Related papers: State-extended uncertainly relations and tomograph…
For noncomposite systems in classical and quantum domains, we obtain new inequalities such as the subadditivity and strong subadditivity conditions for Shannon entropies and information determined by the probability distributions and for…
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical Physics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in…
A factor-graph representation of quantum-mechanical probabilities (involving any number of measurements) is proposed. Unlike standard statistical models, the proposed representation uses auxiliary variables (state variables) that are not…
Quantum state tomography, aimed at deriving a classical description of an unknown state from measurement data, is a fundamental task in quantum physics. In this work, we analyse the ultimate achievable performance of tomography of…
In view of the photon-number tomograms of two-mode light states, using the qubit-portrait method for studying the probability distributions with infinite outputs, the separability and entanglement detection of the states are studied.…
The systems with multimode nonstationary Hamiltonians quadratic in position and momentum operators are reviewed. The tomographic probability distributions (tomograms) for the Fock states and Gaussian states of the quadratic systems are…
The method of constructing the tomographic probability distributions describing quantum states in parallel with density operators is presented. Known examples of Husimi-Kano quasi-distribution and photon number tomography are reconsidered…
The tomographic description of a quantum state is formulated in an abstract infinite dimensional Hilbert space framework, the space of the Hilbert-Schmidt linear operators, with trace formula as scalar product. Resolutions of the unity,…
We study entanglement-related properties of random quantum states which are unitarily invariant, in the sense that their distribution is left unchanged by conjugation with arbitrary unitary operators. In the large matrix size limit, the…
In quantum-state tomography on sources with quantum degrees of freedom of large Hilbert spaces, inference of quantum states of light for instance, a complete characterization of the quantum states for these sources is often not feasible…
This paper delves into the significance of the tomographic probability density function (pdf) representation of quantum states, shedding light on the special classes of pdfs that can be tomograms. Instead of using wave functions or density…
The uncertainty relation of three quantities in quantum mechanics is estimated in terms of commutators. The Pauli matrices are used to find a contribution of third-order commutators. The resulting inequality refines the Heisenberg…
Majorization uncertainty relations are generalized for an arbitrary mixed quantum state $\rho$ of a finite size $N$. In particular, a lower bound for the sum of two entropies characterizing probability distributions corresponding to…
The tomographic method is employed to investigate the presence of quantum correlations in two classes of parameter-dependent states of two qutrits. The violation of some Bell's inequalities in a wide domain of the parameter space is shown.…
The continuous quantum measurement within the probability representation of quantum mechanics is discussed. The partial classical propagator of the symplectic tomogram associated to a particular measurement outcome is introduced, for which…
We report the experimental measurement of bipartite quantum correlations of an unknown two-qubit state. Using a liquid state Nuclear Magnetic Resonance (NMR) setup and employing geometric discord, we evaluate the quantum correlations of a…
We introduce new representations to formulate quantum mechanics on noncommutative coordinate space, which explicitly display entanglement properties between degrees of freedom of different coordinate components and hence could be called…
Gaussian states have played on important role in the physics of continuous-variable quantum systems. They are appealing for the experimental ease with which they can be produced, and for their compact and elegant mathematical description.…
In quantum mechanics, the variance-based Heisenberg-type uncertainty relations are a series of mathematical inequalities posing the fundamental limits on the achievable accuracy of the state preparations. In contrast, we construct and…
Quantum state tomography is the standard tool in current experiments for verifying that a state prepared in the lab is close to an ideal target state, but up to now there were no rigorous methods for evaluating the precision of the state…