Related papers: Three-qubit pure-state canonical forms
We propose an explicit formula for an entanglement measure of pure multipartite quantum states, then study a general pure tripartite state in detail, and at end we give some simple but illustrative examples on four-qubits and m-qubits…
Motivated by studies of typical properties of quantum states in statistical mechanics, we introduce phase-random states, an ensemble of pure states with fixed amplitudes and uniformly distributed phases in a fixed basis. We first show that…
We consider a partial trace transformation which maps a multipartite quantum state to collection of local density matrices. We call this collection a mean field state. The necessary and sufficient conditions under which a mean field state…
The problem of discriminating with minimum error between two mixed quantum states is reviewed, with emphasize on the detection operators necessary for performing the measurement. An analytical result is derived for the minimum probability…
The classification of the multipartite entanglement is an important problem in quantum information theory. We propose a class of two qubit mixed states $\sigma_{AB}=…
Apart from relating interesting quantum mechanical systems to equations describing a parabolic discrete minimal surface, the quantization of a cubic minimal surface in $\mathbb{R}^4$ is considered.
We classify completely the surfaces of general type whose canonical map is 3-to-1 onto a surface of minimal degree in projective space. These surfaces fall into 5 distinct classes and we give explicit examples belonging to each of these…
Quantum state preparation plays an equally important role with quantum operations and measurements in quantum information processing. The previous methods of preparing initial state for bulk quantum computation all have inevitable…
The different time-dependent distances of two arbitrarily close quantum or classical-statistical states to a third fixed state are shown to imply an experimentally relevant notion of state sensitivity to initial conditions. A quantitative…
We investigate the geometry of the four qubit systems by means of algebraic geometry and invariant theory, which allows us to interpret certain entangled states as algebraic varieties. More precisely we describe the nullcone, i.e., the set…
We give a canonical form of PPT states in ${\cal C}^2 \otimes {\cal C}^2\otimes {\cal C}^2 \otimes {\cal C}^N$ with rank=$N$. From this canonical form a necessary separable condition for these states is presented.
The notions of qubits and coherent states correspond to different physical systems and are described by specific formalisms. Qubits are associated with a two-dimensional Hilbert space and can be illustrated on the Bloch sphere. In contrast,…
Recently, there is growing interest in the study of genuine nonlocality, which serves to explore the local accessability of global information encoded in orthogonal multipartite quantum states under scenarios where not all subsystems are…
k-uniform mixed states are a significant class of states characterized by all k-party reduced states being maximally mixed. Novel methodologies are constructed for constructing k-uniform mixed states with the highest possible purity. By…
The article undertakes the problem of pure state estimation from projective measurements based on photon counting. Two generic frames for qubit tomography are considered -- one composed of the elements of the SIC-POVM and the other defined…
Necessary and sufficient conditions for the equivalence of arbitrary n-qubit pure quantum states under Local Unitary (LU) operations are derived. First, an easily computable standard form for multipartite states is introduced. Two generic…
In this paper we obtain 32 canonical forms for 3D piecewise smooth vector fields presenting the so called cusp-fold singularity. All these canonical forms are topologically distinct and collect the main topological aspects of the…
We construct a class of algebraic invariants for N-qubit pure states based on bipartite decompositions of the system. We show that they are entanglement monotones, and that they differ from the well know linear entropies of the sub-systems.…
We study the equivalence of quantum states under local unitary transformations by using the singular value decomposition. A complete set of invariants under local unitary transformations is presented for several classes of tripartite mixed…
In this paper, an unextendible product basis and exact-entanglement bases of three qubit is given, and the properties of entanglement for exact-entanglement bases are also discussed. In addition, the bound entangled mixed state is obtained…