Scientific Series

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.  

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.

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.

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.

This is practice for a talk at Berkeley, so it will involve explaining stuff many people here probably already know.  I'll try to summarize what I've learned about 3 dimensional N=4 supersymmetric quantum field theories, their twists and how these manifest in terms of interesting objects in mathematics.  If nothing else, hopefully there will be some comedy value in my attempt.  

I will discuss the computation of second-order terms in the entanglement entropy and subregion complexity for a spherical entangling region in the AdS black hole background relative to pure AdS. I will suggest an extension of the conjectured relationship between subregion complexity and Fisher information into a relation that is reminiscent of the first law of thermodynamics. By analogy, entanglement and complexity play the roles of heat and work, respectively. Time permitting, I will also discuss the computation of third- and fourth-order terms in the relative entropy. 

In this talk, I will discuss some interesting connections between Hamiltonian complexity, error correction, and quantum circuits. First, motivated by the Quantum PCP Conjecture, I will describe a construction of a family of local Hamiltonians where the complexity of ground states — even when subject to large amounts of noise — is superpolynomial (under plausible complexity assumptions). The construction is simple, making use of the well-known Feynman-Kitaev circuit Hamiltonian construction.

Next, I will describe how this complexity result can be repurposed to construct local approximate error correcting codes with (nearly) linear distance and (nearly) constant rate. By contrast, it remains an open problem to construct quantum low-density parity check (QLDPC) stabilizer codes that achieve similarly good parameters.

An interesting component of our code construction is the Brueckmann-Terhal spacetime circuit Hamiltonian construction, and a novel analysis of its spectral gap. Our codes are ground spaces of non-commuting  — but frustration-free -- local Hamiltonians. We believe that our results present additional evidence that the study of approximate error correction and non-stabilizer codes may be much richer than previously thought.

This talk will have more questions than answers, and is based on two papers:

·  https://arxiv.org/abs/1802.07419 (joint with Chinmay Nirkhe and Umesh Vazirani)

·  https://arxiv.org/abs/1811.00277 (joint work with Thom Bohdanowicz, Elizabeth Crosson, and Chinmay Nirkhe)

Gravity theories naturally allow for edge states generated by non-trivial boundary-condition preserving diffeomorphisms. I present a specific set of boundary conditions inspired by near horizon physics, show that it leads to soft hair excitations of black hole solutions and discuss implications for black hole entropy.

So far artificial neural networks have been applied to discover phase diagrams in many different physical models. However, none of these studies have revealed any fundamentally new physics. A major problem is that these neural networks are mainly considered as black box algorithms. On the journey to detect new physics it is important to interpret what artificial neural networks learn. On the one hand this allows us to judge whether to trust the results, and on the other hand this can give us insight to possible new physics. In this talk I will 
discuss applications to different models where we successfully interpreted what was learned by the neural networks.

In the usual paradigm of quantum error correction, the information to be protected can be encoded in a system of abstract qubits or modes.  But how does this work for physical information, which cannot be described in this way?  Just as direction information cannot be conveyed using a sequence of words if the parties involved do not share a reference frame, physical quantum information cannot be conveyed using a sequence of qubits or modes without a shared reference frame.  Covariant quantum error correction is a procedure for protecting such physical information against noise in such a way that the encoding and decoding operations transform covariantly with respect to an external symmetry group. In this talk, we'll study covariant QEC, and we will see that there do not exist finite dimensional quantum codes that are covariant with respect to continuous symmetries.  Conversely, we'll see that there do exist finite codes for finite groups, and continuous variable (CV) codes for continuous groups.  This leads to a CV method of circumventing the Eastin-Knill theorem.  By relaxing our requirements to allow for only approximate error correction and covariance, we'll find a fundamental tension between a code's ability to approximately correct errors and covariance with respect to a continuous symmetry.  In this way, we'll arrive at an approximate version of the Eastin-Knill theorem, and we'll end by learning what covariant QEC tells us about continuous symmetries in AdS/CFT, among other applications.