Encrypted quantum state tomography with phase estimation for quantum Internet

Abstract

Quantum state tomography (QST) is a fundamental tool requiring privacy in future distributed systems where unknown states are measured for extracting information. Gentle measurement and differential privacy (DP)-based privacy solutions minimize the damage on unknown state and leakage about the quantum information respectively. In this article we propose a fundamentally different design for privacy-preserving QST in a multi-party setting. We assume that Alice delegates QST task of a distant source for which she has no access to a third-party player Bob accessing to the source while preserving the source privacy against the operations realized by Bob. Encrypted QST algorithm is proposed which encodes or maps source computational basis states by exploiting phase estimation and feature mapping concept of quantum machine learning (QML). Bob maps basis states to eigenvalues of a specially designed unitary operator in an entangled manner with his ancillary qubits while teleporting the source qubits back to Alice before applying conventional QST. Encoding mechanism is conjectured as having NP-hard decoding complexity based on difficulty of subset-sum problem combined with Hadamard transform. Linear optical design and quantum circuit implementations are presented for future experiments in noisy intermediate-scale quantum (NISQ) devices. Theoretical and numerical supporting evidences are proposed supporting the proposed eigenstructure. EQST promises further applications for multiple source classification tasks and as a novel feature mapping method for future data embedding tasks in QML.