2006/01/02 by Noam Elron, Yonina C. Eldar, Elron, Noam +1
Computer Science · Engineering · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Wireless Communication Security Techniques
paper · pdf · doi:10.48550/arxiv.quant-ph/0601010
openalex publication_date 2006/01/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate optimal encoding and retrieval of digital data, when the storage/communication medium is described by quantum mechanics. We assume an m-ary alphabet with arbitrary prior distribution, and an n-dimensional quantum system. Under these constraints, we seek an encoding-retrieval setup, comprised of code-states and a quantum measurement, which maximizes the probability of correct detection. In our development, we consider two cases. In the first, the measurement is predefined and we seek the optimal code-states. In the second, optimization is performed on both the code-states and the measurement. We show that one cannot outperform `pseudo-classical transmission', in which we transmit n symbols with orthogonal code-states, and discard the remaining symbols. However, such pseudo-classical transmission is not the only optimum. We fully characterize the collection of optimal setups, and briefly discuss the links between our findings and applications such as quantum key distribution and quantum computing. We conclude with a number of results concerning the design under an alternative optimality criterion, the worst-case posterior probability, which serves as a measure of the retrieval reliability.