Related papers: Complete Separability and Fourier representations …
We construct minimum-uncertainty states and a non-negative quasi probability distribution for quantum systems on a finite-dimensional space. We reexamine the theorem of Massar and Spindel for the uncertainty relationof the two unitary…
It is well established that unpolarized light is invariant with respect to any SU(2) polarization transformation. This requirement fully characterizes the set of density matrices representing unpolarized states. We introduce the degree of…
In this thesis we study the problem of unambiguously discriminating two mixed quantum states. We first present reduction theorems for optimal unambiguous discrimination of two generic density matrices. We show that this problem can be…
The completeness of quantum state space, is usually expressed as \sum_{m=0}^{\infty}|m><m|=1, where {|m>} is selected set of quantum states (basis). Density matrix |m><m| describes a pure quantum state. In this paper, by virtue of the…
We study the quantum separability problem by using general symmetric informationally complete measurements and present separability criteria for both $d$-dimensional bipartite and multipartite systems. The criterion for bipartite quantum…
We derive a necessary condition for the existence of a completely-positive, linear, trace-preserving map which deterministically transforms one finite set of pure quantum states into another. This condition is also sufficient for…
Mutually unbiased bases for quantum degrees of freedom are central to all theoretical investigations and practical exploitations of complementary properties. Much is known about mutually unbiased bases, but there are also a fair number of…
Starting with a set of conditions for bipartite separability of arbitrary quantum states in any dimension and expressed in terms of arbitrary operators whose commutator is a $c$-number, we derive a hierarchy of conditions for tripartite…
With the aid of the concept of stable independence we can construct, in an efficient way, a compact representation of a semi-graphoid independence relation. We show that this representation provides a new necessary condition for the…
We present a detailed computational and algebraic study of Mutually Unbiased Bases (MUBs) in finite-dimensional Hilbert spaces, with a particular focus on dimensions 2, 3, 4, and the challenging case of 6. Starting from the Hadamard-phase…
I investigate some properties of proposed definitions for subsystem/mixed state complexity and uncomplexity. A very strong dependence arises on the density matrix's degeneracy which gives a large separation in the scaling of maximum…
We study an optimized measurement which discriminates N mixed quantum states occurring with given prior robabilities. The measurement yields the maximum achievable confidence for each of the N conclusive outcomes, thereby keeping the…
We present a mapping which associates pure N-qubit states with a polynomial. The roots of the polynomial characterize the state completely. Using the properties of the polynomial we construct a way to determine the separability and the…
We present detailed derivations, various improvements and application to concrete experimental data of spin squeezing inequalities formulated recently by some of us [Phys. Rev. Lett. {\bf 95}, 120502 (2005)]. These inequalities generalize…
We obtain a set of necessary and sufficient conditions for $| \bar{N}, p_{n} |_{k} $ to imply $|\bar{N}, q_{n} |_{s}$ for $1 < k \leq s < \infty$. Using this result we establish several inclusion theorems as well as conditions for the…
Positivity of the density operator reflects itself in terms of sequences of inequalities on observable moments. Uncertainty relations for non-commuting observables form a subset of these inequalities. In addition, criterion of positivity…
A new quantum mechanical notion -- Conditional Density Matrix -- is discussed and is applied to describe some physical processes. This notion is a natural generalization of von Neumann density matrix for such processes as divisions of…
The study of conditional $q$-entropies in composite quantum systems has recently been the focus of considerable interest, particularly in connection with the problem of separability. The $q$-entropies depend on the density matrix $\rho$…
We put forward a method of constructing discrete coherent states for n qubits. After establishing appropriate displacement operators, the coherent states appear as displaced versions of a fiducial vector that is fixed by imposing a number…
The conditions are established for nullity of quantum discord for mixed states of a general two-qubit system whose dynamical behaviour is given by an X-state form density matrix. It is found that quantum discord can vanish at a finite time…