相关论文: N-qubit states as points on the Bloch sphere

The spinor representation of spin-1/2 states can equally well be mapped to a single unit quaternion, yielding a new perspective despite the equivalent mathematics. This paper first demonstrates a useable map that allows Bloch-sphere…

We use polarization operators known from quantum theory of angular momentum to expand the $N \times N$ dimensional density operators. Thereby, we construct generalized Bloch vectors representing density matrices. We study their properties…

Pure quantum spin-$s$ states can be represented by $2s$ points on the sphere, as shown by Majorana in 1932 --- the description has proven particularly useful in the study of rotational symmetries of the states, and a host of other…

Several designs of inter-qubit coupling are considered. It is shown that by a combination of Josephson and capacitive coupling one can realize qubit interactions of variable spin content. Qubit arrays are discussed as models of quantum spin…

This is a review of the geometry of quantum states using elementary methods and pictures. Quantum states are represented by a convex body, often in high dimensions. In the case of n-qubits, the dimension is exponentially large in n. The…

Permutation-symmetric n qubit pure states can be represented by n points on the surface of the unit sphere by means of the Majorana representation. Here this representation is employed to characterize and compare the three entanglement…

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…

The Majorana stellar representation translates abstract quantum spin states into intuitive geometric constellations on the Bloch sphere, revealing symmetries, degeneracies, and correlations that traditional algebraic methods often obscure.…

The Bloch Sphere visualization of the possible states of a single qubit has proved a useful pedagogical and conceptual tool as a one-to-one map between qubit states and points in a 3-D space. However, understanding many important concepts…

Physical constraints such as positivity endow the set of quantum states with a rich geometry if the system dimension is greater than two. To shed some light on the complicated structure of the set of quantum states, we consider a…

We provide a graphical description of the entanglement of pure-state multiparty systems based on an analogy between a bipartite purity analysis and the centroid of a collection of point masses. This description applies to quantum systems…

The geometric measure of entanglement is investigated for permutation symmetric pure states of multipartite qubit systems, in particular the question of maximum entanglement. This is done with the help of the Majorana representation, which…

Three unit spheres were used to represent the two-qubit pure states. The three spheres are named the base sphere, entanglement sphere, and fiber sphere. The base sphere and entanglement sphere represent the reduced density matrix of the…

We introduce a discrete Q-function of N qubit system projected into the space of symmetric measurements as a tool for analyzing general properties of quantum systems in the macroscopic limit. For known states the projected Q-function helps…

We analyze the estimation of a qubit pure state by means of local measurements on $N$ identical copies and compare its averaged fidelity for an isotropic prior probability distribution to the absolute upper bound given by collective…

We present a novel inequality on the purity of a bipartite state depending solely on the difference of the local Bloch vector lengths. For two qubits this inequality is tight for all marginal states and so extends the previously known…

We present an optical implementation of two programmable quantum measurement devices. The first one serves for unambiguous discrimination of two nonorthogonal states of a qubit. The particular pair of states to be discriminated is specified…

The aim of the present paper is to introduce and to discuss the most basic fundamental concepts of quantum physics by means of a simple and pedagogical example. An appreciable part of its content presents original results. We start with the…

Majorana Representation (MR) of symmetric $ N $-qubit pure states has been used successfully in entanglement classification. Generalization of this has been a long standing open problem due to the difficulties faced in the construction of a…

Quantum state tomography and other measures of the global properties of a quantum state are indispensable tools in understanding many body physics through quantum simulators. Unfortunately, the number of experimental measurements of the…