Related papers: Necessary and sufficient conditions for positive s…
For two qubits and for general bipartite quantum systems, we give a simple spectral condition in terms of the ordered eigenvalues of the density matrix which guarantees that the corresponding state is separable.
We derive a classification and a measure of classical- and quantum-correlation of multipartite qubit, qutrit, and in general, $n$-level systems, in terms of SU$(n)$ representations of density matrices. We compare the measure for the case of…
In this study the determinant of the average quadratic error matrix is used as the measure of state estimation efficiency. This quantity is easily computable in some cases, so it gives us a reasonable tool to find optimal measurement setup…
Given an unknown quantum state distributed over two systems, we determine how much quantum communication is needed to transfer the full state to one system. This communication measures the "partial information" one system needs conditioned…
We study the invariants of arbitrary dimensional multipartite quantum states under local unitary transformations. For multipartite pure states, we give a set of invariants in terms of singular values of coefficient matrices. For…
A uniform matrix product state defined on a tripartite system of spins, denoted by $ABC,$ is shown to be an approximate quantum Markov chain when the size of subsystem $B,$ denoted $|B|,$ is large enough. The quantum conditional mutual…
Quantifying entanglement is vital to understand entanglement as a resource in quantum information processing, and many entanglement measures have been suggested for this purpose. When mathematically defining an entanglement measure, we…
Relevance of key quantum information measures for analysis of quantum systems is discussed. It is argued that possible ways of measuring quantum information are based on compatibility/incompatibility of the quantum states of a quantum…
The concept of the {\em half density matrix} is proposed. It unifies the quantum states which are described by density matrices and physical processes which are described by completely positive maps. With the help of the half-density-matrix…
Subsystems of composite quantum systems are described by reduced density matrices, or quantum marginals. Important physical properties often do not depend on the whole wave function but rather only on the marginals. Not every collection of…
Density matrices are the most general descriptions of quantum states, covering both pure and mixed states. Positive semidefiniteness is a physical requirement of density matrices, imposing nonnegative probabilities of measuring physical…
We consider universal methods for obtaining (uniform) continuity bounds for characteristics of multipartite quantum systems. We pay a special attention to infinite-dimensional multipartite quantum systems under the energy constraints. By…
We demonstrate that incomplete quantum tomography can give conclusive information in experimental realizations. We divide the state space into a union of multiple disjoint subsets and determine conclusively which of the subsets a system,…
We address the problem of information completeness of quantum measuremets in connection to quantum state tomography and with particular concern to quantum symplectic tomography. We put forward some non-trivial situations where…
We derive several expressions for the quantum Fisher information matrix (QFIM) for the multi-parameter estimation of multi-mode Gaussian quantum states, the corresponding symmetric logarithmic derivatives, and conditions for saturability of…
A state on a tripartite quantum system $A \otimes B \otimes C$ forms a Markov chain if it can be reconstructed from its marginal on $A \otimes B$ by a quantum operation from $B$ to $B \otimes C$. We show that the quantum conditional mutual…
We study the classical, classical-quantum, and quantum parts of conditional mutual information in the ``system-environment-ancilla'' setting of open quantum systems. We perform the separation of conditional mutual information by…
In the past decades, quantum entanglement has been recognized to be the basic resource in quantum information theory. A fundamental need is then the understanding its qualification and its quantification: Is the quantum state entangled, and…
We discuss how to calculate genuine multipartite quantum and classical correlations in symmetric, spatially invariant, mixed $n$-qubit density matrices. We show that the existence of symmetries greatly reduces the amount of free parameters…
We present a framework for deciding whether a quantum state is separable or entangled using covariance matrices of locally measurable observables. This leads to the covariance matrix criterion as a general separability criterion. We…