Kavli Affiliate: Jing Wang
| First 5 Authors: , , , ,
| Summary:
In the fields of quantum mechanics and quantum information science, the
traces of reduced density matrix powers play a crucial role in the study of
quantum systems and have numerous important applications. In this paper, we
propose a universal framework to simultaneously estimate the traces of the
$2$nd to the $n$th powers of a reduced density matrix using a single quantum
circuit with $n$ copies of the quantum state. Specifically, our approach
leverages the controlled SWAP test and establishes explicit formulas connecting
measurement probabilities to these traces. We further develop two algorithms: a
purely quantum method and a hybrid quantum-classical approach combining
Newton-Girard iteration. Rigorous analysis via Hoeffding inequality
demonstrates the method’s efficiency, requiring only
$M=Oleft(frac1epsilon^2log(fracndelta)right)$ measurements to
achieve precision $epsilon$ with confidence $1-delta$. Additionally, we
explore various applications including the estimation of nonlinear functions
and the representation of entanglement measures. Numerical simulations are
conducted for two maximally entangled states, the GHZ state and the W state, to
validate the proposed method.
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