Quantum Physics

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.

Relativistic quantum tasks are quantum computations which have inputs and outputs that occur at designated spacetime locations.

Understanding which tasks are possible to complete, and what resources are required to complete them, captures spacetime-specific aspects of quantum information. In this talk we explore the connections between such tasks and quantum gravity, specifically in the context of the AdS/CFT correspondence. We find that tasks reveal a novel connection between causal features of bulk geometry and boundary entanglement.

Further, we find that AdS/CFT suggests quantum non-local computations, a specific task with relevance to position-based cryptography, can be performed with linear entanglement. This would be an exponential improvement on existing protocols.

Consistent dynamics which couples classical and quantum systems exists, provided it is stochastic. This provides a way to
study the back-reaction of quantum systems on classical ones and has recently been explored in the context of quantum fields back-reacting
on space-time. Since the dynamics is completely positive and circumvents various no-go theorems this can either be thought of as a fundamental theory, or as an effective theory describing the limit of quantum gravity where the gravitational degrees of freedom are taken to be classical. In this talk we explore some of the consequences of complete positivity on the dynamics of classical-quantum systems. We show that complete positivity necessarily results in the decoherence of the quantum system, and a breakdown of predictability in the classical-phase space. We prove there is a trade-off between the rate of this decoherence and the degree of diffusion in the metric: long coherence times require strong diffusion relative to the strength of the coupling, which potentially provides a long-distance experimental test of the quantum nature of gravity  We discuss the consequences of complete positivity on preparing superpositions of gravitationally different states. Each state produces different distributions of the gravitational field determined by the constraints of the theory. The overlap of these distributions imposes an upper bound on the degree of coherence of the superposition.

I will introduce a tool to construct self-testing Bell inequalities from the stabiliser formalism and present two applications in the framework of device-independent certification protocols. Firstly, I will show how the method allows to derive Bell inequalities maximally violated by the family of multi-qubit graph states and suited for their robust self-testing. Secondly, I will present how the same method allows to introduce the first examples of subspace self-testing, a form of certification that the measured quantum state belongs to a given quantum error correction code subspace, which remarkably includes also mixed states.

We often say that quantum mechanics allows to calculate the probability of future events. In fact, quantum mechanics does not discriminate between predicting the future or postdicting the past. I will present the results of a recent work by Rovelli, Donà and me, where we address the apparent tension between the time symmetry of elementary quantum mechanics and the intrinsic time orientation of the formulations of quantum theory used in the quantum information and foundations communities. Additionally, I will sketch a way to think time symmetrically about causality in quantum theory by using the new notion of a causal-inferential theory recently proposed by Schimd, Selby and Spekkens.

Aaronson and Ambainis (2009) and Chailloux (2018) showed that fully symmetric (partial) functions do not admit exponential quantum query speedups. This raises a natural question: how symmetric must a function be before it cannot exhibit a large quantum speedup? In this work, we prove that hypergraph symmetries in the adjacency matrix model allow at most a polynomial separation between randomized and quantum query complexities. We also show that, remarkably, permutation groups constructed out of these symmetries are essentially the only permutation groups that prevent super-polynomial quantum speedups. We prove this by fully characterizing the primitive permutation groups that allow super-polynomial quantum speedups. In contrast, in the adjacency list model for bounded-degree graphs (where graph symmetry is manifested differently), we exhibit a property testing problem that shows an exponential quantum speedup. These results resolve open questions posed by Ambainis, Childs, and Liu (2010) and Montanaro and de Wolf (2013). Based on: arxiv:2006.12760