Two particle entanglement and its geometric duals

Wasay, Muhammad Abdul; Bashir, Asma

doi:10.1140/epjc/s10052-017-5399-z

Cited by 4 publications

(5 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To switch from standard quantum interpretation of Eq. (1) into the pilotwave limit, the wave function is factored into amplitude and phase [20,[28][29][30][31], as follows…”

Section: The Modelmentioning

confidence: 99%

“…The geometrisation of the Klein-Gordon equation for a conformally curved spacetime was done in [20], and in [30] it was generalized for the nonrelativistic case, i.e., the Schrödinger equation. A Finslerian version of the Klein-Gordon equation was presented in [33] and in another relevant work two particle entanglement was written geometrically for Finsler spacetimes [31]. Details about Finsler space can be found in [34,35] and references therein.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Geometric description of Schrödinger equation in Finsler and Funk geometry

Bashir

Koch

Wasay

2019

Int. J. Geom. Methods Mod. Phys.

Self Cite

View full text Add to dashboard Cite

For a system of n non-relativistic spinless bosons, we show by using a set of suitable matching conditions that the quantum equations in the pilot-wave limit can be translated into a geometric language for a Finslerian manifold. We further link these equations to Euclidean timelike relative Funk geometry and show that the two different metrics in both of these geometric frameworks lead to the same coupling.PACS numbers:

show abstract

“…To switch from standard quantum interpretation of Eq. (1) into the pilotwave limit, the wave function is factored into amplitude and phase [20,[28][29][30][31], as follows…”

Section: The Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Geometric description of Schrödinger equation in Finsler and Funk geometry

Bashir

Koch

Wasay

2019

Int. J. Geom. Methods Mod. Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…[8], and a different approach to find geometric duality for quantum equations in the pilot-wave limit was presented in Refs. [9][10][11]. Studies on Dirac approach for particle constrained on a helicoid and for a free particle on S 3 were carried out in [12,13].…”

Section: Introductionmentioning

confidence: 99%

Dynamics and uncertainty for maximally entangled bipartite system constrained on a helicoid

et al. 2022

Self Cite

View full text Add to dashboard Cite

The classical and quantum dynamics of particles constrained on a right helicoid is discussed via Dirac approach. We show how the uncertainty in measurement for observables of maximally entangled system is affected by the total number of constrained particles $$\sigma $$ σ , external magnetic field $$\vec {\mathcal {B}}$$ B → ; as well as by geometric parameters like the pitch$$\rho $$ ρ and the radial position of particles. In doing so we also highlight numeric bounds on the external field strengths to tune both intraparticle and bipartite entanglement and we remark that the bipartite entanglement is more robust to changes in the fields than the intraparticle entanglement, in this framework. We also highlight specific parameter regimes which lead the uncertainty (in measurement) to achieve respective parameter independence and, for a particular subset of commutation relations, the system remains confined in the quantum regime even in the limit $$\sigma \rightarrow \infty $$ σ → ∞ . It is observed that the uncertainties are strongly influenced by the geometric parameters e.g., $$\rho $$ ρ , and the strength of bipartite as well as intraparticle entanglement might be controllable through $$\rho $$ ρ . The energy equation for this setup is obtained and the additional terms are discussed which arise due to quantum correlations, orbit–orbit interaction and the normal Zeeman effect, which leads to the splitting of the energy level into 11 non-degenerate levels. Finally we comment that, a linkage of this phenomenology with Aharonov–Bohm like effect might be possible by strictly confining $$\vec {\mathcal {B}}$$ B → along the central axis of the helicoid.

show abstract

“…A similar study in this direction was made in [12] for the Dirac quantization of particle constrained on a helicoid and in [13] for quantizing the dynamics of a free particle on a D-dimensional sphere. A different approach to dualize quantum with geometry in the pilot-wave limit is presented in [14][15][16], and with topological properties in [17]. Dirac quantization on curved spaces adds some additional terms in the Schrödinger equation that can be linked with the curvature of the space or distortion in the energy spectrum.…”

Section: Introductionmentioning

confidence: 99%

Constrained dynamics of maximally entangled bipartite system

Bashir

Wasay

2021

Eur. Phys. J. C

Self Cite

View full text Add to dashboard Cite

The classical and quantum dynamics of two particles constrained on $$S^1$$ S 1 is discussed via Dirac’s approach. We show that when state is maximally entangled between two subsystems, the product of dispersion in the measurement reduces. We also quantify the upper bound on the external field $$\vec {B}$$ B → such that $$\vec {B}\ge \vec {B}_{upper }$$ B → ≥ B → upper implies no reduction in the product of dispersion pertaining to one subsystem. Further, we report on the cut-off value of the external field $$\vec {B}_{cutoff }$$ B → cutoff , above which the bipartite entanglement is lost and there exists a direct relationship between uncertainty of the composite system and the external field. We note that, in this framework it is possible to tune the external field for entanglement/unentanglement of a bipartite system. Finally, we show that the additional terms arising in the quantum Hamiltonian, due to the requirement of Hermiticity of operators, produce a shift in the energy of the system.

show abstract

Two particle entanglement and its geometric duals

Cited by 4 publications

References 34 publications

Geometric description of Schrödinger equation in Finsler and Funk geometry

Geometric description of Schrödinger equation in Finsler and Funk geometry

Dynamics and uncertainty for maximally entangled bipartite system constrained on a helicoid

Constrained dynamics of maximally entangled bipartite system

Contact Info

Product

Resources

About