Contributed Talks 5b: Device Independence

Abstract: We develop an extension of a recently introduced subspace coset state monogamy-of-entanglement game [Coladangelo, Liu, Liu, and Zhandry; Crypto'21] to general group coset states, which are uniform superpositions over elements of a subgroup to which has been applied a group-theoretic generalization of the quantum one-time pad. We give a general bound on the winning probability of a monogamy game constructed from subgroup coset states that applies to a wide range of finite and infinite groups. To study the infinite-group case, we use and further develop a measure-theoretic formalism that allows us to express continuous-variable measurements as operator-valued generalizations of probability measures. We apply the monogamy game bound to various physically relevant groups, yielding realizations of the game in continuous-variable modes as well as in rotational states of a polyatomic molecule. We obtain explicit strong bounds in the case of specific group-space and subgroup combinations. As an application, we provide the first proof of one sided-device independent security of a squeezed-state continuous-variable quantum key distribution protocol against general coherent attacks.

Abstract: In device-independent (DI) quantum protocols, the security statements are oblivious to the characterization of the quantum apparatus– they are based solely on the classical interaction with the devices as well as some well-defined assumptions. The most commonly known setup is the so-called non-local one, in which two devices that cannot communicate with each other present a violation of a Bell inequality. In recent years, a new variant of DI protocols, requiring only a single device, arose. In this novel research avenue, the no-communication assumption is replaced with a computational assumption which states that the device cannot solve certain post-quantum cryptographic tasks. The protocols in literature that have been analyzed in this setting, e.g., randomness certification, used ad hoc proof techniques. In addition, the strength of the achieved results is hard to judge due to their complexity. Here, we build on ideas coming from the study of non-local DI protocols and develop a new modular proof technique for the single-device computational setting. We present a flexible framework for proving the security of such protocols by utilizing a combination of tools from quantum information theory, such as the entropic uncertainty relation and the entropy accumulation theorem. This leads to an insightful and simple proof of security as well as to explicit quantitative bounds. Our work thus acts as the basis for the analysis of future protocols for DI randomness generation, expansion, amplification, and key distribution based on post-quantum cryptographic assumptions.

Abstract: Given that reliable cloud quantum computers are becoming closer to reality, the concept of delegation of quantum computations and its verifiability is of central interest. Many models have been proposed, each with specific strengths and weaknesses. Here, we put forth a new model where the client trusts only its classical processing, makes no computational assumptions, and interacts with a quantum server in a \emph{single} round. In addition, during a set-up phase, the client specifies the size $n$ of the computation and receives an untrusted, \emph{off-the-shelf (OTS)} quantum device that is used to report the outcome of a single constant-sized measurement from a predetermined logarithmic-sized input. In the OTS model, we thus picture that a single quantum server does the bulk of the computations, while the OTS device is used as an untrusted and generic verification device, all in a single round. We show how to delegate polynomial-time quantum computations in the OTS model. Scaling up the technique also yields an interactive proof system for all of QMA, which, furthermore, we show can be accomplished in statistical zero-knowledge. This yields the first relativistic (one-round), two-prover zero-knowledge proof system for QMA. As a proof approach, we provide a new self-test for $n$-EPR pairs using only constant-sized Pauli measurements, and show how it provides a new avenue for the use of simulatable codes for local Hamiltonian verification. Along the way, we also provide an enhanced version of a well-known stability result due to Gowers and Hatami and show how it completes a common argument used in self-testing.