible with current technology. When all the network constraints are exploited, the obtained self-testing certification is stronger than what is achievable in any Bell-type scenario. Our work does not only solve an open question in the field but also shows how properly designed networks offer new opportunities for the certification of quantum phenomena.