Quantum Physics

To analyze the performance of adaptive measurement protocols for the detection and quantification of state resources, we introduce the framework of quantum preparation games. A preparation game is a task whereby a player sequentially sends a number of quantum states to a referee, who probes each of them and announces the measurement result. The measurement setting at each round, as well as the final score of the game, are decided by the referee based on the past history of settings and measurement outcomes. We show how to compute the maximum average score that a player can achieve under very general constraints on their preparation devices and provide practical methods to carry out optimizations over n-round preparation games. We apply our general results to devise new adaptive protocols for entanglement detection and quantification. Given a set of experimentally available local measurement settings, we provide an algorithm to derive, via convex optimization, optimal n-shot protocols for entanglement detection using these settings. We also present families of adaptive protocols for multiple-target entanglement detection with arbitrarily many rounds. Surprisingly, we find that there exist instances of entanglement detection problems with just one target entangled state where the optimal adaptive protocol supersedes all non-adaptive alternatives.

The predictions of quantum theory resist generalised noncontextual explanations. In addition to the foundational relevance of this fact, the particular extent to which quantum theory violates noncontextuality limits available quantum advantage in communication and information processing. In the first part of this work, we formally define contextuality scenarios via prepare-and-measure experiments, along with the polytope of general contextual behaviours containing the set of quantum contextual behaviours. This framework allows us to recover several properties of set of quantum behaviours in these scenarios . Most surprisingly, we discover contextuality scenarios and associated noncontextuality inequalities that require for their violation the individual quantum preparation and measurement procedures to be mixed states and unsharp measurements. With the framework in place, we formulate novel semidefinite programming relaxations for bounding these sets of quantum contextual behaviours. Most significantly, to circumvent the inadequacy of pure states and projective measurements in contextuality scenarios, we present a novel unitary operator based semidefinite relaxation technique. We demonstrate the efficacy of these relaxations by obtaining tight upper bounds on the quantum violation of several noncontextuality inequalities and identifying novel maximally contextual quantum strategies. To further illustrate the versatility of these relaxations we demonstrate the monogamy of preparation contextuality in a tripartite setting, and present a secure semi-device independent quantum key distribution scheme powered by quantum advantage in parity oblivious random access codes.

In the last two decades the field of nonequilibrium quantum many-body physics
has seen a rapid development driven, in particular, by the remarkable progress
in quantum simulators, which today provide access to dynamics in quantum
matter with an unprecedented control. However, the efficient numerical
simulation of nonequilibrium real-time evolution in isolated quantum matter
still remains a key challenge for current computational methods especially
beyond one spatial dimension. In this talk I will present a versatile and
efficient machine learning inspired approach. I will first introduce the
general idea of encoding quantum many-body wave functions into artificial
neural networks. I will then identify and resolve key challenges for the
simulation of real-time evolution, which previously imposed significant
limitations on the accurate description of large systems and long-time
dynamics. As a concrete example, I will consider the dynamics of the
paradigmatic two-dimensional transverse field Ising model, where we observe
collapse and revival oscillations of ferromagnetic order and demonstrate that
the reached time scales are comparable to or exceed the capabilities of state-
of-the-art tensor network methods.

With ongoing efforts to observe quantum effects in larger and more complex systems, both for the purposes of quantum computing and fundamental tests of quantum gravity, it becomes important to study the consequences of extending quantum theory to the macroscopic domain. Frauchiger and Renner have shown that quantum theory, when applied to model the memories of reasoning agents, can lead to a conflict with certain principles of logical deduction. Is this incompatibility a peculiar feature of quantum theory, or can modelling reasoning agents using other physical theories also lead to such contradictions? What features of physical theories are responsible for such paradoxes? 

