相关论文: Geometric Quantum Mechanics
The evolution of $N$ spin-$1/2$ system with all-range Ising-type interaction is considered. For this system we study the entanglement of one spin with the rest spins. It is shown that the entanglement depends on the amount of spins and the…
Grid states form a discrete set of mixed quantum states that can be described by graphs. We characterize the entanglement properties of these states and provide methods to evaluate entanglement criteria for grid states in a graphical way.…
We propose a detailed study of the geometric entanglement properties of pure symmetric N-qubit states, focusing more particularly on the identification of symmetric states with a high geometric entanglement and how their entanglement…
The Hermiticity condition in quantum mechanics required for the characterisation of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose…
Quantum geometry governs a wide range of transport and optical phenomena in quantum materials. Recent works have explored analogue electromagnetism and gravity in terms of the quantum geometric tensor, whose real and imaginary parts…
In the standard geometric approach, the entanglement of a pure state is $\sin^2\theta$, where $\theta$ is the angle between the entangled state and the closest separable state of products of normalised qubit states. We consider here a…
We study the dimension of the manifold of quantum states (called orbit) that a given quantum state of light can reach under the dynamics of linear or Gaussian quantum optics. That is, we investigate how many directions in the Hilbert space…
We present a complete classification of the geometry of the mutually complementary sets of entangled and separable states in three-dimensional Hilbert subspaces of bipartite and multipartite quantum systems. Our analysis begins by finding…
The use of geometric methods has proved useful in the hamiltonian description of classical constrained systems. In this note we provide the first steps toward the description of the geometry of quantum constrained systems. We make use of…
Uncertainty relations are usually stated as bounds on selected combinations of variances, but the full covariance matrix contains substantially richer information about the geometry of quantum state space and about the operational…
We adopt the point of view that (Riemannian) classical and (loop-based) quantum descriptions of geometry are macro- and micro-descriptions in the usual statistical mechanical sense. This gives rise to the notion of geometrical entropy,…
We present a concise introduction to quantum entanglement. Concentrating on bipartite systems we review the separability criteria and measures of entanglement. We focus our attention on geometry of the sets of separable and maximally…
It is proposed to give up the description of physical states in terms of ensembles of state vectors with various probabilities, relying instead solely on the density matrix as the description of reality. With this definition of a physical…
The uncertainty relation is a distinctive characteristic of quantum theory. The uncertainty is essentially rooted in quantum states. In this work we regard the uncertainty as an intrinsic property of quantum state and characterize it…
By viewing entanglement as a state function, a new kind of phase transition takes place: the geometric phase transition. This phenomenon occurs due to singularities in the shape of the entangled states set. It is shown how this result can…
We present an analytical approach to evaluate the geometric measure of multiparticle entanglement for mixed quantum states. Our method allows the computation of this measure for a family of multiparticle states with a certain symmetry and…
Pure-state manifestations of geometric phase are well established and have found applications across essentially all branches of physics, yet their generalization to mixed-state regimes remains largely unexplored experimentally. The Uhlmann…
We reconsider the geometry of pure and mixed states in a finite quantum system. The rangesof eigenvalues of the density matrices delimit a regular simplex (Hypertetrahedron TN) in any dimension N; the polytope isometry group is the…
The formalism of quantum state space geometry on manifolds of generalised coherent states is proposed as a natural setting for the construction of geometric dual descriptions of non-relativistic quantum systems. These state manifolds are…
Field mediated entanglement experiments probe the quantum superposition of macroscopically distinct field configurations. We show that this phenomenon can be described by using a transparent quantum field theoretical formulation of…