A Topological Framework for Defining Quasi-Efficiency in Quantum Encryption

Quantum computers, governed by the principles of quantum mechanics, have opened new avenues in computation and communication. Over the past two decades, the development of quantum channels and communication algorithms has spurred the design of quantum encryption schemes for ensuring secure communication over insecure quantum networks. Typically, the physical design of quantum circuits for encrypting qubits is driven by specific efficiency metrics. In this work, we introduce a relaxed notion of efficiency, termed quasi-efficiency, which can be achieved during the encryption of qubits for transmission. Quasi-efficiency intuitively captures the energy expenditure during computation by analyzing redundancy. Additionally, we propose a topological framework based on homological algebra to assist experimentalists in crafting quasi-efficient quantum encryption schemes.