Quantum Physics

Cellular automata are a central notion for the formulation of physical laws in an abstract information-theoretical scenario, and lead in recent years to the reconstruction of free relativistic quantum field theory. In this talk we extend the notion of a Quantum Cellular Automaton to general Operational Probabilistic Theories. For this purpose, we construct infinite composite systems, illustrating the main features of their states, effects and transformations. We discuss the generalization of the concepts of homogeneity and locality, in an framework where space-time is not a primitive object. We show that homogeneity leads to a Cayley graph structure of the memory array, thus proving the universality of the connection between homogeneity and discrete groups. We conclude illustrating the special case of Fermionic cellular automata, discussing three relevant examples: Weyl and Dirac quantum walks, the Thirring automaton and the simplest families of automata on finite graphs.

I’ll describe a novel application for near-term quantum computers with 50-70 qubits: namely, generating cryptographic random bits, whose randomness can be certified even if the quantum computer is untrusted (e.g., has been backdoored by an adversary).  Unlike schemes based on Bell inequality violation, ours requires only a single device able to solve classically hard sampling problems.  Our protocol harvests the outputs of the sampling process and feeds them into a randomness extractor, while occasionally verifying the outputs using exponential classical time.  I’ll also compare to the beautiful independent work of Brakerski et al., who proposed a scheme for the same problem that has much more efficient verification, but that probably can’t be implemented on near-term devices.  Paper still in preparation.

In physics, every observation is made with respect to a frame of reference. Although reference frames are usually not considered as degrees of freedom, in all practical situations it is a physical system which constitutes a reference frame. Can a quantum system be considered as a reference frame and, if so, which description would it give of the world? The relational approach to physics suggests that all the features of a system —such as entanglement and superposition— are observer-dependent: what appears classical from our usual laboratory description might appear to be in a superposition, or entangled, from the point of view of such a quantum reference frame. In this work, we develop an operational framework for quantum theory to be applied within quantum reference frames. We find that, when reference frames are treated as quantum degrees of freedom, a more general transformation between reference frames has to be introduced. With this transformation we describe states, measurement, and dynamical evolution in different quantum reference frames, without appealing to an external, absolute reference frame. The transformation also leads to a generalisation of the notion of covariance of dynamical physical laws, which we explore in the case of ‘superposition of Galilean translations’ and ‘superposition of Galilean boosts’. In addition, we consider the situation when the reference frame moves in a ‘superposition of accelerations’, which leads us to extend the validity of the weak equivalence principle to quantum reference frames.

For many optimal measurement problems of interest, the problem may be re-cast as a semi-definite program, for which efficient numerical techniques are available. Nevertheless, numerical solutions give limited insight into more general instances of the problem, and further, analytical solutions may be desirable when an optimised measurement appears as a sub-problem in a larger problem of interest. I will discuss analytical techniques for finding optimal measurements for state discrimination with minimum error and present applications to studying the gap between the theoretically optimal measurement and simpler, experimentally achievable schemes for bi-partite measurement problems.

When a particle is accelerated, as in a scattering event, it will radiate gravitons and, if electrically charged, photons. The infrared tail of the spectrum of this radiation has a divergence: an arbitrarily small amount of total energy is divided into an arbitrarily large number of radiated bosons. Each of these in turn carries a momentum and a helicity degree of freedom, and thus this radiation carries significant amounts of quantum information. I will demonstrate that the infrared bosonic radiation causes nearly complete decoherence of the final state of the hard particles into the momentum basis. When applied to radiation coming from the incoming state, it appears that the entire dynamical history of the process will be distinguishable by the radiation, thus causing a loss of any interference effects between branches of an incoming momentum superposition, such as in a wavepacket. I will explain how infrared dressed states, in the framework of Fadeev and Kulish, evade this issue. Finally, I'll conclude with some remarks on the potential relevance of these issues to black hole information loss

[joint work with: Victor Albert, John Preskill (Caltech), Sepehr Nezami, Grant Salton, Patrick Hayden (Stanford University), and Fernando Pastawski (Freie Universität Berlin)]

Quantum error correction and symmetries are concepts that are relevant in many physical systems, such as in condensed matter physics and in holographic quantum gravity, and play a central role in error correction of reference frames [Hayden et al., arXiv:1709.04471]. I will show that codes that are covariant with respect to a continuous local symmetry necessarily have a limit to their ability to serve as approximate error-correcting codes against erasures at known locations. This is because the environment necessarily gets information about the global logical charge of the encoded state due to the covariance of the code. Our bound vanishes either in the limit of large individual subsystems, or in the limit of a large number of subsystems; in either case there exist codes which approximately achieve the scaling of our bound and become good covariant error-correcting codes. Our results can be interpreted as an approximate version of the Eastin-Knill theorem, quantifying to which extent it is not possible to carry out universal computation approximately on encoded states. In the context of holographic AdS/CFT, our approach provides some insight on time evolution in the bulk versus time evolution on the boundary. We expect further implications for symmetries in holography and in condensed matter physics.

Suppose the eigenvalue distributions of two matrices $M_1$ and $M_2$ are known. What is the eigenvalue distribution of the sum $M_1+M_2$? This problem has a rich pure mathematics history dating back to H. Weyl (1912) with many applications in various fields. Free probability theory (FPT) answers this question under certain conditions, which often involves some degree of randomness (disorder). We will describe FPT and show examples of its powers for the qualitative understanding (often approximations) of physical quantities such as density of states, and gapped vs. gapless phases of some Floquet systems. These physical quantities are often hard to compute exactly. Nevertheless, using FPT and other ideas from random matrix theory excellent approximations can be obtained. Besides the applications presented, we believe the techniques will find new applications in new contexts.

There has been a dissatisfaction with the postulates of quantum mechanics essentially since the moment that those postulates were first written down. Over the years since there have therefore been many attempts (some successful and some less so) to reconstruct quantum theory from various sets of postulates. The aim being to gain a deeper understanding of the theory by providing a conceptually clear underpinning from which the standard formalism can be derived. In this talk I present recent work with Carlo Maria Scandolo and Bob Coecke (arXiv:1802.00367) in which we reconstruct quantum theory from purely diagrammatic postulates within the process theory framework, showing that the conceptual bare-bones of quantum theory concerns the manner in which systems and processes compose.

When a system interacts with an environment with which it is initially uncorrelated, its evolution is described by a completely positive map.  The common wisdom in the field of quantum information theory, however, is that when the system is initially correlated with the environment, the map describing its evolution may fail to be completely positive. This has motivated many researchers to try and characterize this putatively more general sort of dynamics, and even the textbook of Nielsen and Chuang suggests that "It is an interesting problem for further research to study quantum information processing beyond the quantum operations formalism."  This talk will demonstrate that this common wisdom is mistaken.  The error can be traced to the standard argument for how the evolution map ought to be defined in such circumstances.  One can show that anomolous dynamics would arise even in completely classical examples if one were to follow the prescription of the standard argument.  The framework of classical causal models specifies how dynamics ought to be defined in such circumstances, and

the quantum analogue of this framework provides the correct definition of the quantum evolution map, which is found to be always completely positive.

Joint work with David Schmid