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arXiv:1704.02235 · Physical Review A

Universal feedback control of two-qubit entanglement

Morteza Rafiee, Alireza Nourmandipour, Stefano Mancini

Published Jul 31, 2017• 20 citations
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Abstract

We consider two qubits undergoing local dissipation and subject to local driving. We then determine the optimal Markovian feedback action to preserve initial entanglement as well as to create stationary entanglement with the help of an $\text{XY}$ interaction Hamiltonian. Such feedback actions are worked out in a way not depending on the initial two-qubit state, whence called universal.

DOI
10.1103/physreva.96.012340

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We consider two qubits undergoing local dissipation and subject to local driving. We then determine the optimal Markovian feedback action to preserve initial entanglement as well as to create stationary entanglement with the help of an XY\text{XY}XY interaction Hamiltonian. Such feedback actions are worked out in a way not depending on the initial two-qubit state, whence called universal.
We study the correction of errors intervening in two qubits dissipating into their own environments. This is done by resorting to local feedback actions with the aim of preserving as much as possible the initial amount of entanglement. Optimal control is found first by gaining insights from the subsystem purity and then by numerical analysis on the concurrence. This is tantamount to a double optimization on the actuation and on the measurement processes. Repeated feedback action is also investigated, thus paving the way for a continuous-time formulation and a solution of the problem.
Abstract We discuss the generation and the long-time persistence of entanglement in open two-qubit systems whose reduced dissipative dynamics is not a priori engineered but is instead subjected to filtering and Markovian feedback. In particular, we analytically study (1) whether the latter operations may enhance the environment capability of generating entanglement at short times and (2) whether the generated entanglement survives in the long-time regime. We show that, in the case of particularly symmetric Gorini–Kossakowski–Sudarshan–Lindblad it is possible to fully control the convex set of stationary states of the two-qubit reduced dynamics, therefore the asymptotic behaviour of any initial two-qubit state. We then study the impact of a suitable class of feed-back operations on the considered dynamics.
Optimal control theory is a powerful tool for improving figures of merit in quantum information tasks. Finding the solution to any optimal control problem via numerical optimization depends crucially on the choice of the optimization functional. Here, we derive a functional that targets the full set of two-qubit perfect entanglers, gates capable of creating a maximally entangled state out of some initial product state. The functional depends on easily computable local invariants and unequivocally determines whether a gate is a perfect entangler. Optimization with our functional is most useful if the two-qubit dynamics allows for the implementation of more than one perfect entangler. We discuss the reachable set of perfect entanglers for a generic Hamiltonian that corresponds to several quantum information platforms of current interest.
It has recently been shown that finding the optimal measurement on the environment for stationary linear quadratic Gaussian control problems is a semidefinite program. We apply this technique to the control of the Einstein-Podolsky-Rosen correlations between two bosonic modes interacting via a parametric Hamiltonian at steady state. The optimal measurement turns out to be nonlocal homodyne measurement---the outputs of the two modes must be combined before measurement. We also find the optimal local measurement and control technique. This gives the same degree of entanglement but a higher degree of purity than the local technique previously considered [S. Mancini, Phys. Rev. A 73, 010304(R) (2006)].
Abstract Expanding utilization of entangled states in quantum technologies, such as quantum information, is a motivating force of developing new methods for enhancement and stabilization of quantum entanglement. This study focuses on using asymmetric lawsto control the entangled states of a quantum systemconsistingof two atoms, each confined in a cavity.The effect of asymmetry laws has been explored in three different scenarios. First, the effect of an asymmetric drive Hamiltonian on a closed quantum system, in which neither the cavity nor the atoms exhibit losses, is studied. Here, the eigenvalues and eigenstates of the total system Hamiltonian have been obtained and the time evolution of the system state has been derived. Also, the fidelity of the system in terms of the asymmetric drive Hamiltonian has been derived analytically. In the second scenario, the stationary solution of an open quantum system, which includes losses in a master equation approach, is derived and the concurrence is studied in terms of the asymmetric drive Hamiltonian and coupling constant. The last scenario is devoted to applying feedback rulesto an open quantum system where some heuristic feedback control laws have been proposed. The simulation results show the concurrence boosting in a larger range of driving field and feedback strength when applying the introduced feedback rules.
Abstract We study the optimal way of creating bi-partite entanglement using a general two-qubit in­ teraction. On the one hand, we analyze the entanglement capability of an arbitrary non-local Hamiltonian acting on two qubits. We explicitly calculate the state which maximizes the entangle­ ment produced per time step 81 during the non-local evolution. On the other hand, we determine the maximal amount of entanglement which can be produced by an arbitrary two-qubit gate. We also give the separable state which leads to the output state containing this amount of entanglement. Furthermore, we consider the situation where auxiliary systems are present. Finally, we determine the non-unitary processes which are able to create entanglement from an initially separable state of two systems.