Chirag Srivastava

We propose a framework for quantum residual management, in which states discarded after a resource distillation process are repurposed as inputs for subsequent quantum information tasks. This approach extends conventional quantum resource theories by incorporating secondary resource extraction from residual states, thereby enhancing overall resource utility. As a concrete example, we investigate the distillation of private randomness from the residual states remaining after quantum key distribution (QKD). More specifically, we quantitatively show that after performing a well-known coherent Devetak-Winter protocol, one can locally extract private randomness from its residual. We further consider the Gottesman-Lo QKD protocol and provide the achievable rate of private randomness from the discarded states that are left after its performance. We also provide a formal framework that highlights a general principle for improving quantum resource utilization across sequential information processing tasks.

Quantum resource theories use distillation protocols to convert less resourceful states into fully resourceful ones. However, these protocols often also generate an additional, unused output—referred to as a residual. We propose a framework for the quantum residual management, in which states discarded after a resource distillation protocol are repurposed as inputs for subsequent quantum information tasks. This approach extends conventional quantum resource theories by incorporating secondary resource extraction from residual states, thereby enhancing overall resource utility. As a concrete example, we investigate the distillation of private randomness from the residual states remaining after quantum key distribution (QKD). More specifically, we quantitatively show that after performing a well-known coherent Devetak-Winter protocol, one can locally extract private randomness from its residual. We further consider the Gottesman-Lo QKD protocol and provide the achievable rate of private randomness from the discarded states that are left after its performance. We also provide a formal framework that highlights a general principle for improving quantum resource utilization across sequential information processing tasks.

Performing a measurement on one half of an entangled pair of systems remotely prepares the other half in an ensemble of quantum states. Now consider any set of ensembles that mix to the same density operator. The Schrödinger--HJW theorem states that one can remotely prepare any chosen ensemble from this set by a choice of measurement performed on one half of a fixed entangled state. We generalise this result to show that any set of ensembles can be remotely prepared if one is allowed to post-select on the outcome of the preparing measurement. The probability that the remote preparation is successful is then lower bounded in terms of the distance between the ensembles. In a prepare-and-measure quantum key distribution protocol the distance between the ensembles represents the amount of information that is leaked about the choice of ensemble, e.g. the choice of basis in the BB84 protocol. Using our generalised result, we can prove the security of such protocols from only the fundamental assumption of how much information is leaked about the choice of ensemble/basis, i.e. from bounded basis-dependency.