Contributed Talks 2b: Device-independence (Chair: Roger Colbeck)

Abstract: Device-independent protocols use untrusted quantum devices to achieve a cryptographic task. Such protocols are typically based on Bell inequalities and require the assumption that the quantum device is composed of separated non-communicating components. In this submission, we present protocols for self-testing and device-independent quantum key distribution (DIQKD) that are secure even if the components of the quantum device can exchange arbitrary quantum communication. Instead, we assume that the device cannot break a standard post-quantum cryptographic assumption. Importantly, the computational assumption only needs to hold during the protocol execution and only applies to the (adversarially prepared) device in possession of the (classical) user, while the adversary herself remains unbounded. The output of the protocol, e.g. secret keys in the case of DIQKD, is information-theoretically secure. For our self-testing protocol, we build on a recently introduced cryptographic tool (Brakerski et al., FOCS 2018; Mahadev, FOCS 2018) to show that a classical user can enforce a bipartite structure on the Hilbert space of a black-box quantum device, and certify that the device has prepared and measured a state that is entangled with respect to this bipartite structure. Using our self-testing protocol as a building block, we construct a protocol for DIQKD that leverages the computational assumption to produce information-theoretically secure keys. The security proof of our DIQKD protocol uses the self-testing theorem in a black-box way. Our self-testing theorem thus also serves as a first step towards a more general translation procedure for standard device-independent protocols to the setting of computationally bounded (but freely communicating) devices.

Abstract: The security of finite-length keys is essential for the implementation of device-independent quantum key distribution (DIQKD). Presently, there are several finite-size DIQKD security proofs, but they are mostly focused on standard DIQKD protocols and do not directly apply to the recent improved DIQKD protocols based on techniques such as noisy preprocessing and random key measurements. Here, we provide a general finite-size security proof that can simultaneously encompass these approaches, using tighter finite-size bounds than previous analyses. In doing so, we develop a method to compute tight lower bounds on the asymptotic keyrate for any such DIQKD protocol with binary inputs and outputs. With this, we show that positive asymptotic keyrates are achievable up to depolarizing noise values of 9.26%, exceeding all previously known noise thresholds. Furthermore, we also consider in greater detail a particular form of generalized CHSH inequality, and derive partial closed-form results for such cases. We discuss the potential advantage of this approach for realistic photonic implementations of DIQKD.

Abstract: We prove an achievability result for privacy amplification and decoupling in terms of the sandwiched Rényi entropy of order α ∈ (1,2]; this extends previous results which worked for α=2. The fact that this proof works for α close to 1 means that we can bypass the smooth min-entropy in the many applications where the bound comes from the fully quantum AEP or entropy accumulation (EAT), and carry out the whole proof using the Rényi entropy, thereby easily obtaining an error exponent for the final task. This effectively replaces smoothing, which is a difficult high-dimensional optimization problem, by an optimization problem over a single real parameter α. This can be applied directly to QKD security proofs---including device independent protocols---by combining it with the entropy accumulation theorem.