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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…

Quantum Physics · Physics 2024-05-31 Li-Heng Henry Chang , Shea Roccaforte , Ziyu Xu , Paul Cadden-Zimansky

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…

Quantum Physics · Physics 2023-04-25 Shaolun Ruan , Ribo Yuan , Qiang Guan , Yanna Lin , Ying Mao , Weiwen Jiang , Zhepeng Wang , Wei Xu , Yong Wang

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…

Quantum Physics · Physics 2026-03-11 Satoru Shoji

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…

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…

Quantum Physics · Physics 2023-04-26 Max Z. Festenstein

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…

Quantum Physics · Physics 2026-02-17 Athanasios Kostikas , Yaroslav Valchyshen , Paul Cadden-Zimansky

Understanding the evolution of a multi-qubit quantum system, or elucidating what portion of the Hilbert space is occupied by a quantum dataset becomes increasingly hard with the number of qubits. In this context, the visualisation of sets…

Quantum Physics · Physics 2023-02-07 Alice Barthe , Michele Grossi , Jordi Tura , Vedran Dunjko

The qutrit comes next in complexity after qubit as a resource for quantum information processing. The qubit density matrix can be easily visualized using Bloch sphere representation of its states. In contrast, this simplicity is in general…

Quantum Physics · Physics 2017-09-29 Vinod K. Mishra

The aim of this paper is to introduce a new graphic representation of quantum states by means of a specific application: the analysis of two models of quantum copying machines. The graphic representation by diagrams of states offers a clear…

Quantum Physics · Physics 2007-05-23 Sara Felloni , Giuliano Strini

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 Physics · Physics 2024-03-19 Stanislav Filatov , Marcis Auzinsh

We explore the main processes involved in the evolution of general quantum systems by means of Diagrams of States, a novel method to graphically represent and analyze how quantum information is elaborated during computations performed by…

Quantum Physics · Physics 2009-12-02 Sara Felloni , Alberto Leporati , Giuliano Strini

In quantum information transformation and quantum computation, the most critical issues are security and accuracy. These features, therefore, stimulate research on quantum state characterization. A characterization tool, Quantum state…

Quantum Physics · Physics 2023-06-01 Xudan Chai , Teng Ma , Qihao Guo , Zhangqi Yin , Hao Wu , Qing Zhao

We propose and demonstrate the scaling up of photonic graph state through path qubit fusion. Two path qubits from separate two-photon four-qubit states are fused to generate a two-dimensional seven-qubit graph state composed of polarization…

Geometric intuition is a crucial tool to obtain deeper insight into many concepts of physics. A paradigmatic example of its power is the Bloch ball, the geometrical representation for the state space of the simplest possible quantum system,…

Quantum Physics · Physics 2021-07-01 Christopher Eltschka , Marcus Huber , Simon Morelli , Jens Siewert

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.…

Quantum Physics · Physics 2013-03-21 Pawel Kurzynski

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…

Quantum Physics · Physics 2016-07-04 Pawel Kurzynski , Adrian Kolodziejski , Wieslaw Laskowski , Marcin Markiewicz

Quantum state tomography, the ability to deduce the state of a quantum system from measured data, is the gold standard for verification and benchmarking of quantum devices. It has been realized in systems with few components, but for larger…

The geometry of the Quantum State Space, described by Bloch vectors, is a very intricate one. A deeper understanding of this geometry could lead to the solution of some difficult problems in Quantum Foundations and Quantum Information such…

Quantum Physics · Physics 2013-09-30 Jose Ignacio Rosado

Existing graphical user interfaces for circuit simulators often show small visual summaries of the reduced state of each qubit, showing the probability, phase, purity, and/or Bloch sphere coordinates associated with each qubit. These…

Quantum Physics · Physics 2025-10-02 Michael J. McGuffin , Jean-Marc Robert

As the variety of commercially available quantum computers continues to increase so does the need for tools that can characterize, verify and validate these computers. This work explores using quantum state tomography for characterizing the…

Quantum Physics · Physics 2022-05-06 Adrien Suau , Marc Vuffray , Andrey Y. Lokhov , Lukasz Cincio , Carleton Coffrin
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