We address quantum estimation in situations where one has at disposal data from the measurement of an incomplete set of observables and some a priori information on the state itself. By expressing the a priori information in terms of a bias toward a given state the problem may be faced by minimizing the quantum relative entropy (Kullback entropy) with the constraint of reproducing the data. We exploit the resulting minimum Kullback entropy principle for the estimation of a quantum state from the measurement of a single observable, either from the sole mean value or from the complete probability distribution, and apply it as a tool for the estimation of weak Hamiltonian processes. Qubit and harmonic oscillator systems are analyzed in some details.
Correlation in fermion or boson systems as the minimum of entropy relative to all free states
在多费米子系统中，“关联”指的是独立粒子模型的不足。使用“自由”状态作为我们的独立粒子模型的原型，我们提出了一个相关性的度量，我们称之为“非自由性”[Int. J. Quant. Inf.5，815（2007）]。多费米子态的非自由度定义为多费米子态相对于具有相同1-矩阵的唯一自由态的熵。本文证明了一个态的非自由度是它的熵相对于所有自由态的最小值。我们还将非自由度的定义扩展到多玻色子态，并讨论了几个例子。
A constructive violation of additivity of minimum output von Neumann entropy
Joint Quantum Institute, Department of Physics, NIST/University of Maryland（量子联合研究所，物理系，美国国家标准与技术研究院/马里兰大学）；Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（量子信息与计算科学联合中心，美国国家标准与技术研究院/马里兰大学）
