Quantum Physics

I'll discuss some recent results, motivated by the black-hole firewall paradox and the AdS/CFT correspondence, about the quantum circuit complexity of preparing certain entangled states and implementing certain unitary transformations.  One result is a strengthening of an argument by Harlow and Hayden: I'll show that, under plausible assumptions, "decoding" useful information from Hawking radiation, as called for by the AMPS "firewall" thought experiment, requires the computational power to invert arbitrary cryptographic one-way functions, something we think not even quantum computers could do in sub-astronomical time.  A second result, joint with Lenny Susskind, considers the circuit complexity of the kinds of states that could arise in AdS/CFT, and shows that, under a reasonable conjecture about complexity classes (PSPACE is not in PP/poly), the complexity indeed becomes superpolynomially large, as predicted by a conjectured relationship between complexity and geometry.  I'll also discuss more general open questions about the complexities of states and unitary transformations (and the connections to quantum money, quantum proofs, and other topics), which I find fascinating even apart from the quantum-gravity motivation.

In this talk we will discuss the relation between the incompatibility of quantum measurements and quantum nonlocality. We show that any set of measurements that is not jointly measurable (i.e. incompatible) can be used for demonstrating EPR steering, a form of quantum nonlocality. This implies that EPR steering and (non) joint measurability can be viewed as equivalent. Moreover, we discuss the connection between Bell nonlocality and joint measurability, and give evidence that both notions are inequivalent. This suggest the existence of incompatible quantum measurements which are Bell local, similarly to certain entangled states which admit a local hidden variable model. Finally, we discuss applications of these results to problems in joint mesurability, and for EPR steering using randomly chosen measurements.

Inspired by quantum information approaches to thermodynamics, we introduce a general framework for resource theories, from the perspective of subjective agents. First we formalize a way to think of subjective knowledge through what we call specification spaces, where states of knowledge (or specifications) are represented by sets whose elements are the possible states of reality admitted by an observer. We explore how to conciliate different views of reality via embeddings between specification spaces. Then we introduce resource theories on specification spaces, which are constructed from a set of allowed operations, imposing a pre-order structure in the specification space. We see how to relate, combine and create different resource theories. The local structure of a specification space (which in quantum theory is given by tensoring different Hilbert spaces) is not assumed a priori. Instead, we derive it operationally from commutativity relations in the set of transformations. Further applications are discussed.

To best distinguish between classical and non-classical models of nature requires a good notion of classicality. I will argue that noncontextuality is a good candidate for this notion. Until now, certain theoretical and experimental roadblocks have stood in the way of a test of noncontextuality which is free of unattainable experimental idealizations. I will present solutions to these roadblocks as well as the results of an experimental test.