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Concepts in Magnetic Resonance Part A

Dynamics of Pair of Entangled Spin-1/2 Particles and Quantification of the Dynamics in terms of Correlations

Venkata Satya Surya Phaneendra Pydimarri, Timothy R Field

Published Apr 8, 2023• 1 citation
Publisher

Abstract

The dynamics of an identical pair of entangled spin-1/2 particles, both subjected to the same random magnetic field, are studied. The dynamics of the pure joint state of the pair are derived using stochastic calculus. An ensemble of such pure states is combined using the modified spin joint density matrix, and the joint relaxation time for the pair of spin-1/2 particles is obtained. The dynamics can be interpreted as a special kind of correlation involving the spatial components of the Bloch polarization vectors of the constituent entangled spin-1/2 particles.

DOI
10.1155/2023/4182623

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The dynamics of an identical pair of entangled spin-1/2 particles, both subjected to the same random magnetic field, are studied. The dynamics of the pure joint state of the pair are derived using stochastic calculus. An ensemble of such pure states is combined using the modified spin joint density matrix, and the joint relaxation time for the pair of spin-1/2 particles is obtained. The dynamics can be interpreted as a special kind of correlation involving the spatial components of the Bloch polarization vectors of the constituent entangled spin-1/2 particles.
The dynamics of a maximally entangled pair of spin-1/2 particles is obtained in the presence of random magnetic fields which are correlated. The two spin-1/2 particles are assumed to be maximally entangled initially and are then disturbed by the magnetic fields modeled as Gaussian vector random processes whose corresponding spatial components are correlated. The dynamics is derived in terms of the joint density matrix of the entangled pair using the ideas of stochastic calculus, from which the steady-state density matrix and the associated timescale for it to be reached are obtained. The asymptotic density matrix represents a state of (partial) disentanglement.
The correlation and fluctuation of both entangled electrons and spin-polarized pairs affected by two rotating magnetic fields in a setup proposed by J. Carlos Egues etc. (Phys. Rev. Lett. {\bf 89}(2002) 176401) are studied theoretically by using scattering approach. Differing from polarized pair, the entangled electron pairs are shown to behave like a composite particle with the total spins and its zzz components. The singlet and triplet states exhibit different bunching and antibunching features, which can be easily adjusted by the magnetic fields. The correlations and variances can show up distinguish output signals for the four incident states. Our results are expected to be tested by using coincident technique.
We characterize and classify the quantum states of a pair of spin-½ particles in terms of the entanglement of the pair. We describe a general strategy for classifying the quantum states of entangled systems, and apply it to the simplest entangled system available - a pair of spin-½ particles. The method is based on local unitary transformations. We give a set of six parameters that describe an arbitrary pure state of a pair of spins, one of which is the entanglement of the pair. We discuss visual representations of the state of this system, and propose a visualization using a Bloch sphere for each subsystem and a disc to record the `shared' information.
We consider the action of a heat bath on one particle of a pair of spin-12\frac{1}{2}21​ particles in a singlet state. The related relaxation effects are described by the Pauli master equation. We show that the density matrix of the two-particle system tends toward a product. The interpretation of this result is, however, complicated by the nonuniqueness of the decomposition of a given density matrix into pure states. To circumvent this difficulty we study separately the terms describing the fluctuations and the friction. The first one does not modify the correlations, although it screens them but the second one separates the systems. The action of a fluctuating magnetic field on one particle of a correlated pair is also investigated.
We study the dynamical generation of entanglement for a very simple system: a pair of interacting spins, s1 and s2, in a constant magnetic field. Two different situations are considered:(a) s1 ->\\infty, s2 = 1/2 and (b) s1 = s2 ->\\infty, corresponding, respectively, to a quantum degree of freedom coupled to a semiclassical one (a qubit in contact with an environment) and a fully semiclassical system, which in this case displays chaotic behavior. Relations between quantum entanglement and classical dynamics are investigated.
The aim of this topical review is a systematic and concise presentation of the results of a series of theoretical works on the quantum dynamics of two-spin-qubit systems towards the elaboration of a physical mechanism of the quantum information transfer between two spin-qubits. For this purpose the main attention is paid to exactly solvable models of two-spin-qubit systems, since the analytical expressions of the elements of their reduced density matrices explicitly exhibit the mutual dependence of the quantum information encoded into the spin-qubits. The treatment of their decoherence due to the interaction with the environment is performed in the Markovian approximation. Rate equations for axially symmetric systems of two coupled spin-qubits non-interacting, as well as interacting, with the environment are exactly solved. It is shown how the solutions of rate equations demonstrate the physical mechanism of the quantum information exchange between the spin-qubits. This mechanism holds also in all two-spin-qubit systems whose rate equations can be solved only by means of numerical calculations. Exact solutions of rate equations for two uncoupled spin-qubits interacting with two separate environments reveal an interesting physical phenomenon in the time evolution of the qubit-qubit entanglement generated by their interaction with the environments: the entanglement sudden death and revival. A two-spin-qubit system with an asymptotically decoherence free subspace was also explicitly constructed. The presented calculations and reasonings can be extended for application to the study of spin-qubit chains or networks.