Seminar

Quantum money leverages the fundamental uncloneability of quantum information to create a money system in which copying money is computationally infeasible, yet verifying it is efficient. However, in addition to fault tolerant quantum computers, many quantum money schemes also require quantum communication. I will discuss the possibility of schemes with classical communication in place of quantum. In particular, I will focus on the private key semi-quantum money of Radian et al, placing it in context with other types of dequantization we could hope for.

Recent optical probes have used excitons, electron-hole bound states, to probe correlated insulating phases of two-dimensional semiconducting materials. Motivated by these experiments, we investigate these composite particles involving Mott physics. In this talk, we will discuss the formalism of two types of Mott excitons: Intraband exciton with both charges from a single band Hubbard model, and interband exciton with only one charge in the Mott.

In a previous talk we saw that Brakerski et al. [1] used the hardness of the Learning with Errors (LWE) problem to not only construct an interactive Proof of Quantumness but also certifiably generate a random bit.

Quantum state and unitary $t$-designs play an important role in several applications, including tomography, randomized benchmarking, state discrimination, cryptography, sensing, and fundamental physics. In this work, we generalize the notion of state designs to infinite-dimensional, separable Hilbert spaces. We first prove that under the definition of continuous-variable (CV) state $t$-designs from [Comm. Math. Phys 326, 755-771 (2014)], no state designs exist for $t\geq2$. Similarly, we prove that no CV unitary $t$-designs exist for $t\geq 2$.

Hybridizing light and matter by means of cavities can be used as a tool to influence material properties.  In my talk I will discuss a model for strongly correlated fermions close to a quantum phase-transition coupled to a single mode of an optical cavity. Close to the critical point, light and matter degrees of freedom hybridize, which can be observed in an increase in their entanglement.

Recently, Yamakawa and Zhandry constructed a problem and proved that it admits a super-polynomial quantum speedup in the average case. Before their work, we only knew of problems that admit a super-polynomial quantum speedup in the worst case. In this talk, I will describe their problem and go over some key steps in their proof. I will also briefly discuss how their result can be construed as a non-interactive proof of quantumness relative to a random oracle.

The central philosophy of statistical mechanics and random-matrix theory of complex systems is that while individual instances are essentially intractable to simulate, the statistical properties of random ensembles obey simple universal “laws”. This same philosophy promises powerful methods for studying the dynamics of quantum information in ideal and noisy quantum circuits – for which classical description of individual circuits is expected to be generically intractable.

The non-equilibrium dynamics of quantum many-body systems is a notoriously difficult topic of study, but one in which much progress is currently being made. Lieb-Robinson bounds have proven to be a valuable tool for obtaining both rigorous results and physical intuition. In this talk, after an introduction to the physical content of Lieb-Robinson bounds and a description of various applications, we discuss our recent work constructing bounds for systems with quenched disorder in 1D.

Remote state preparation (RSP) has become an essential subroutine to ''dequantize'' the quantum channel in various quantum cryptographic schemes. Some of the applications of RSP include proofs of quantumness, delegated quantum computations, quantum money, unclonable quantum encryption, quantum copy protection and more. In this talk, we will talk about security aspects and some of these applications. 

In this talk I will introduce the remote state preparation primitive, which can enable a fully classical party to participate in different quantum protocols.  Next, I will present two simple protocols based on trapdoor one-way functions with extra properties and show how to construct them based on the Learning-With-Errors problem.