Quantum Physics

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

A large class of Λ < 0 cosmologies have big-bang / big crunch spacetimes with time-symmetric backgrounds and asymptotically AdS Euclidean continuations suggesting a possible holographic realization. We argue that these models generically have time-dependent scalar fields, and these can lead to realistic cosmologies at the level of the homogeneous background geometry, with an accelerating phase prior to the turnaround and crunch. We first demonstrate via explicit effective field theory examples that models with an asymptotically AdS Euclidean continuation can also exhibit a period of accelerated expansion without fine tuning. We then show that certain significantly more tuned examples can give predictions arbitrarily close to a ΛCDM model. Finally, we demonstrate via an explicit construction that the potentials of interest can arise from a superpotential, thus suggesting that these solutions may be compatible with an underlying supersymmetric theory.

This talk is based on 2212.00050.

Zoom link:  https://pitp.zoom.us/j/93499736007?pwd=Qmw5cmZERUN3UmtwTzdKcEdXejJ5UT09

Typicality, the feature that almost any microstate living in the microcanonical subspace cannot be locally distinguished from a thermal ensemble, lies at the fundamental part of statistical physics. However, one may wonder if there exists a sufficient amount of orthogonal atypical states to account for the whole entropy. 
In this talk, we show that, in some physical systems, there exists a sufficient amount of certain orthogonal atypical states to account for the leading order of the entropy in the following two scenarios, by finding proper upper bounds of the entanglement of formation (EoF) for each case and applying other techniques from quantum information theory. 
In the first scenario, the physical system under consideration is AdS black holes at the semiclassical limit G_N —> 0. In this case, microcanonical subspace is the subspace formed by the black hole microstates, and typical states are usually considered to have a smooth horizon as well as the black hole interior. We consider a class of atypical states called disentangled states which have large entanglement deficits compared to typical states such that they cannot have smooth horizons. In this scenario, we use a geometric quantity called entanglement wedge cross section to give upper bounds to EoF. 
In the second scenario, we consider generic quantum many-body systems with short-ranged interactions at the standard thermodynamic limit V —> ∞. In this case, it is known that typical microstates have volume law entanglement. We consider area-law entangled microstates as atypical states. We use reflected entropy to give upper bounds to EoF. 
We will also discuss the relations of our results with the additivity conjectures and atypical black hole microstate counting. 
This talk is based on 2211.11787. 

Zoom link:  https://pitp.zoom.us/j/94823687961?pwd=V3QrSjUrTklheG1iU0RsckwzQmRTUT09

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

Error-correcting codes were invented to correct errors on noisy communication channels. Quantum error correction (QEC), however, has a wider range of uses, including information transmission, quantum simulation/computation, and fault-tolerance. These invite us to rethink QEC, in particular, the role that quantum physics plays in terms of encoding and decoding. The fact that many quantum algorithms, especially near-term hybrid quantum-classical algorithms, only use limited types of local measurements on quantum states, leads to various new techniques called Quantum Error Mitigation (QEM). We examine the task of QEM from several perspectives. Using some intuitions built upon classical and quantum communication scenarios, we clarify some fundamental distinctions between QEC and QEM. We then discuss the implications of noise invertibility for QEM, and give an explicit construction called Drazin-inverse for non-invertible noise, which is trace-preserving while the commonly-used MoorePenrose pseudoinverse may not be. Finally, we study the consequences of having imperfect knowledge about system noise and derive conditions when noise can be reduced using QEM.

Zoom link:  https://pitp.zoom.us/j/91543402893?pwd=b09IS3VWNk5KZi8ya3gzSmRKRFJidz09

Recent advances in mechanical sensing technologies have led to the suggestion that heavy dark matter candidates around the Planck mass range could be detected through their gravitational interaction alone. The Windchime collaboration is developing the necessary techniques, systems, and experimental apparatus using arrays of optomechanical sensors that operate in the regime of high-bandwidth force detection, i.e., impulse metrology.  Today's sensors can be limited by the added noise due to the act of measurement itself. Techniques to go beyond this limit include squeezing of the light used for measurement and backaction evading measurement by estimating quantum non-demolition operators — typically the momentum of a mechanical resonator well above its resonance frequency. In this talk, we will discuss the theoretical limits to noise reduction using such quantum enhanced readout techniques for these optomechanical sensors.

 In holography, spacetime is emergent and its properties depend on the entanglement structure of the dual theory. An interesting question is how changes in the entanglement structure affect the bulk dual description. In this talk, I will describe how local projective measurements performed on a subregion  of the boundary theory modify the bulk dual spacetime. The post-measurement bulk is cut off by end-of-the-world branes and is dual to the complementary unmeasured region . Using a bulk calculation in —which involves a phase transition triggered by the measurement—and tensor network models of holography, I will show that the portion of bulk preserved after the measurement depends on the size of  and the state we project on. Interestingly, the post-measurement bulk includes regions that were part of the entanglement wedge of  before the measurement. Our results indicate that the effect of a measurement performed on a subregion  of the boundary is to teleport part of the bulk information contained in  into the complementary region . Finally, I will comment on applications to the eternal black hole in JT gravity (dual to the SYK thermofield double state) and the relationship between measurements and traversable wormholes.

I will present a general bulk reconstruction technique in AdS/CFT suitable for addressing a facet of the black hole information problem: How to unambiguously predict the results of measurements performed by an infalling observer in the black hole interior.
 
I will explicitly apply the method in the AdS_2/SYK correspondence. My proposal provides an internal notion of time for quantum gravitational systems that may be useful for cosmology.

Monitored many-body systems fall broadly into two dynamical phases, ``entangling'' or ``disentangling'', separated by a transition as a function of the rate at which measurements are made on the system. Producing an analytical theory of this measurement-induced transition is an outstanding challenge. Recent work made progress in the context of tree tensor networks, which can be related to all-to-all quantum circuit dynamics with forced (postselected) measurement outcomes. So far, however, there are no exact solutions for dynamics of spin-1/2 degrees of freedom (qubits) with ``real'' measurements, whose outcome probabilities are sampled according to the Born rule. Here we define dynamical processes for qubits, with real measurements, that have a tree-like spacetime interaction graph, either collapsing or expanding the system as a function of time. The former case yields an exactly solvable measurement transition. We explore these processes analytically and numerically, exploiting the recursive structure of the tree. We compare the case of ``real'' measurements with the case of ``forced'' measurements. Both cases show a transition at a nontrivial value of the measurement strength, with the real measurement case exhibiting a smaller entangling phase. Both exhibit exponential scaling of the entanglement near the transition, but they differ in the value of a critical exponent. An intriguing difference between the two cases is that the real measurement case lies at the boundary between two distinct types of critical scaling. On the basis of our results we propose a protocol for realizing a measurement phase transition experimentally via an expansion process.

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