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A review of the tomographic-probability representation of classical and quantum states is presented. The tomographic entropies and entropic uncertainty relations are discussed in connection with ambiguities in the interpretation of the…
The new inequality recently found by Trifonov and called the state-extended inequality is considered in the tomographic-probability representation of quantum mechanics. The Trifonov uncertainty relations are expressed in terms of optical…
New inequalities for symplectic tomograms of quantum states and their connection with entropic uncertainty relations are discussed within the framework of the probability representation of quantum mechanics.
The contextuality and noncontextuality notions are considered in framework of probability representation of quantum states. Example of qutrit states and violation of the noncontextuality inequalities are presented by using the spin tomogram…
The probability representation of quantum mechanics including propagators and tomograms of quantum states of the universe and its application to quantum gravity and cosmology are reviewed. The minisuperspaces modeled by oscillator, free…
It is usually believed that a picture of Quantum Mechanics in terms of true probabilities cannot be given due to the uncertainty relations. Here we discuss a tomographic approach to quantum states that leads to a probability representation…
Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In…
A linear map of qudit tomogram onto qubit tomogram (qubit portrait) is proposed as a characteristics of the qudit state. Using the qubit portrait method the Bell inequalities for two qubits and two qutrits are discussed in framework of…
Starting from the famous Pauli problem on the possibility to associate quantum states with probabilities, the formulation of quantum mechanics in which quantum states are described by fair probability distributions (tomograms, i.e.…
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…
The density matrix of composite spin system is discussed in relation to the adjoint representation of unitary group U(n). The entanglement structure is introduced as an additional ingredient to the description of the linear space carrying…
Multi-qudit systems are studied in tomographic probability representations of quantum qudit states. Results of calculations for Bell-type numbers within the framework of classical probability theory and in quantum tomography are compared.…
The tomographic approach to quantum mechanics is revisited as a direct tool to investigate violation of Bell-like inequalities. Since quantum tomograms are well defined probability distributions, the tomographic approach is emphasized to be…
The gauge invariance of the evolution equations of tomographic probability distribution functions of quantum particles in an electromagnetic field is illustrated. Explicit expressions for the transformations of ordinary tomograms of states…
It is often stated that quantum mechanics only makes statistical predictions and that a quantum state is described by the various probability distributions associated with it. Can we describe a quantum state completely in terms of…
The probability representation, in which cosmological quantum states are described by a standard positive probability distribution, is constructed for minisuperspace models selected by Noether symmetries. In such a case, the tomographic…
Continuous-variable quantum systems are foundational to quantum computation, communication, and sensing. While traditional representations using wave functions or density matrices are often impractical, the tomographic picture of quantum…
We give a review of the tomographic probability representation of quantum mechanics. We present the formalism of quantum states and quantum observables using the formalism of standard probability distributions and classical-like random…
In view of the tomographic-probability representation of quantum states, we reconsider the approach to quantumness tests of a single system developed in [Alicki and Van Ryn 2008 J. Phys. A: Math. Theor. 41 062001]. For qubits we introduce a…
Probability representation entropy (tomographic entropy) of arbitrary quantum state is introduced. Using the properties of spin tomogram to be standard probability distribution function the tomographic entropy notion is discussed. Relation…