In this article, we present quantum algorithms for estimating von Neumann entropy and Renyi entropy, which are crucial physical and information-theoretical properties of a given quantum state $\rho$. Although there have been existing works that have achieved the same goal, some prior developments assume the unitary that prepares the purification to the target state $\rho$. Here, we consider an alternative setting where only copies of $\rho$ are given and we construct a quantum algorithm that estimates the desired entropy. Our framework completes the given task by measuring a small number of ancilla qubits without directly measuring the system, and it achieves significant improvement over prior relevant developments. For example, for the Renyi entropy of the order of nonintegral $\alpha$, our method achieves almost a power-of-2 improvement in sample complexity with respect to the rank of the given state and almost a power-of-2 improvement in error tolerance compared with the work by Wang et al. [Y. Wang, B. Zhao, and X. Wang, Phys. Rev. Appl. 19, 044041 (2023)].

Close

PrevNext

View figure in article

• Quantum algorithms & computation
• Quantum computation
• Quantum information theory