Related papers: Quantum states and knowledge: Between pure states …
We discuss a model for quantum computing with initially mixed states. Although such a computer is known to be less powerful than a quantum computer operating with pure (entangled) states, it may efficiently solve some problems for which no…
A framework for a quantum information theory is introduced that is based on the measure of quantum information associated with probability distribution predicted by quantum measuring of state. The entanglement between states of measured…
The probability representation of states in standard quantum mechanics where the quantum states are associated with fair probability distributions (instead of wave function or density matrix) is shortly commented and bibliography related to…
We clarify different definitions of the density matrix by proposing the use of different names, the full density matrix for a single-closed quantum system, the compressed density matrix for the averaged single molecule state from an…
An exploratory approach to the possibility of analyzing nonorthogonality as a quantifiable property is presented. Three different measures for the nonorthogonality of pure states are introduced, and one of these measures is extended to…
A given density matrix may be represented in many ways as a mixture of pure states. We show how any density matrix may be realized as a uniform ensemble. It has been conjectured that one may realize all probability distributions that are…
The density matrix formalism which is widely used in the theory of measurements, quantum computing, quantum description of chemical and biological systems always imply the averaging over the states of the environment. In practice this is…
A mixed quantum state can be taken as capturing an unspecified form of ignorance; or as describing the lack of knowledge about the true pure state of the system ("proper mixture"); or as arising from entanglement with another system that…
The main goal of this paper is to give a pedagogical introduction to Quantum Information Theory-to do this in a new way, using network diagrams called Quantum Bayesian Nets. A lesser goal of the paper is to propose a few new ideas, such as…
It is well known that density matrices can be used in quantum mechanics to represent the information available to an observer about either a system with a random wave function (``statistical mixture'') or a system that is entangled with…
Complexity is an interdisciplinary concept which, first of all, addresses the question of how order emerges out of randomness. For many reasons matrices provide a very practical and powerful tool in approaching and quantifying the related…
It is a hard and important problem to find the criterion of the set of positive-definite matrixes which can be written as reduced density operators of a multi-partite quantum state. This problem is closely related to the study of many-body…
Uncertainty relations are old, yet potentially rewarding to explore. By introducing a quantity called the uncertainty matrix, we provide a link between purity and observable incompatibility, and derive several stronger uncertainty relations…
The properties of coherence and polarization of light has been the subject of intense investigations and form the basis of many technological applications. These concepts which historically have been treated independently can now be…
The principle of superposition is an intriguing feature of Quantum Mechanics, which is regularly exploited at various instances. A recent work [PRL \textbf{116}, 110403 (2016)] shows that the fundamentals of Quantum Mechanics restrict the…
Purity and coherence of a quantum state are recognized as useful resources for various information processing tasks. In this article, we propose a fidelity based valid measure of purity and coherence monotone and establish a relationship…
We introduce two methods for estimating the density matrix for a quantum system: Quantum Maximum Likelihood and Quantum Variational Inference. In these methods, we construct a variational family to model the density matrix of a mixed…
Quantum state tomography (QST) is the process of reconstructing the state of a quantum system (mathematically described as a density matrix) through a series of different measurements, which can be solved by learning a parameterized…
Information, in its communications sense, is a transactional property. If the received signals communicate choices made by the sender of the signals, then information has been transmitter by the sender to the receiver. Given this reality,…
This article is an introduction to quant-ph/0302092. We propose to quantify how "quantum" a set of quantum states is. The quantumness of a set is the worst-case difficulty of transmitting the states through a classical communication…