Multi-agent paradoxes have been previously analysed only in quantum theory. To address the above questions, a framework for analysing multi-agent paradoxes in general physical theories is required. Here, we develop such a framework that can in particular be applied to generalized probabilistic theories (GPTs). We apply the framework to model how observers’ memories may evolve in box world, a post-quantum GPT and using this, derive a stronger paradox that does not rely on post-selection. Our results reveal that reversible, unitary evolution of agents’ memories is not necessary for deriving multi-agent logical paradoxes, and suggest that certain forms of contextuality might be. 

https://iopscience.iop.org/article/10.1088/1367-2630/ab4fc4

Many physical states of interest, such as ground states of gapped quantum many-body systems, are expected to obey an area law of entanglement entropy. I will report on a series of recent results that suggest a deep connection between area law and two seemingly unrelated subjects: topological quantum field theory and quantum marginal problem. Recently, we deduced --- only using area law and quantum information-theoretic tools --- the existence of new topological charges and invariants associated with the domain walls between topologically ordered systems in two spatial dimensions. Moreover, the same set of tools were also used in finding a solution to the quantum marginal problem. This is the problem in which one asks whether a set of reduced density matrices on bounded subsystems are compatible with some globally well-defined many-body quantum state. Since this problem was first posed in 1959, a solution that goes beyond the mean-field ansatz has remained elusive until now. These results suggest that area law is not just a qualitative statement about entanglement; it is an important equation that lets us "solve" quantum many-body systems that appear in nature.

Based on arXiv:2008.11793 and arXiv:2010.07424

Information theory offers mathematically precise theory of communication and data storage that guided and fueled the information age.  Initially, quantum effects were thought to be an annoying source of noise, but we have since learned that they offer new capabilities and vast opportunities. Quantum information theory seeks to identify, quantify, and ultimately harness these capabilities. A basic resource in this context is a noisy quantum communication channel, and a central goal is to figure out its capacities---what can you do with it?  I’ll highlight the new and fundamentally quantum aspects that arise here, such as the role of entanglement, ways to quantify it, and bizarre new kinds of synergies between resources.  These ideas elucidate the nature of communication in a quantum context, as well as revealing new facets of quantum theory itself.

A series of recent works has shown that placing communication channels in a coherent superposition of alternative configurations can boost their ability to transmit information. Instances of this phenomenon are the advantages arising from the use of communication devices in a superposition of alternative causal orders, and those arising from the transmission of information along a superposition of alternative trajectories. The relation among these advantages has been the subject of recent debate, with some authors claiming that the advantages of the superposition of orders could be reproduced, and even surpassed, by other forms of superpositions. To shed light on this debate, we develop a general framework of resource theories of communication. In this framework, the resources are communication devices, and the allowed operations are (a) the placement of communication devices between the communicating parties, and (b) the connection of communication devices with local devices in the parties' laboratories. The allowed operations are required to satisfy the minimal condition that they do not enable communication independently of the devices representing the initial resources. The resource-theoretic analysis reveals that the aforementioned criticisms on the superposition of causal orders were based on an uneven comparison between different types of quantum superpositions, exhibiting different operational features.

Ref. https://iopscience.iop.org/article/10.1088/1367-2630/ab8ef7

A central challenge in quantum many-body physics is a characterization of properties of `natural' quantum states, such as the ground states and Gibbs states of a local hamiltonian. The area-law conjecture, which postulates a remarkably simple structure of entanglement in gapped ground states, has resisted a resolution based on information-theoretic methods. We discuss how the right set of insights may come, quite unexpectedly, from polynomial approximations to boolean functions. Towards this, we describe a 2D sub-volume law for frustration-free locally-gapped ground states and highlight a pathway that could lead to an area law. Similar polynomial approximations have consequences for entanglement in Gibbs states and lead to the first provably linear time algorithm to simulate Gibbs states in 1D. Next, we consider the task of learning a Hamiltonian from a Gibbs state, where many-body entanglement obstructs rigorous algorithms. Here, we find that the effects of entanglement can again be controlled using tools from computer science, namely, strong convexity and sufficient statistics. 

