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The most peculiar, specifically quantum, features of quantum mechanics --- quantum nonlocality, indeterminism, interference of probabilities, quantization, wave function collapse during measurement --- are explained on a logical-geometrical…
For a quantum system undergoing a unitary process work is commonly defined based on the Two Projective Measurement (TPM) protocol which measures the energies of the system before and after the process. However, it is well known that…
Joint measurements of non-commuting observables are characterized by unavoidable measurement uncertainties that can be described in terms of the error statistics for input states with well-defined values for the target observables. However,…
This paper explores the problem of quantum measurement complexity. In computability theory, the complexity of a problem is determined by how long it takes an effective algorithm to solve it. This complexity may be compared to the difficulty…
Quantum mechanics predicts correlation between spacelike separated events which is widely argued to violate the principle of Local Causality. By contrast, here we shall show that the Schr\"odinger equation with Born's statistical…
The uncertainty relation is a distinctive characteristic of quantum theory. The uncertainty is essentially rooted in quantum states. In this work we regard the uncertainty as an intrinsic property of quantum state and characterize it…
We describe quantum tomography as an inverse statistical problem and show how entropy methods can be used to study the behaviour of sieved maximum likelihood estimators. There remain many open problems, and a main purpose of the paper is to…
We describe a scheme, operating in a manner analogous to a reversed Raman output coupler, for measuring the phase-sensitive quadrature statistics of an atom laser beam. This scheme allows for the transferral of the atomic field statistics…
Negative probability values have been widely employed as an indicator of the nonclassicality of quantum systems. Known as a quasiprobability distribution, they are regarded as a useful tool that provides significant insight into the…
Measurements with randomly chosen settings determine many important properties of quantum states without the need for a shared reference frame or calibration. They naturally emerge in the context of quantum communication and quantum…
The apparent random outcome of a quantum measurement is conjectured to be fundamentally determined by the microscopic state of the macroscopic measurement apparatus. The apparatus state thus plays the role of a hidden variable which, in…
The uncertainty principle is one of the fundamental features of quantum mechanics and plays an essential role in quantum information theory. We study uncertainty relations based on variance for arbitrary finite $N$ quantum observables. We…
We develop a general formulation of quantum statistical mechanics in terms of probability currents that satisfy continuity equations in the multi-particle position space, for closed and open systems with a fixed number of particles. The…
Quantum estimation theory is a reformulation of random statistical theory with the modern language of quantum mechanics. In fact, the density operator plays a role similar to that of probability distribution functions in classical…
Any observable with finite eigenvalue spectrum can be measured using a multiport apparatus realizing an appropriate unitary transformation and an array of detector instruments, where each detector operates as an indicator of one possible…
Distances between quantum states are reviewed within the framework of the tomographic-probability representation. Tomographic approach is based on observed probabilities and is straightforward for data processing. Different states are…
Complete characterization of states and processes that occur within quantum devices is crucial for understanding and testing their potential to outperform classical technologies for communications and computing. However, solving this task…
There is a constraining relation between the reliability of a quantum measurement and the extent to which the measurement process is, in principle, reversible. The greater the information that is gained, the less reversible the measurement…
In this Letter we investigate the concept of quantum work and its measurability from the viewpoint of quantum measurement theory. Very often, quantum work and fluctuation theorems are discussed in the framework of projective two-point…
In many a traditional physics textbook, a quantum measurement is defined as a projective measurement represented by a Hermitian operator. In quantum information theory, however, the concept of a measurement is dealt with in complete…