Rapid and robust generation of Einstein-–Podolsky–-Rosen pairs with spin chains

Abstract

We investigate the ability of dimerized spin chains with defects to generate EPR pairs to very high fidelity through their natural dynamics. We propose two protocols based on different initializations of the system, which yield the same maximally entangled Bell state after a characteristic time. This entangling time can be varied through engineering the weak/strong couplings' ratio of the chain, with larger values giving rise to an exponentially faster quantum entangling operation. We demonstrate that there is a set of characteristic values of the coupling, for which the entanglement generated remains extremely high. We investigate the robustness of both protocols to diagonal and off-diagonal disorder. Our results demonstrate extremely strong robustness to both perturbation types, up to strength of 50\% of the weak coupling. Robustness to disorder can be further enhanced by increasing the coupling ratio. The combination of these properties makes the use of our proposed device suitable for the rapid and robust generation of Bell states in quantum information processing applications.

Generation and Robustness of Quantum Entanglement in Spin Graphs

“…This configuration is attained by imposing a coupling distribution of two different energies, ∆ and δ, that results in having three sites (named A, B and C) distributed symmetrically and weakly coupled (δ) to the rest of the system, such that they appear to be defects in an otherwise strongly coupled (∆) graph. The reason that makes this particular configuration interesting is that it can be approximated to a trimer chain, which has the ability to dynamically create maximally entangled Bell state between the edge sites when the system is initialised with a spin up in the middle site [14,26]. Figure 7 shows the result of using this configuration in our original graph and its two quotient structures.…”

“…From an experimental point of view, the evaluation of the first peak is a useful metric as it will be most likely to fall ahead of the decoherence times of the experimental realisation. The dependence of the time when the first entanglement operation happens can be analytically approximated from the reduced trimer as done in [26]. From that, we get…”

Comparison of entangling protocols in ABC-type spin chains

“…For protocol demonstration, here we focus on a spin chain configuration with N = 7 sites. However, longer chains could be considered for implementation of the same protocols [1,2]. This spin chain can be described by the following time-independent Hamiltonian…”

“…For each spin qubit, the standard computational basis states are represented by spin up, |1 , and spin down, |0 , with the ground, or zero, state of the system being all spins down. It has been demonstrated [31,32,33] that related dimerised chains have high fidelity quantum state transfer (QST) properties, something that we exploit in our protocols in order to generate the desired entangled states [1,2]. The operation of these spin chain devices relies on their natural dynamics.…”

“…the time needed for an arbitrary initial state to evolve to its mirror position with respect to the centre of the chain. For the Bell state generation [2], the 'entangling time' is approximately half the mirroring time (t E ≈ t M /2). In all cases, at t E the system state becomes maximally entangled between sites A and C, from which the two entangled qubits can be extracted, if desired 1 .…”