Related papers: Informationally complete measurements and groups r…
We provide a detailed analysis of the question: how many measurement settings or outcomes are needed in order to identify a quantum system which is constrained by prior information? We show that if the prior information restricts the system…
In the general theory of quantum measurement, one associates a positive semidefinite operator on a $d$-dimensional Hilbert space to each of the $n$ possible outcomes of an arbitrary measurement. In the special case of a projective…
Quantum measurements can be described by operators that assign conditional probabilities to different outcomes while also describing unavoidable physical changes to the system. Here, we point out that operators describing information gain…
In the present work, we suggest an approach for describing dynamics of finite-dimensional quantum systems in terms of pseudostochastic maps acting on probability distributions, which are obtained via minimal informationally complete quantum…
We show that any unitary transformation performed on the quantum state of a closed quantum system, describes an inner, reversible, generalized quantum measurement. We also show that under some specific conditions it is possible to perform a…
Generalized quantum measurements play a crucial role in quantum mechanics, and symmetric informationally complete positive operator-valued measurements (SIC POVMs) provide a powerful and flexible framework for extracting information from…
Hilbert space operators may be mapped onto a space of ordinary functions (operator symbols) equipped with an associative (but noncommutative) star-product. A unified framework for such maps is reviewed. Because of its clear probabilistic…
In this paper, we establish a dynamical quantum state tomography framework. Under this framework, it is feasible to obtain complete knowledge of any unknown state of a $d$-level system via only an arbitrary operator of certain types of…
The concept of randomized measurements on individual particles has proven to be useful for analyzing quantum systems and is central for methods like shadow tomography of quantum states. We introduce $\textit{collective}$ randomized…
In this study the determinant of the average quadratic error matrix is used as the measure of state estimation efficiency. This quantity is easily computable in some cases, so it gives us a reasonable tool to find optimal measurement setup…
To mitigate dissipative effects from environmental interactions and efficiently stabilize quantum states, time-optimal control has emerged as an effective strategy for open quantum systems. This paper extends the framework by incorporating…
The mechanism of describing quantum states by standard probability (tomographic one) instead of wave function or density matrix is elucidated. Quantum tomography is formulated in an abstract Hilbert space framework, by means of the identity…
Observational entropy is interpreted as the uncertainty an observer making measurements associates with a system. So far, properties that make such an interpretation possible rely on the assumption of ideal projective measurements. We show…
The concept of intrinsic and operational observables in quantum mechanics is introduced. It is argued that, in any realistic description of a quantum measurement that includes a detecting device, it is possible to construct from the…
Generalized quantum measurements (also known as POVMs) are of great importance in quantum information and quantum foundations, but often difficult to perform. We present an experimental approach which can in principle be used to perform…
A quantum measurement, often referred to as positive operator-valued measurement (POVM), is a set of positive operators $P_j=P_j^\dag\geq 0$ summing to identity, $\sum_jP_j=\mathbb{1}$. This can be seen as a generalization of a probability…
We consider the problem of estimating the ensemble average of an observable on an ensemble of equally prepared identical quantum systems. We show that, among all kinds of measurements performed jointly on the copies, the optimal unbiased…
We consider a quaternionic quantum formalism for the description of quantum states and quantum dynamics. We prove that generalized quantum measurements on physical systems in quaternionic quantum theory can be simulated by usual quantum…
We introduce the informational power of a quantum measurement as the maximum amount of classical information that the measurement can extract from any ensemble of quantum states. We prove the additivity by showing that the informational…
Quantum coherence is a fundamental feature of quantum physics and plays a significant role in quantum information processing. By generalizing the resource theory of coherence from von Neumann measurements to positive operator-valued…