High entanglement generation and high fidelity quantum state transfer in a non-Markovian environment

Yan‐Ling Li, Mao-Fa Fang

This paper analyses a system of two independent qubits off-resonantly coupled to a common non-Markovian reservoir at zero temperature. Compared with the results in Markovian reservoirs, we find that much higher values of entanglement can be obtained for an initially factorized state of the two-qubit system. The maximal value of the entanglement increases as the detuning grows. Moreover, the entanglement induced by non-Markovian environments is more robust against the asymmetrical couplings between the two qubits and the reservoir. Based on this system, we also show that quantum state transfer can be implemented for arbitrary input states with high fidelity in the non-Markovian regime rather than the Markovian case in which only some particular input states can be successfully transferred.

Ting Yu, Joseph H. Eberly

Chun Miao, Ming Yang, Zhuo‐Liang Cao

Da-Wei Luo, Edward T. Yu, Ting Yu

We consider the transfer of continuous-variable entangled states in coupled oscillator chains embedded in a generic environment. We demonstrate high-fidelity transfer via optimal control in two configurations-a linear chain and an X-shaped chain. More specifically, we use the Krotov optimization algorithm to design control fields that achieve the desired state transfer. Under environmental memory effects, the Krotov algorithm needs to be modified, since the dissipative terms in non-Markovian dynamics are generally governed by the time-dependent system Hamiltonian. Remarkably, we can achieve high-fidelity transfer by simply tuning the frequencies of the oscillators while keeping the coupling strength constant, even in the presence of open-system effects. For the system under consideration, we find that quantum memory effects can aid in the transfer of entanglement and show improvement over the memoryless case. In addition, it is possible to target a range of entangled states, making it unnecessary to know the parameters of the initial state beforehand.

David Lucas

Alexandre Cesa

In the first part of this thesis, we investigate the dynamics of open quantum systems coupled in a purely dephasing way to their environment, which is a paradigmatic example of decoherent dynamics. We focus more specifically on the emergence of non-Markovian effects in the dynamics of such open systems. After reviewing different measures of non-Markovianity, we obtain an analytical expression for the reduced density operator of a finite-dimensional open system coupled with its environment through time-dependent purely dephasing interactions. When the system is initially uncorrelated with its environment, we obtain the time-local master equation that describes its dynamics. In this case, we also derive an exact expression for the witness of non-Markovianity based on the volume of accessible states of the open system. These results are then applied to spin systems coupled to either a spin or a bosonic environment. For spin environments, we study non-Markovianity for different ranges of interaction and in different thermodynamical limits. Moreover, the generation of entanglement between the open system and its environment as well as between spins within the open system is investigated. For bosonic environments, we study the effect of the initial state of the environment on non-Markovianity. We also show that time-dependent modulations of the system-environment coupling can dramatically alter the non-Markovian behavior of the open system. Finally, we consider the case of an open quantum system simultaneously coupled to spin and bosonic baths. In that case, we study how the coupling between the different baths and of the presence of initial correlations in the environment affect the non-Markovianity displayed by the open quantum system. The second part of this thesis is a contribution to the investigation of how quantum systems can be used to process information. More precisely, we focus on the implementation of gate-based quantum computing using neutral atoms trapped in optical or magnetic lattices and interacting through dipole-dipole interactions when excited to Rydberg states. In this context, we present protocols implementing two-qubit quantum gates between atoms far apart in the lattice. To this end, we propose to use a chain of non-coding ancilla atoms to transfer the state of the control qubit to an atom near the target qubit. Before discussing entangling gates between distant qubits, we present two protocols that implement state transfer along a chain of two-level atoms relying respectively on single- and two-atom laser pulses combined with dipole blockade. After reviewing protocols implementing CZ and CNOT gates between nearby qubits using dipole-dipole interactions, we show how the state-transfer protocols previously presented can be used to perform entangling gates between distant qubits. The performance of the state-transfer and gate protocols are assessed using the process fidelity. Moreover, we provide a theoretical explanation for the behavior of the process fidelity with respect to dissipation and imperfect blockade.