13 papers
Quantisation of Abstract Data Types
Mingsheng Ying, Zhicheng Zhang, Kean Chen
In this paper, we introduce a notion of abstract quantum data type within the framework of universal algebra. This notion provides an algebraic foundation for describing data abstr…
Nearly Sample-Optimal Estimators for Quantum Rényi and Tsallis Entropies
Kean Chen, Qisheng Wang
In this paper, we provide estimators for quantum Rényi and Tsallis entropies with nearly optimal sample complexity. Specifically, for order , dimension , and additive error $…
Quantum Multi-Level Estimation of Functionals of Discrete Distributions
Kean Chen, Minbo Gao, Tongyang Li +2
We propose a quantum multi-level estimation framework for a functional of a discrete distribution . We partition the values into logarith…
Strict Hierarchy for Quantum Channel Certification to Unitary
Kean Chen, Qisheng Wang, Zhicheng Zhang
We consider the problem of quantum channel certification to unitary, where one is given access to an unknown -dimensional channel , and wants to test whether $\math…
Quantum channel tomography: optimal bounds and a Heisenberg-to-classical phase transition
Kean Chen, Filippo Girardi, Aadil Oufkir +2
How many black-box queries to a quantum channel are needed to learn its full classical description? This question lies at the heart of quantum channel tomography (also known as qua…
Optimal lower bound for quantum channel tomography in away-from-boundary regime
Kean Chen, Zhicheng Zhang, Nengkun Yu
Consider quantum channels with input dimension , output dimension and Kraus rank at most . Any such channel must satisfy the constraint , and the parame…