Siddhartha Das

In this paper, we develop the resource theory of quantum secret key. Operating under the assumption that entangled states with zero distillable key do not exist, we define the key cost of a quantum state, and device. We study its properties through the lens of a quantity that we call the key of formation. The main result of our paper is that the regularized key of formation is an upper bound on the key cost of a quantum state. The core protocol underlying this result is privacy dilution, which converts states containing ideal privacy into ones with diluted privacy. Next, we show that the key cost is bounded from below by the regularized relative entropy of entanglement, which implies the irreversibility of the privacy creation-distillation process for a specific class of states. We further focus on mixed-state analogues of pure quantum states in the domain of privacy, and we prove that a number of entanglement measures are equal to each other for these states, similar to the case of pure entangled states. The privacy cost and distillable key in the single-shot regime exhibit a yield-cost relation, and basic consequences for quantum devices are also provided.

In this work, we develop upper bounds for key rates for device-independent key distribution protocols, devices, and channels. We study the reduced cc-squashed entanglement and show that it is a convex functional. As a result, we show that the convex hull of the currently known bounds is a tighter upper bound on the device-independent key rates of standard CHSH-based protocol. We further provide tighter bounds for DIQKD key rates achievable by any protocol applied to the CHSH-based device. This bound is based on reduced relative entropy of entanglement optimized over decompositions into local and non-local parts. In the scenario of quantum channels, we obtain upper bounds for device-independent private capacity for the CHSH based protocols. We show that the DI private capacity for the CHSH based protocols on depolarizing and erasure channels is limited by the secret key capacity of dephasing channels.

Entanglement is an intriguing quantum phenomenon with crucial implications for both fundamental physics and technological applications, e.g., quantum key distribution (QKD). In this paper, we show that multipartite private states from which secret keys are directly accessible to trusted partners are genuinely multipartite entangled states. With application to secure Quantum Internet, we consider the most general setup of multipartite quantum process (channel) in a network setting: multiplex quantum channel with involved parties having one of the three possible roles-- that of only sender or receiver, or both sender and receiver. We derive divergence-based measures for entangling abilities of multipartite quantum channels. We describe an LOCC-assisted secret key agreement (SKA) protocol for generation or distillation of key (private random bits) among multiple trusted allies connected through a quantum multiplex channel secure against a quantum eavesdropper, of which measurement-device-independent QKD and SKA protocols over quantum network laced with key repeaters are particular instances. We are able to provide upper bounds on the non-asymptotic private capacities, maximum rate at which secret key can be distilled via finite uses of channels, and lower bounds on asymptotic capacities. These bounds are expressed in terms of the divergence-based entanglement measures of the channels. Some of these measures lead to strong converse bounds on the private capacities. Our upper bounds on the private capacities also are upper bound on the multipartite quantum capacities where goal is to distill Greenberger{Horne{Zeilinger (GHZ) state. Also, we are able to derive upper bound on the secret key bits that can be distilled via LOCC among trusted allies sharing finite copies of multipartite quantum states.