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arXiv:2105.00096 · The European Physical Journal C

Constrained dynamics of maximally entangled bipartite system

Asma Bashir, Muhammad Abdul Wasay

Published Apr 1, 2021• 2 citations
arXivHTMLPDF

Abstract

Abstract The classical and quantum dynamics of two particles constrained on $$S^1$$ S1 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.

DOI
10.1140/epjc/s10052-021-09111-x

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Abstract The classical and quantum dynamics of two particles constrained on S1S^1S1 S1 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 B⃗\vec {B}B B→ such that B⃗≥B⃗upper\vec {B}\ge \vec {B}_{upper }B≥Bupper​ 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 B⃗cutoff\vec {B}_{cutoff }Bcutoff​ 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.
Abstract 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 σ\sigma σ σ , external magnetic field B⃗\vec {\mathcal {B}}B B → ; as well as by geometric parameters like the pitch ρ\rho ρ 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 σ→∞\sigma \rightarrow \infty σ→∞ σ → ∞ . It is observed that the uncertainties are strongly influenced by the geometric parameters e.g., ρ\rho ρ ρ , and the strength of bipartite as well as intraparticle entanglement might be controllable through ρ\rho ρ 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 B⃗\vec {\mathcal {B}}B B → along the central axis of the helicoid.
The speed limit on entanglement is defined as the maximal rate at which entanglement can be generated or degraded in a physical process. We derive the speed limits on entanglement, using the relative entropy of entanglement and trace-distance entanglement, for unitary and arbitrary quantum dynamics, where we assume that the dynamics of the closest separable state can be approximately described by the closest separable dynamics of the actual dynamics of the system. For the unitary dynamics of isolated bipartite systems which are described by pure states, the rate of entanglement production is bounded by the product of fluctuations of the system's driving Hamiltonian and the surprisal operator, with an additional term reflecting the time-dependent nature of the closest separable state. Removing restrictions on the purity of the input and on the unitarity of the evolution, the two terms in the bound get suitably altered. Furthermore, we find a lower bound on the time required to generate or degrade a certain amount of entanglement by arbitrary quantum dynamics. We demonstrate the tightness of our speed limits on entanglement by considering quantum processes of practical interest.
We propose an alternative evaluation of quantum entanglement by measuring the maximum violation of the Bell’s inequality without information of the reduced density matrix of a system. This proposal is demonstrated by bridging the maximum violation of the Bell’s inequality and a concurrence of a pure state in an n-qubit system, in which one subsystem only contains one qubit and the state is a linear combination of two product states. We apply this relation to the ground states of four qubits in the Wen-Plaquette model and show that they are maximally entangled. A topological entanglement entropy of the Wen-Plaquette model could be obtained by relating the upper bound of the maximum violation of the Bell’s inequality to the generalized concurrence of a pure state with respect to different bipartitions.
Understanding the relationship between various different forms of nonclassicality and their resource character is of great importance in quantum foundation and quantum information. Here we discuss a quantitative link between quantum entanglement and the anomalous or nonclassical nonreal values of Kirkwood-Dirac (KD) quasiprobability in a bipartite setting. We first construct an entanglement monotone for a pure bipartite state based on the nonreality of the KD quasiprobability defined over a pair of orthonormal bases, in which one of them is a product, and optimizations over these bases. It admits a closed expression as a Schur concave function of the state of the subsystem having a form of nonadditive quantum entropy. We then construct a bipartite entanglement monotone for generic quantum states using the convex roof extension. Its normalized value is upper bounded by the concurrence of formation, and for two-qubit systems, they are equal. We also derive lower and upper bounds in terms of different forms of uncertainty in the subsystem quantified by an extremal trace-norm asymmetry and a nonadditive quantum entropy, respectively. The entanglement monotone can be expressed as the minimum total state disturbance due to a nonselective local binary measurement. Finally, we discuss its estimation using weak value measurement and classical optimization, and its connection with strange weak value and quantum contextuality.
We consider multiqubit systems and relate quantitatively the problems of generating cluster states with high values of concurrence of assistance, and of generating states with maximal bipartite entanglement. We prove an upper bound for the concurrence of assistance. We consider dynamics of spin-1∕21∕21∕2 systems that model qubits, with different couplings and possible presence of magnetic field, to investigate the appearance of the discussed entanglement properties. We find that states with maximal bipartite entanglement can be generated by an isotropic XYXYXY Hamiltonian, and their generation can be controlled by the initial state of one of the spins. The same Hamiltonian is capable of creating states with high concurrence of assistance from a suitably chosen initial state. We show that the production of graph states using the Ising Hamiltonian is controllable via a single-qubit rotation of one spin-1∕21∕21∕2 subsystem in the initial multiqubit state. We show that the property of Ising dynamics to convert a product-state basis into a special maximally entangled basis is temporally enhanced by the application of a suitable magnetic field. Similar basis transformations are found to be feasible in the case of isotropic XYXYXY couplings with a magnetic field.