Randomized encoding is a powerful cryptographic primitive with various applications such as secure multiparty computation, verifiable computation, parallel cryptography, and complexity lower bounds. Intuitively, randomized encoding
f^ of a function
f is another function such that
f(x) can be recovered from
f^(x), and nothing except for
f(x) is leaked from
f^(x). Its quantum version, quantum randomized encoding, has been introduced recently [Brakerski and Yuen, arXiv:2006.01085]. Intuitively, quantum randomized encoding
F^ of a quantum operation
F is another quantum operation such that, for any quantum state
ρ,
F(ρ) can be recovered from
F^(ρ), and nothing except for
F(ρ) is leaked from
F^(ρ). In this paper, we show three results. First, we show that if quantum randomized encoding of BB84 state generations is possible with an encoding operation
E, then a two-round verification of quantum computing is possible with a classical verifier who can additionally do the operation
E. One of the most important goals in the field of the verification of quantum computing is to construct a verification protocol with a verifier as classical as possible. This result therefore demonstrates a potential application of quantum randomized encoding to the verification of quantum computing: if we can find a good quantum randomized encoding (in terms of the encoding complexity), then we can construct a good verification protocol of quantum computing. Our second result is, however, to show that too good quantum randomized encoding is impossible: if quantum randomized encoding for the generation of even simple states (such as BB84 states) is possible with a classical encoding operation, then the no-cloning is violated. Finally, we consider a natural modification of blind quantum computing protocols in such a way that the server gets the output like quantum randomized encoding. We show that the modified protocol is not secure.
Applications of the proposed primitive: Quantum Primitive for Output-Hiding Function Sharing, are discussed for secure quantum communications and computation protocols. In particular, QKD applications provide notable enhanced security and efficiency properties relative to status-quo protocols. Additionally, we provide examples when parties may wish to encode joint functions, or decisions, which remain information-theoretically hidden from external parties and those internal to the quantum system, without additional private keys, hidden randomness, or classical communication. In particular these applications may be useful in domains such as; financial transactions, joint signaling or coordination decisions, and navigation systems, among others.
Polarization drift due to propagation medium birefringence is a primary cause of increased quantum bit error ratio (QBER) in polarization-encoded quantum key distribution (QKD). The random nature of polarization drift and environmental instabilities cause it to vary over time, necessitating algorithms for effective polarization drift compensation in polarization-encoded optical fiber QKD links. I propose an algorithm based on processing time-multiplexed control pulses by unscented Kalman filter that minimizes the number of additional measurements that interrupt key exchange. I evaluated the robustness of the algorithm under various conditions, including random polarization drift velocities, and additional noise due to depolarization for weak-coherent BB84-like protocols, to determine the applicability limits of the proposed algorithm and its overhead.