Majorana representation of quantum states by a constellation of $n$ ``stars'' (points on the sphere) can be used to describe any pure state of a simple system of dimension $n+1$ or a permutation symmetric pure state of a composite system consisting of $n$ qubits. We analyze the variance of the distribution of the stars, which can serve as a measure of the degree of noncoherence for simple systems or an entanglement measure for composed systems. Dynamics of the Majorana points induced by a unitary dynamics of a pure state is investigated.Majorana representation of quantum states by a constellation of $n$ ``stars'' (points on the sphere) can be used to describe any pure state of a simple system of dimension $n+1$ or a permutation symmetric pure state of a composite system consisting of $n$ qubits. We analyze the variance of the distribution of the stars, which can serve as a measure of the degree of noncoherence for simple systems or an entanglement measure for composed systems. Dynamics of the Majorana points induced by a unitary dynamics of a pure state is investigated.

arXiv:1112.0437Physical Review AMar 14, 201248 citations

The Majorana-Hubbard Model

Ian K. Affleck

Bulletin of the American Physical SocietyMar 8, 20190 citations

Majorana Representation for the Mutilevel Adiabatic-impluse Model

Z. Y. Wang, A. X. Xie, H. D. Liu

International Journal of Theoretical PhysicsDec 23, 20240 citations

Majorana's stellar representation of single-particle reduced density matrix for completely symmetric states

Liyao Zhan, Xi Lu, Jie Chen +6 more

The completely symmetric states play an essential role in quantum physics. In this paper, we calculate the reduced density matrix (RDM) for a single particle of the completely symmetric system coupled by $N$ spin- $\frac{1}{2}$ particles, because it helps to investigate the evolution of expectation value for the observable and to calculate the entanglement between the subsystems. Furthermore, we use Majorana's stellar representation (MSR) to represent the results because it provides an intuitive geometric perspective to comprehend the quantum states in the high-dimensional Hilbert space with distributions and trajectories of the Majorana stars on a Bloch sphere. With the operation properties of the generalized many-body anticommutator, we get the general MSR form of a single-qubit RDM. As the application and verification, we calculate the single-qubit RDM for the Dicke states with the results. Similarly, we further solve the RDM of the spin- $\frac{N}{2}$ state in a uniform magnetic field and study the systems with symmetric structures on the Bloch sphere. The results exhibit the relations between the composite systems and the subsystems, and provide a new idea for the numerical solution of multiqubit systems.The completely symmetric states play an essential role in quantum physics. In this paper, we calculate the reduced density matrix (RDM) for a single particle of the completely symmetric system coupled by $N$ spin-$\frac{1}{2}$ particles, because it helps to investigate the evolution of expectation value for the observable and to calculate the entanglement between the subsystems. Furthermore, we use Majorana's stellar representation (MSR) to represent the results because it provides an intuitive geometric perspective to comprehend the quantum states in the high-dimensional Hilbert space with distributions and trajectories of the Majorana stars on a Bloch sphere. With the operation properties of the generalized many-body anticommutator, we get the general MSR form of a single-qubit RDM. As the application and verification, we calculate the single-qubit RDM for the Dicke states with the results. Similarly, we further solve the RDM of the spin-$\frac{N}{2}$ state in a uniform magnetic field and study the systems with symmetric structures on the Bloch sphere. The results exhibit the relations between the composite systems and the subsystems, and provide a new idea for the numerical solution of multiqubit systems.

Physical Review AMay 30, 20231 citation

Heisenberg Representation

Harry A. Mavromatis

Reidel texts in the mathematical sciencesJan 1, 19921 citation

Majorana representation of quantum states by a constellation of

n

``stars'' (points on the sphere) can be used to describe any pure state of a simple system of dimension

n+1

or a permutation symmetric pure state of a composite system consisting of

n

qubits. We analyze the variance of the distribution of the stars, which can serve as a measure of the degree of noncoherence for simple systems or an entanglement measure for composed systems. Dynamics of the Majorana points induced by a unitary dynamics of a pure state is investigated.

N

spin-

\frac{1}{2}

particles, because it helps to investigate the evolution of expectation value for the observable and to calculate the entanglement between the subsystems. Furthermore, we use Majorana's stellar representation (MSR) to represent the results because it provides an intuitive geometric perspective to comprehend the quantum states in the high-dimensional Hilbert space with distributions and trajectories of the Majorana stars on a Bloch sphere. With the operation properties of the generalized many-body anticommutator, we get the general MSR form of a single-qubit RDM. As the application and verification, we calculate the single-qubit RDM for the Dicke states with the results. Similarly, we further solve the RDM of the spin-

\frac{N}{2}

state in a uniform magnetic field and study the systems with symmetric structures on the Bloch sphere. The results exhibit the relations between the composite systems and the subsystems, and provide a new idea for the numerical solution of multiqubit systems.