Related papers: Geometric Visualizations of Quantum Mixed States a…
The computational complexity of a quantum state quantifies how hard it is to make. `Complexity geometry', first proposed by Nielsen, is an approach to defining computational complexity using the tools of differential geometry. Here we…
Exactly soluble models can serve as excellent tools to explore conceptual issues in non-perturbative quantum gravity. In perturbative approaches, it is only the two radiative modes of the linearized gravitational field that are quantized.…
Geometric phases, arising from cyclic evolutions in a curved parameter space, appear in a wealth of physical settings. Recently, and largely motivated by the need of an experimentally realistic definition for quantum computing applications,…
The geometric properties of quantum states are crucial for understanding many physical phenomena in quantum mechanics, condensed matter physics, and optics. The central object describing these properties is the quantum geometric tensor,…
Quantum geometry is a key quantity that distinguishes electrons in a crystal from those in the vacuum. Its study continues to provide insights into quantum materials, uncovering new design principles for their discovery. However, unlike the…
Geometric phase has found a broad spectrum of applications in both classical and quantum physics, such as condensed matter and quantum computation. In this paper we introduce an operational geometric phase for mixed quantum states, based on…
Entanglement is an important concept in quantum information, quantum communication, and quantum computing. We provide a geometrical analysis of entanglement and separability for all the rank-2 quantum mixed states: complete analysis for the…
The geometric quantum discord of a two-qudit state has been studied in many papers, however, its exact analytical value in the explicit form is known only for a general two-qubit state, a general qubit-qudit state and some special families…
Given the algebra of observables of a quantum system subject to selection rules, a state can be represented by different density matrices. As a result, different von Neumann entropies can be associated with the same state. Motivated by a…
Quantum metrology holds the promise of an early practical application of quantum technologies, in which measurements of physical quantities can be made with much greater precision than what is achievable with classical technologies. In this…
When quantum mechanical qubits as elements of two dimensional complex Hilbert space are generalized to elements of even subalgebra of geometric algebra over three dimensional Euclidian space, geometrically formal complex plane becomes…
There exist many attempts to define a Wigner function for qudits, each of them coming with its advantages and limitations. The existing finite versions have simple definitions, but they are artificial in their construction and do not allow…
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…
Usually models for quantum computations deal with unitary gates on pure states. In this paper we generalize the usual model. We consider a model of quantum computations in which the state is an operator of density matrix and the gates are…
We present graphical representation for genaralized quantum measurements (POVM). We represent POVM elements as Bloch vectors and find the conditions these vectors should satisfy in order to describe realizable physical measurements. We show…
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…
In this paper, we address a foundational challenge in quantum field theory on curved spacetime by developing a consistent framework within loop quantum gravity. We introduce a methodology for defining meaningful superpositions of quantum…
Quantum state space is endowed with a metric structure and Riemannian monotone metric is an important geometric entity defined on such a metric space. Riemannian monotone metrics are very useful for information-theoretic and statistical…
Quantum geometry, describing the geometric properties of the Bloch wave function in momentum space, has recently been recognized as a fundamental concept in condensed matter physics. The flat-band system offers the paradigmatic platform…
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…