We study the real-time dynamics of a small bubble of "false vacuum'' in a quantum spin chain near criticality, where the low-energy physics is described by a relativistic (1+1)-dimensional quantum field theory. Such a bubble can be thought of as a confined kink-antikink pair (a meson). We carefully construct bubbles so that particle production does not occur until the walls collide. To achieve this in the presence of strong correlations, we extend a Matrix Product State (MPS) ansatz for quasiparticle wavepackets [Van Damme et al., arXiv:1907.02474 (2019)] to the case of confined, topological quasiparticles. By choosing the wavepacket width and the bubble size appropriately, we avoid strong lattice effects and observe relativistic kink-antikink collisions. We use the MPS quasiparticle ansatz to identify scattering outcomes: In the Ising model, with transverse and longitudinal fields, we do not observe particle production despite nonintegrability (supporting recent numerical observations of nonthermalizing mesonic states). With additional interactions, we see production of confined and unconfined particle pairs. Although we simulated these low-energy, few-particle events with moderate resources, we observe significant growth of entanglement with energy and with the number of collisions, suggesting that increasing either will ultimately exhaust our methods. Quantum devices, in contrast, are not limited by entanglement production, and promise to allow us to go far beyond classical methods. We anticipate that kink-antikink scattering in 1+1 dimensions will be an instructive benchmark problem for relatively near-term quantum devices.

Walgate and Scott have determined the maximum number of generic pure quantum states in multipartite space that can be unambiguously discriminated by an LOCC measurement [Journal of Physics A: Mathematical and Theoretical, 41:375305, 08 2008]. In this work, we determine this number in a more general setting in which the local parties have access to pre-shared entanglement in the form of a resource state. We find that, for an arbitrary pure resource state, this number is equal to the Krull dimension of (the closure of) the set of pure states obtainable from the resource state by SLOCC. This dimension is known for several resource states, for example the GHZ state.

Local state discrimination is closely related to the topic of entangled subspaces, which we study in its own right. We introduce r-entangled subspaces, which naturally generalize previously studied spaces to higher multipartite entanglement. We use algebraic geometric methods to determine the maximum dimension of an r-entangled subspace, and present novel explicit constructions of such spaces. We obtain similar results for symmetric and antisymmetric r-entangled subspaces, which correspond to entangled subspaces of bosonic and fermionic systems, respectively.

In this talk, I argue that the question of whether a physical system can be simulated on a computer is important not just from a practical perspective but also a fundamental one. We consider the complexity of simulating Hamiltonians with respect to both dynamics and equilibrium properties. This gives us a classification and a phase diagram of the complexity.  I will cover recent results in this topic, such as a dynamical complexity phase diagram for a long-range bosonic Hamiltonian and a complexity classification of the local Hamiltonian problem in the presence of a spectral gap. I will talk about the physical implications of these results and cover some of the basic proof ideas if time permits.

While spacetime and quantum theory are crucial parts of modern theoretical physics, the problem of quantum gravity demonstrates that their full relationship is not yet completely understood. In my talk, I report on two recent results that aim to shed light on this relationship via ideas and tools from quantum foundations.

We start with the setting of (semi-) device-independent quantum information protocols. In this scenario one considers abstract black boxes that are characterised by their input-output statistics. Typically, these inputs and outputs are assumed to be abstract labels from a finite set of integers. We replace the abstract inputs with physical inputs that correspond to continuous spatio-temporal degrees of freedom, e.g. angles of polarisers and time-durations of laser pulses. This framework gives new insights about the relation between space, time, and quantum correlations, and it gives rise to new kinds of Bell non-locality witnesses.

We then turn to the topic of quantum reference frames. Specifically, we consider a composite quantum system and an outside experimenter who does not have access to an external reference frame to specify all of the system's properties. We show that for such an observer the possible descriptions of states and observables are related by quantum reference frame transformations that have been independently proposed in recent works. We give an explicit description of the observables that are measurable by agents constrained by such quantum symmetries, and we introduce a relational generalisation of the partial trace that applies to such situations.