Quantum metrology with quantum Wheatstone bridge composed of Bose systems

The quantum version of a special classical Wheatstone bridge built with a boundary-driven spin system has recently been proposed. We propose a quantum Wheatstone bridge consisting of Bose systems, which can simulate the general classical Wheatstone bridge. Unknown coupling can be obtained when the quantum Wheatstone bridge is balanced, which can be determined simply by homodyne detection. When the expectation value of the homodyne detection is 0, the quantum Wheatstone bridge is unbalanced. When the expectation value of the homodyne detection is proportional to the square root of the initial number of bosons by regulating a known coupling strength, the quantum Wheatstone bridge is balanced. By calculating the quantum Fisher information, we show that the measurement precision is optimal when the quantum Wheatstone bridge is balanced. And the homodyne detection is close to the optimal measurement in the case of low-temperature baths.