Quantum α-fidelity of diagonalizable second-order Hamiltonians in multi-dimensional systems

Abstract

How to characterize the similarity between two quantum states has received much attention recently. Motivated by the continued push in this direction, we propose a computable analytical formula for the quantum α-fidelity between diagonalizable second-order Hamiltonians, which is simply expressed in terms of the matrix representation of operators. Further, using this analytical formula, we calculate the α-fidelity of the one-dimensional and two-dimensional displaced-squeezed thermal states, the Liu-Tombesi oscillators, and twin-beam amplitude-squeezed states. Since α-fidelity can precisely characterize the approximation accuracy between two quantum states by adjusting the value of the parameter α, our results offer a richer fidelity family to quantify the similarity between diagonalizable second-order Hamiltonians in multi-dimensional systems, and hence may have potential applications in quantum information and quantum computing.