Related papers: On Metric of Quantum States with Lorentzian Signat…
A generalised definition of the metric of quantum states is proposed by using the techniques of differential geometry. The metric of quantum state space derived earlier by Anandan, is reproduced and verified here by this generalised…
A state sum model based on the group SU(1,1) is defined. Investigations of its geometry and asymptotics suggest it is a good candidate for modelling (2+1) Lorentzian quantum gravity.
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…
In this paper, we study metrics of quantum states. These metrics are natural generalization of trace metric and Bures metric. We will prove that the metrics are joint convex and contractive under quantum operation. Our results can find…
Quantum metrology uses quantum states with no classical counterpart to measure a physical quantity with extraordinary sensitivity or precision. Most metrology schemes measure a single parameter of a dynamical process by probing it with a…
This is a collection of notes on the properties of left-invariant metrics on the eight-dimensional compact Lie group SU(3). Among other topics we investigate the existence of invariant pseudo-Riemannian Einstein metrics on this manifold. We…
Coherence and correlation are key features of the quantum system. Quantifying these quantities are astounding task in the framework of resource theory of quantum information processing. In this article, we identify an affinity-based metric…
We explore potential uses of physics formulated in Kleinian (i.e., $2+2$) signature spacetimes as a tool for understanding properties of physics in Lorentzian (i.e., $3+1$) signature. Much as Euclidean (i.e., $4+0$) signature quantities can…
Measurements can be considered as a genuine example of processes that crush quantum coherence. In the case of an observable with degeneracy, the formulations of L\"{u}ders and von Neumann are known. These pictures postulate the two…
We show that the sum over geometries in the Lorentzian 4-D state sum model for quantum GR in [1] includes terms which correspond to geometries on manifolds with conical singularities. Natural approximations suggest that they can be…
A metric with signature (-+++) can be constructed from a metric with signature (++++) and a double-sided vector field called the line element field. Some of the classical and quantum properties of this vector field are studied.
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…
This paper treats the isometries of metric spaces of quantum states. We consider two metrics on the set all quantum states, namely the Bures metric and the one which comes from the trace-norm. We describe all the corresponding (nonlinear)…
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…
Discussions about quantum interference, indistinguishability and superpostion between quantum states goes back to the beginning of quantum mechanics, but the theoretical problem concerning quantitative measures for quantum coherence was…
We consider Lorentzian manifolds as examples of partially ordered measure spaces, sets endowed with compatible partial order relations and measures, in this case given by the causal structure and the volume element defined by each…
Quantifying coherence is an essential endeavor for both quantum foundations and quantum technologies. In this paper, we put forward a quantitative measure of coherence by following the axiomatic definition of coherence measures introduced…
Recently, Chau [Quant. Inform. & Comp. 11, 721 (2011)] found a family of metrics and pseudo-metrics on $n$-dimensional unitary operators that can be interpreted as the minimum resources (given by certain tight quantum speed limit bounds)…
It is nowadays accepted that truly quantum correlations can exist even in the absence of entanglement. For the case of symmetric states, a physically trivial unitary transformation can alter a quantum state from entangled to separable and…
A possible causal solution to the problem of providing a spacetime description of the transmission of signals in quantum entangled states is described using a `bimetric' spacetime structure, in which the quantum entanglement measurements…