Universal quantum data compression via gentle tomography

Gentle Measurement of Quantum States and Differential Privacy

In differential privacy (DP), we want to query a database about n users, in a way that "leaks at most eps about any individual user," even conditioned on any outcome of the query. Meanwhile, in gentle measurement, we want to measure n quantum states, in a way that "damages the states by at most alpha," even conditioned on any outcome of the measurement. In both cases, we can achieve the goal by techniques like deliberately adding noise to the outcome before returning it. This paper proves a new and general connection between the two subjects. Specifically, we show that on products of n quantum…

维度无关且计算高效的影子层析成像

Dimension Independent and Computationally Efficient Shadow Tomography

该研究提出一种维度无关的高效影子层析成像算法，样本复杂度为n=Θ(√m log m/ε²)且在ε上最优，兼具多方面计算与内存效率，通过聚焦影子中的温和性证明含噪测量不显著扰动态的期望值。

Gentle Measurement as a Principle of Quantum Theory

We propose the gentle measurement principle (GMP) as one of the principles at the foundation of quantum mechanics. It asserts that if a set of states can be distinguished with high probability, they can be distinguished by a measurement that leaves the states almost invariant, including correlation with a reference system. While GMP is satisfied in both classical and quantum theories, we show, within the framework of general probabilistic theories, that it imposes strong restrictions on the law of physics. First, the measurement uncertainty of a pair of observables cannot be significantly larg…

Non-local Operations: Purification, storage, compression, tomography, and probabilistic implementation

We provide several applications of a previously introduced isomorphism between physical operations acting on two systems and entangled states [1]. We show: (i) how to implement (weakly) non-local two qubit unitary operations with a small amount of entanglement; (ii) that a known, noisy, non-local unitary operation as well as an unknown, noisy, local unitary operation can be purified; (iii) how to perform the tomography of arbitrary, unknown, non-local operations; (iv) that a set of local unitary operations as well as a set of non-local unitary operations can be stored and compressed; (v) how t…

使用温和测量的量子态样本最优学习

Sample-optimal learning of quantum states using gentle measurements

本文引入α-局部温和测量类，通过改进温和性与量子差分隐私的关系证明强量子数据处理不等式，并用于推导量子层析和量子态认证的样本复杂度下界，提出量子标签切换方法达到该下界。

量子事件学习与温和随机测量

Quantum Event Learning and Gentle Random Measurements

本文提出温和随机测量引理，研究量子事件学习相关问题，给出量子OR等协议，并基于此得到样本复杂度匹配当前最优的阴影层析成像算法。