Multiphoton-state-assisted entanglement purification of material qubits

Abstract

We propose an entanglement purification scheme based on material qubits and ancillary coherent multiphoton states. We consider a typical QED scenario where material qubits implemented by two-level atoms fly sequentially through a cavity and interact resonantly with a single-mode of the radiation field. We explore the theoretical possibilities of realizing a high-fidelity two-qubit quantum operation necessary for the purification protocol with the help of a postselective balanced homodyne photodetection. We demonstrate that the obtained probabilistic quantum operation can be used as a bilateral operation in the proposed purification scheme. It is shown that the probabilistic nature of this quantum operation is counterbalanced in the last step of the scheme where qubits are not discarded after inadequate qubit measurements. As this protocol requires present-day experimental setups and generates high fidelity entangled pairs with high repetition rates, it may offer interesting perspectives for applications in quantum information theory.

Hybrid quantum repeater based on resonant qubit-field interactions

“…In the next step, entangled state obtained in the first building block of the quantum repeater have been considered as input states for an entanglement purification protocol, a recurrence protocol, introduced by us [19,51]. The theoretical model consists of two qubits, which sequentially interact with a single-mode cavity, and postselective field measurements.…”

“…By solving the Jaynes-Cummings-Paul model in sequence for interaction times characterizing the collapse phenomena [26] and projecting onto the field state contribution |α in the full solution by means of balanced homodyne photodetection [19], one is able to generate the probabilistic two-qubit quantum operation at each node:M…”

Atomic Bell measurement via two-photon interactions

“…The appearance of this flip operator is due to the fact that in (27) the initial atomic probability amplitudes of the state in the second row are interchanged. For certain atomic probability amplitudes, the above projection postselect the atoms in an entangled state in a similar fashion as in [39].…”

“…In order to convert this scheme into a von Neumann measurement of the four Bell states, i.e., a Bell measurement, one has to implement a procedure to flip some of the Bell states. Fortunately, this can be accomplished with the help of the following pair of single-atom unitary transformations σ φ = e iφ |e g| + e −iφ |g e|, σ z = |e e| − |g g|, (39) that transform the Bell states according to the following rules…”

Conditions for entanglement purification with general two-qubit states

“…We have studied in Ref. [8] the performance of the modified protocol using Werner and other Bell-diagonal states. A natural question arises whether this protocol can still work for arbitrary input states making the step of random local unitary rotations ("twirling") superfluous.…”