Noise-Induced Quantum Synchronization and Entanglement\nin a Quantum Analogue of Huygens’ Clock

We propose a quantum\nanalogue of the Huygens clock, where the phases\nof two spins synchronize through their interaction with a shared environment.\nThis environment acts like the escapement mechanism in a mechanical\nclock, regulating the gear train and allowing discrete timing advances.\nIn our model, the relative phases of the two spins synchronize via\na mutually correlated environment. We demonstrate that several arguments\ncan significantly reduce the cardinality of the allowed measurements\nfor a system of qubits, thus simplifying the problem. We present a\nnumerically efficient method to calculate the degree of quantumness\nin the correlations of the final density matrix, providing a tight\nupper bound for rank 3 and rank 4 density matrices. We suggest a potential\nrealization of noise-induced synchronization between two nuclear spins\ncoupled to a common ancilla undergoing dynamical decoupling.