Talks

Optimally encoding classical information in a quantum system is one of the oldest and most fundamental challenges of quantum information theory. Holevo’s bound places a hard upper limit on such encodings, while the Holevo-Schumacher-Westmoreland (HSW) theorem addresses the question of how many classical messages can be “packed” into a given quantum system. In this article, we use Sen’s recent quantum joint typicality results to prove a one-shot multiparty quantum packing lemma generalizing the HSW theorem. The lemma is designed to be easily applicable in many network communication scenarios. As an illustration, we use it to straightforwardly obtain quantum generalizations of well-known classical coding schemes for the relay channel: multihop, coherent multihop, decode-forward, and partial decode-forward. We provide both finite blocklength and asymptotic results, the latter matching existing formulas. Given the key role of the classical packing lemma in network information theory, our packing lemma should help open the field to direct quantum generalization.

Over the years, many rich ideas have been exchanged between particle theory and condensed matter theory, such as particle/hole theory, superconductivity and dynamical symmetry breaking, universality and critical phenomena. Here I discuss the interesting case of how the two fields converged independently along different paths on the physics of symmetry-protected topological order: condensed matter physicists motivated by the quantum Hall effect and superconductivity, the particle physicists driven by the desire to understand anomalies and chirality, and to compute QCD and supersymmetry on a lattice -- where the Quantum Hall effect, the Quantum Spin Hall effect and Majorana surface modes have all played a role in practical computations since the 1990s.  

We study the possibility of a deconfined quantum phase transition in a realistic model of a two dimensional Shastry-Sutherland quantum magnet, using both numerical and field theoretic techniques. We argue that the quantum phase transition between a two fold degenerate plaquette valence bond  solid (pVBS) order and N\'eel ordered phase may be described by a deconfined quantum critical point (DQCP) with emergent O(4) symmetry. Further, using the infinite density matrix renormalization group (iDMRG) numerical technique, we verify the emergence of an intermediate pVBS order, between the dimer and Neel ordered phases. By analyzing the correlation length spectrum, we provide evidence for deconfinement and emergent O(4) symmetry at the phases transistion between the pVBS and N\'eel orders. Such a phase transition has been reported in the recent pressure tuned experiments in the Shastry-Sutherland lattice material  SrCu2(BO3)2. The non-symmorphic lattice structure of the Shastry-Sutherland compound leads to extinction points in the scattering, where we predict sharp signatures of a DQCP in both the phonon and magnon spectra associated with the spinon continuua. Our results can guide future experimental studies of DQCP in quantum magnets.

A common criticism directed against many-world theories is that, being deterministic, they cannot make sense of probability. I argue that, on the contrary, deterministic theories with branching provide us the only known coherent definition of objective probability. I illustrate this argument with a toy many-worlds theory known as Kent's universe, and discuss its limitations when applied to the usual Many-Worlds interpretation of quantum mechanics.

I'll also argue that subjective probabilities are unproblematic in the many-worlds setting by showing how the usual decision-theoretical axioms apply there, and finish by showing that together with a proper definition of measurement they suffice to derive the Born rule.

Defects and their RG flows play an important role in many systems, with perhaps the most famous example being the Kondo effect. We study Kondo-like interface flows in D1/D5 holography from the point of view of both probe branes and of the corresponding backreacted supergravity solutions.

In the context of geometric quantisation, one starts with the data of a symplectic manifold together with a pre-quantum line bundle, and obtains a quantum Hilbert space by means of the auxiliary structure of a polarisation, i.e. typically a Lagrangian foliation or a Kähler structure. One common and widely studied problem is that of quantising Hamiltonian flows which do not preserve it. In the simple case of Kähler quantisation of a symplectic vector space, one may consider the space of all Kähler structures, and organise the corresponding Hilbert spaces to form an infinite-rank vector bundle on it, so the quantisation of symplectic transformations may be understood in terms of their action on this bundle.
In this talk I shall consider a variation of this construction for the case of a hyper-Kähler vector space V, in which case the symplectic form and the pre-quantum line bundle are allowed to change together with the complex structure. In a joint work with Andersen and Rembado, we construct a bundle of Hilbert spaces on the sphere of Kähler structures, on which a flat connection is naturally defined. The group of isometries of V which preserve this sphere globally also acts on the bundle, and the construction determines a quantisation of this group. Time permitting, I shall discuss our main application of this construction—the quantisation of the circle action on the moduli space of reductive Higgs bundles over an elliptic curve.