Talks

I will describe a new proposal for defining the holographic
entanglement entropy at subleading orders in N (on the boundary) or
hbar (in the bulk). This involves a new concept of "quantum extremal
surfaces" defined as the surface which extremizes the sum of the area
and the bulk entanglement entropy. This conjecture reduces to
previous conjectures in suitable limits, and satisfies some nontrivial
consistency checks. Based on arXiv:1408.3203

From the general difficulty of simulating quantum systems using classical systems, and in particular the existence of an efficient quantum algorithm for factoring, it is likely that quantum computation is intrinsically more powerful than classical computation. At present, the best upper bound known for the power of quantum computation is that BQP is in AWPP, where AWPP is a classical complexity class (known to be included in PP, hence PSPACE). This work investigates limits on computational power that are imposed by simple physical, or information theoretic, principles. To this end, we define a circuit-based model of computation in a class of operationally-defined theories more general than quantum theory, and ask: what is the minimal set of physical assumptions under which the above inclusions still hold? We show that given only an assumption of tomographic locality (roughly, that multipartite states and transformations can be characterised by local measurements), efficient computations are contained in AWPP. This inclusion still holds even without assuming a basic notion of causality (where the notion is, roughly, that probabilities for outcomes cannot depend on future measurement choices). Then, following Aaronson, we extend the computational model by allowing post-selection on measurement outcomes. Aaronson showed that the corresponding quantum complexity class, PostBQP, is equal to PP. Given only the assumption of tomographic locality, the inclusion in PP still holds for post-selected computation in general theories. Hence in a world with post-selection, quantum theory is optimal for computation in the space of all operational theories. We then consider whether one can obtain relativised complexity results for general theories. It is not obvious how to define a sensible notion of a computational oracle in the general framework that reduces to the standard notion in the quantum case. Nevertheless, it is possible to define computation relative to a `classical oracle'. Then, we show there exists a classical oracle relative to which efficient computation in any theory satisfying the causality assumption does not include NP. This provides some degree of evidence that NP-complete problems cannot be solved efficiently in any theory satisfying tomographic locality and causality. Based on arXiv:1412.8671. Joint work with Jon Barrett.

Shape Dynamics is a theory of gravity which replaces relativity of simultaneity for spatial conformal invariance, maintaining the same degree of symmetry of General Relativity while avoiding some of its shortcomings.

In SD several kinds of singularities of GR become unphysical gauge artefacts, and the presence of a preferred notion of simultaneity fits better into the structure of quantum theory. In this talk I will outline the present status of research in SD on black holes and gravitational collapse, on the emergence of spacetime and on the first-order formulation of the theory.

The analogy between Multi-scale Entanglement Renormalization
Ansatz (MERA) and the spatial slice of three-dimensional anti-de
Sitter space (AdS3) has motivated a great interest in tensor networks
among holographers. I discuss a way to promote this analogy to a
rigorous, quantitative, and constructive relation. A key quantitative
ingredient is the way the strong subadditivity of entanglement entropy
is encoded in MERA and in a holographic spacetime. The upshot is that
the map between MERA and the spatial slice of AdS3 is mediated through
an additional integral transform. Interpreted directly, MERA is a
discretization not of the spatial slice of AdS3, but of the space of
geodesics on the spatial slice of AdS3.

We introduce and systematically study an expansive class of "orbifold Higgs" theories in which the weak scale is protected by accidental symmetries arising from the orbifold reduction of continuous symmetries. The protection mechanism eliminates quadratic sensitivity of the Higgs mass to higher scales at one loop (or more) and does not involve any new states charged under the Standard Model.