Paper 2024/017

PT-symmetric mapping of three states and its implementation on a cloud quantum processor

Abstract

Recently, PT-symmetric systems have garnered significant attention due to their unconventional properties. Despite the growing interest, there remains an ongoing debate about whether these systems can outperform their Hermitian counterparts in practical applications, and if so, by what metrics this performance should be measured. We developed a novel PT-symmetric approach for mapping N = 3 pure qubit states to address this, implemented it using the dilation method, and demonstrated it on a superconducting quantum processor from the IBM Quantum Experience. For the first time, we derived exact expressions for the population of the post-selected PT-symmetric subspace for both N = 2 and N = 3 states. When applied to the discrimination of N = 2 pure states, our algorithm provides an equivalent result to the conventional unambiguous quantum state discrimination. For N = 3 states, our approach introduces novel capabilities not available in traditional Hermitian systems, enabling the transformation of an arbitrary set of three quantum states into another, at the cost of introducing an inconclusive outcome. Our algorithm has the same error rate for the attack on the three-state QKD protocol as the conventional minimum error, maximum confidence, and maximum mutual information strategies. For post-selection quantum metrology, our results provide precise conditions where PT-symmetric quantum sensors outperform their Hermitian counterparts in terms of information-cost rate. Combined with punctuated unstructured quantum database search, our method significantly reduces the qubit readout requirements at the cost of adding an ancilla, while maintaining the same average number of oracle calls as the original punctuated Grover's algorithm. This provides significant advantages for NISQ-era computers. Our work opens new pathways for applying PT symmetry in quantum communications, computing, and cryptography.