Related papers: Formulas for Rational-Valued Separability Probabil…
The entanglement detection via local measurements can be experimentally implemented. Based on mutually unbiased measurements and general symmetric informationally complete positive-operator-valued measures, we present separability criteria…
We consider entanglement for quantum states defined in vector spaces over the real numbers. Such real entanglement is different from entanglement in standard quantum mechanics over the complex numbers. The differences provide insight into…
Incompatibility of certain measurements -- impossibility of obtaining deterministic outcomes simultaneously -- is a well known property of quantum mechanics. This feature can be utilized in many contexts, ranging from Bell inequalities to…
We conduct a study based on the Bures (minimal monotone) metric, analogous to that recently reported for the Hilbert-Schmidt (flat or Euclidean) metric (arXiv:0704.3723v2). Among the interesting results obtained there had been…
A discussion of discrete Wigner functions in phase space related to mutually unbiased bases is presented. This approach requires mathematical assumptions which limits it to systems with density matrices defined on complex Hilbert spaces of…
We study general ``normally'' distributed random unitary transformations. These distributions can be defined in terms of a diffusive random walk in the respective group manifold, formally underpinned by the concept of infinite divisibility.…
Quantum bits can be isolated to perform useful information-theoretic tasks, even though physical systems are fundamentally described by very high-dimensional operator algebras. This is because qubits can be consistently embedded into…
Quantum mechanics is formulated on a Hilbert space that is assumed to be separable. However, there seems to be no clear reason justifying this assumption. Does it have physical implications? We answer in the positive by proposing a test…
We investigate the internal logic of a quantum computer with two qubits, in the two particular cases of non-entanglement (separable states) and maximal entanglement (Bell's states). To this aim, we consider an internal (reversible)…
Mutually unbiased bases (MUBs) and symmetric informationally complete (SIC) positive operator-valued measurements (POVMs) are two related topics in quantum information theory. They are generalized to mutually unbiased measurements (MUMs)…
The usual notion of separability has to be reconsidered when applied to states describing identical particles. A definition of separability not related to any a priori Hilbert space tensor product structure is needed: this can be given in…
We formulate a discrete two-state stochastic process with elementary rules that give rise to Born statistics and reproduce the probabilities from the Schr\"odinger equation under an associated Hamiltonian matrix, which we identify. We…
We study the Hilbert-Schmidt measure on the manifold of mixed Gaussian states in multi mode continuous variable quantum systems. An analytical expression for the Hilbert-Schmidt volume element is derived. Its corresponding probability…
We consider random integer partitions $\lambda$ that follow the Poissonized Plancherel measure of parameter $t^2$. Using Riemann$-$Hilbert techniques, we establish the asymptotics of the multiplicative averages $$Q(t,s)=\mathbb{E} \left[…
The general expression with the physical significance and positive definite condition of the eigenvalues of $4\times 4$ Hermitian and trace-one matrix are obtained. This implies that the eigenvalue problem of the $4\times 4$ density matrix…
Properties of random mixed states of order $N$ distributed uniformly with respect to the Hilbert-Schmidt measure are investigated. We show that for large $N$, due to the concentration of measure, the trace distance between two random states…
In standard optical tomographic methods, the off-diagonal elements of a density matrix $\rho$ are measured indirectly. Thus, the reconstruction of $\rho$, even if it is based on linear inversion, typically magnifies small errors in the…
We solve for the statistics of the first detection of a quantum system in a particular desired state, when the system is subject to a projective measurement at independent identically distributed random time intervals. We present formulas…
A method allowing to increase a computational efficiency of evaluation of non-local characteristics of a pair of qubits is described. The method is based on the construction of coordinates on a generic section of 2-qubit's entanglement…
The thesis includes the original results of our articles [30, 37, 40, 42, 51, 53, 75]. A method is developed to compute analytically entanglement measures of three-qubit pure states. Owing to it closed-form expressions are presented for the…