相关论文: Bloch Sphere Binary Trees: A method for the visual…

Understanding the structure of multi-qubit quantum states is essential for both quantum information research and education, yet intuitive visualization beyond the single-qubit Bloch sphere remains challenging. In this work, we propose a…

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…

In the field of quantum information science and technology, the representation and visualization of quantum states and related processes are essential for both research and education. In this context, a focus especially lies on ensembles of…

We extend Bloch Sphere formalism to pure two qubit systems. Combining insights from Geometric Algebra and analysis of entanglement in different conjugate bases we identify Two Bloch Sphere geometry that is suitable for representing…

Quantum computing is rapidly gaining popularity, necessitating intuitive visualization tools for complex quantum states. While the Bloch Sphere effectively visualizes single-qubit states, it fundamentally lacks scalability for multi-qubit…

An ability to describe quantum states directly by average values of measurement outcomes is provided by the Bloch vector. For an informationally complete set of measurements one can construct unique Bloch vector for any quantum state.…

An arbitrarily dense discretisation of the Bloch sphere of complex Hilbert states is constructed, where points correspond to bit strings of fixed finite length. Number-theoretic properties of trigonometric functions (not part of the…

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 present a surprisingly simple three-dimensional Bloch sphere representation of a qutrit, i.e., a single three-level quantum system. We start with a symmetric state of a two-qubit system and relate it to the spin-1 representation. Using…

A Bloch sphere is the geometrical representation of an arbitrary two-dimensional Hilbert space. Possible classes of entanglement and separability for the pure and mixed states on the Bloch sphere were suggested by [M. Boyer, R. Liss, T.…

By describing the evolution of a quantum state with the trajectories of the Majorana stars on a Bloch sphere, Majorana's stellar representation provides an intuitive geometric perspective to comprehend a quantum system with high-dimensional…

We represent a two-qubit density matrix in the basis of Pauli matrix tensor products, with the coefficients constituting a Bloch matrix, analogous to the single qubit Bloch vector. We find the quantum state positivity requirements on the…

We present a straightforward, noniterative projection scheme that can represent the electronic ground state of a periodic system on a finite atomic-orbital-like basis, up to a predictable number of electronic states and with controllable…

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…

Visual methods are of great utility in understanding and interpreting quantum mechanics at all levels of understanding. The Bloch sphere, for example, is an invaluable and widely used tool for visualising quantum dynamics of a two level…

Visualizations have played a crucial role in helping quantum computing users explore quantum states in various quantum computing applications. Among them, Bloch Sphere is the widely-used visualization for showing quantum states, which…

This paper presents an introduction to geometric representations of quantum states in which each distinct quantum state, pure and mixed, corresponds to a unique point in a Euclidean space. Beginning with a review of some underappreciated…

The two-qubit pure state is explicitly parameterized by three unit 2-spheres and a phase factor. For separable states, two of the three unit spheres are the Bloch spheres of each qubit. The third sphere parameterizes the degree and phase of…

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,…

Identifying quantum phases and phase transitions is key to understand complex phenomena in statistical physics. In this work, we propose an unconventional strategy to access quantum phases and phase transitions by visualization based on the…