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arXiv:1202.5192 · Physical Review A

Photon-assisted entanglement creation by minimum-error generalized quantum measurements in the strong-coupling regime

József Zsolt Bernád, G. Alber

Published Jan 15, 2013• 10 citations
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Abstract

We explore the possibilities of entangling two distant material qubits with the help of an optical radiation field in the regime of strong quantum electrodynamical couplingwith almost resonant interaction. For this purpose the optimum generalized field measurements are determined which are capable of preparing a two-qubit Bell state by postselection with minimum error. It is demonstrated that in the strong-coupling regime some of the recently found limitations of the nonresonant weak-coupling regime can be circumvented successfully due to characteristic quantum electrodynamical quantum interference effects. In particular, in the absence of photon loss it is possible to postselect two-qubit Bell states with fidelities close to unity by a proper choice of the relevant interaction time. Even in the presence of photon loss this strong-coupling regime offers interesting perspectives for creating spatially well-separated Bell pairs with high fidelities, high success probabilities, and high repetition rates which are relevant for future realizations of quantum repeaters.

DOI
10.1103/physreva.87.012311

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We explore the possibilities of entangling two distant material qubits with the help of an optical radiation field in the regime of strong quantum electrodynamical couplingwith almost resonant interaction. For this purpose the optimum generalized field measurements are determined which are capable of preparing a two-qubit Bell state by postselection with minimum error. It is demonstrated that in the strong-coupling regime some of the recently found limitations of the nonresonant weak-coupling regime can be circumvented successfully due to characteristic quantum electrodynamical quantum interference effects. In particular, in the absence of photon loss it is possible to postselect two-qubit Bell states with fidelities close to unity by a proper choice of the relevant interaction time. Even in the presence of photon loss this strong-coupling regime offers interesting perspectives for creating spatially well-separated Bell pairs with high fidelities, high success probabilities, and high repetition rates which are relevant for future realizations of quantum repeaters.
We propose a hybrid quantum repeater based on ancillary coherent field states and material qubits coupled to optical cavities. For this purpose, resonant qubit-field interactions and postselective field measurements are determined which are capable of realizing all necessary two-qubit operations for the actuation of the quantum repeater. We explore both theoretical and experimental possibilities of generating near-maximally-entangled qubit pairs (F>0.999F>0.999F>0.999) over long distances. It is shown that our scheme displays moderately low repeater rates, between $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ and 23 pairs per second, over distances up to 900 km, and it relies completely on current technology of cavity quantum electrodynamics.
Quantum communication over long distances relies on the ability to create entanglement between two remote quantum nodes. Recent proposals aiming at experimental realization propose a hybrid quantum repeater setup where two distant material qubits are entangled by light-matter interaction. Motivated by these developments, we investigate possible decoherence effects originating from the centre- of-mass motion of the spatially well separated trapped qubits. Within the Lamb-Dicke regime we use photon exchange involving coherent states of the radiation field to entangle the two material qubits. Optimal generalized photonic field measurements are used to achieve entangled qubit pairs with high fidelities and high success probabilities. We demonstrate that the quality of the achievable two-qubit entanglement crucially depends on the trap frequencies involved. Furthermore, dynamical decoupling schemes are proposed which are capable of suppressing centre-of-mass-motion-induced decoherence effects significantly and which involve only local operations acting on the spatially well-separated material qubits.
Passing a photon number state through a balanced beam splitter will produce an entangled state in which the phases of the two output beams are highly correlated. This entangled state can be viewed as a generalized form of a Schr\"odinger cat state where there is an equal probability amplitude for all possible phases. We show that Bell's inequality can be violated using this entangled state and two distant measuring devices that consist of a single-photon interferometer with a Kerr medium in one path, a set of single-photon detectors, and postselection based on a homodyne measurement. These entangled states are sensitive to photon loss and a violation of Bell's inequality requires either that the losses are inherently small or that their effects have been minimized using linear optics techniques [Micuda et al., Phys. Rev. Lett. 109, 180503 (2012)]. Somewhat surprisingly, the use of the fair sampling assumption is not required for a violation of Bell's inequality despite the use of postselection if the measurements are made in the correct order.
Entanglement between a single photon and a matter qubit is an indispensable resource for quantum repeater and quantum networks. With atomic ensembles, the entanglement creation probability is typically very low to inhibit high-order events. In this paper, we propose and experimentally realize a scheme that creates atom-photon entanglement with an intrinsic efficiency of 50%. We make use of Rydberg blockade to generate two collective excitations, lying in separate internal states. By introducing the momentum degree of freedom for the excitations, and interfering them via Raman coupling, we entangle the two excitations. Via retrieving one excitation, we create the entanglement between the polarization of a single photon and the momentum of the remaining atomic excitation, with a measured fidelity of 0.901(8). The retrieved optical field is verified to be genuine single photons. The realized entanglement may be employed to create entanglement between two distant nodes in a fully heralded way and with a much higher efficiency.
Remote entanglement of distant, noninteracting quantum entities is a key primitive for quantum information processing. We present a protocol to remotely entangle two stationary qubits by first entangling them with propagating ancilla qubits and then performing a joint two-qubit measurement on the ancillas. Subsequently, single-qubit measurements are performed on each of the ancillas. We describe two continuous variable implementations of the protocol using propagating microwave modes. The first implementation uses propagating $\mathrm{Schr}\stackrel{\ifmmode \ddot{}\else \"{}\fi{}}{\mathrm{o}}$ dinger cat states as the flying ancilla qubits, a joint-photon-number-modulo-2 measurement of the propagating modes for the two-qubit measurement, and homodyne detections as the final single-qubit measurements. The presence of inefficiencies in realistic quantum systems limit the success rate of generating high fidelity Bell states. This motivates us to propose a second continuous variable implementation, where we use quantum error correction to suppress the decoherence due to photon loss to first order. To that end, we encode the ancilla qubits in superpositions of Schr\"odinger cat states of a given photon-number parity, use a joint-photon-number-modulo-4 measurement as the two-qubit measurement, and homodyne detections as the final single-qubit measurements. We demonstrate the resilience of our quantum-error-correcting remote entanglement scheme to imperfections. Further, we describe a modification of our error-correcting scheme by incorporating additional individual photon-number-modulo-2 measurements of the ancilla modes to improve the success rate of generating high-fidelity Bell states. Our protocols can be straightforwardly implemented in state-of-the-art superconducting circuit-QED systems.
We investigate quantum repeater protocols based upon atomic qubit-entanglement distribution through optical coherent-state communication. Various measurement schemes for an optical mode entangled with two spatially separated atomic qubits are considered in order to nonlocally prepare conditional two-qubit entangled states. In particular, generalized measurements for unambiguous state discrimination enable one to completely eliminate spin-flip errors in the resulting qubit states, as they would occur in a homodyne-based scheme due to the finite overlap of the optical states in phase space. As a result, by using weaker coherent states, high initial fidelities can still be achieved for larger repeater spacing, at the expense of lower entanglement generation rates. In this regime, the coherent-state-based protocols start resembling single-photon-based repeater schemes.