Role of Nonlocality and Counterfactuality in Quantum Cryptography

Abstract

Quantum cryptography is arguably the most successfully applied area of quantum information theory. In this work, We invsetigate the role of quantum indistinguishability in random number generation, quantum temporal correlations, quantum nonlocality and counterfactuality for quantum cryptography. We study quantum protocols for key distribution, and their security in the conventional setting, in the counterfactual paradigm, and finally also in the device-independent scenario as applied to prepare-and-measure schemes. We begin with the interplay of two essential non-classical features like quantum indeterminism and quantum indistinguishability via a process known as bosonic stimulation is discussed. It is observed that the process provides an efficient method for macroscopic extraction of quantum randomness. Next, we propose two counterfactual cryptographic protocols, in which a secret key bit is generated even without the physical transmission of a particle. The first protocol is semicounterfactual in the sense that only one of the key bits is generated using interaction-free measurement. This protocol departs fundamentally from the original counterfactual key distribution protocol in not encoding secret bits in terms of photon polarization. We discuss how the security in the protocol originates from quantum single-particle non-locality. The second protocol is designed for the crypto-task of certificate authorization, where a trusted third party authenticates an entity (e.g., bank) to a client. We analyze the security of both protocols under various general incoherent attack models. The next part of our work includes study of quantum temporal correlations. We consider the use of the Leggett-Garg inequalities for device-independent security appropriate for prepare-and-measure protocols subjected to the higher dimensional attack that would completely undermine standard BB84. In the last part, we introduce the novel concept of nonlocal subspaces constructed using the graph state formalism, and propose their application for quantum information splitting. In particular, we use the stabilizer formalism of graph states to construct degenerate Bell operators, whose eigenspace determines the nonlocal subspace, into which a quantum secret is encoded and shared among an authorized group of agents, or securely transmitted to a designated secret retriever. The security of our scheme arises from the monogamy of quantum correlations. The quantum violation of the Bell-type inequality here is to its algebraic maximum, making this approach inherently suitable for the device-independent scenario.