The Impossibility of a Quantum Phase Operator

Yee Kin Tsui

Dafa Li

The no-cloning theorem, the no-deleting theorem, and other no-go theorems play a crucial role in quantum mechanics and quantum information. In this paper, we show that it is impossible to conjugate or reflect an unknown quantum state or conjugate or reflect the bit-flip (the phase-flip) of an unknown state via a universally unitary evolution. We also indicate that the partial conjugating operations are not anti-unitary and it is impossible to universally partially conjugate an unknown state via a unitary evolution. We compute the fidelities of the optimal physical approximations to conjugating and conjugating the bit-flip and phase-flip operations.

Robert Lynch

Yanyan Feng, Qian Zhang, Jinjing Shi +2 more

The quantum proxy signature is one of the most significant formalisms in quantum signatures. We put forward a quantum proxy signature scheme using quantum walk-based teleportation and quantum one-time pad CNOT (QOTP-CNOT) operation, which includes four phases, i.e., initializing phase, authorizing phase, signing phase and verifying phase. The QOTP-CNOT is achieved by attaching the CNOT operation upon the QOTP and it is applied to produce the proxy signature state. The quantum walk-based teleportation is employed to transfer the encrypted message copy derived from the binary random sequence from the proxy signer to the verifier, in which the required entangled states do not need to be prepared ahead and they can be automatically generated during quantum walks. Security analysis demonstrates that the presented proxy signature scheme has impossibility of denial from the proxy and original signers, impossibility of forgery from the original signatory and the verifier, and impossibility of repudiation from the verifier. Notably, the discussion shows the complexity of the presented algorithm and that the scheme can be applied in many real scenarios, such as electronic payment and electronic commerce.

Masashi Ban

Lukas J. Fiderer, Marek Kuś, Daniel Braun

We study mechanisms that allow one to synchronize the quantum phase of two qubits relative to a fixed basis. Starting from one qubit in a fixed reference state and the other in an unknown state, we find that, contrary to the impossibility of perfect quantum cloning, the quantum phase can be synchronized perfectly through a joined unitary operation. When both qubits are initially in a pure unknown state, perfect quantum-phase synchronization through unitary operations becomes impossible. In this situation we determine the maximum average quantum-phase synchronization fidelity and the distribution of relative phases and fidelities, and we identify optimal quantum circuits that achieve this maximum fidelity. A subset of these optimal quantum circuits enable perfect quantum-phase synchronization for a class of unknown initial states restricted to the equatorial plane of the Bloch sphere.