Related papers: Geometry of quantum state space and quantum correl…
Recently, an explicit relation between a measure of entanglement and a geometric entity has been reported in Quantum Inf. Process. (2016) 15:1629-1638. It has been shown that if a qubit gets entangled with another ancillary qubit then…
The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement, already present in a number of settings [A. Shimony, Ann. NY.…
The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement is explored for bi-partite and multi-partite pure and mixed states.…
The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement, already present in a number of settings (see Shimony 1995 and…
Quantum entanglement between several particles is essential for applications like quantum metrology or quantum cryptography, but it is also central for foundational phenomena like quantum non-locality. This leads to the problem of…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
This paper explores the fundamental relationship between the geometry of entanglement and von Neumann entropy, shedding light on the intricate nature of quantum correlations. We provide a comprehensive overview of entanglement, highlighting…
Quantifying quantum entanglement is a pivotal challenge in quantum information science, particularly for high-dimensional systems, due to its computational complexity. This thesis extends the geometric measure of entanglement (GME) to…
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
The geometric measure of entanglement is the distance or angle between an entangled target state and the nearest unentangled state. Often one considers the geometric measure of entanglement for highly symmetric entangled states because it…
While several measures exist for entanglement of multipartite pure states, a true entanglement measure for mixed states still eludes us. A deeper study of the geometry of quantum states may be the way to address this issue, on which context…
This paper presents a comprehensive perspective of the metric of quantum states with a focus on the background independent metric structures. We also explore the possibilities of geometrical formulations of quantum mechanics beyond the…
Quantifying entanglement is a work in progress which is important for the active field of quantum information and computation. A measure of bipartite pure state entanglement is proposed here, named entanglement coherence, which is…
We introduce a new approach to evaluating entangled quantum networks using information geometry. Quantum computing is powerful because of the enhanced correlations from quantum entanglement. For example, larger entangled networks can…
We point out that a geometric measure of quantum entanglement is related to the matrix permanent when restricted to permutation invariant states. This connection allows us to interpret the permanent as an angle between vectors. By employing…
By applying the projector to the filled lattice eigenstates on a specific position, or applying the local electron annihilation operator on the many-body ground state, one can construct a quantum state localized around a specific position…
Riemannian metric on real 2n-dimensional space associated with the equation governing complex diffusion of pure states of an open quantum system is introduced and studied. Examples of a qubit under the influence of dephasing and thermal…
In this paper we introduce a geometric framework for mixed quantum states based on a K\"ahler structure. The geometric framework includes a symplectic form, an almost complex structure, and a Riemannian metric that characterize the space of…
The geometric formulation of quantum mechanics is a very interesting field of research which has many applications in the emerging field of quantum computation and quantum information, such as schemes for optimal quantum computers. In this…
We investigate different geometries and invariant measures on the space of mixed Gaussian quan- tum states. We show that when the global purity of the state is held fixed, these measures coincide and it is possible, within this constraint,…