Related papers: Probability representation and state-extended unce…
We develop an approach where the quantum system states and quantum observables are described as in classical statistical mechanics -- the states are identified with probability distributions and observables, with random variables. An…
Uncertainty relations are a fundamental feature of quantum mechanics. How can these relations be found systematically? Here we develop a semidefinite programming hierarchy for additive uncertainty relations in the variances of non-commuting…
The coherent and Fock states of a charge moving in varying homogeneous magnetic field are studied in the tomographic probability representation of quantum mechanics. The states are expressed in terms of quantum tomograms. The coherent…
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…
The probability representation of quantum and classical statistical mechanics is discussed. Symplectic tomography, center-of-mass tomography, and spin tomography are studied. The connection of tomographic probabilities with dynamic…
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…
We introduce the probability distributions describing quantum observables in conventional quantum mechanics and clarify their relations to the tomographic probability distributions describing quantum states. We derive the evolution equation…
We study a possible improvement of uncertainty relations. The Heisenberg uncertainty relation employs commutator of a pair of conjugate observables to set the limit of quantum measurement of the observables. The Schroedinger uncertainty…
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…
Any bipartite quantum state has quasi-probability representations in terms of separable states. For entangled states these quasi-probabilities necessarily exhibit negativities. Based on the general structure of composite quantum states, one…
In the preceding Comment (quant-ph/0209032) Trifonov disputes our recently proposed uncertainty relations for a quantum particle on a circle. He states that (i) the quantity $\Delta^2(\hat\phi)$ introduced by us representing the uncertainty…
A novel geometric formalism for statistical estimation is applied here to the canonical distribution of classical statistical mechanics. In this scheme thermodynamic states, or equivalently, statistical mechanical states, can be…
Quantum mechanical uncertainty relations for position and momentum are expressed in the form of inequalities involving the Renyi entropies. The proof of these inequalities requires the use of the exact expression for the (p,q)-norm of the…
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…
The entanglement phenomenon on example of Smolin state of four qubits is discussed. This state is known as bound entangled state and the spin tomogram of the state is found in explicit form. The qubit portrait method is used the Bell…
Uncertainty relations provide constraints on how well the outcomes of incompatible measurements can be predicted, and, as well as being fundamental to our understanding of quantum theory, they have practical applications such as for…
A survey on the generalizations of Heisenberg uncertainty relation and a general scheme for their entangled extensions to several states and observables is presented. The scheme is illustrated on the examples of one and two states and…
As a foundation of modern physics, uncertainty relations describe an ultimate limit for the measurement uncertainty of incompatible observables. Traditionally, uncertain relations are formulated by mathematical bounds for a specific state.…
We derive a quantum extension of the thermodynamic uncertainty relation where dynamical fluctuations are quantified by the Terletsky-Margenau-Hill quasiprobability, a quantum generalization of the classical joint probability. The obtained…
We present an elementary proof of the quantum de Finetti representation theorem, a quantum analogue of de Finetti's classical theorem on exchangeable probability assignments. This contrasts with the original proof of Hudson and Moody [Z.…