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arXiv:1103.2938 · Physical Review A

Entangling photons via the double quantum Zeno effect

Nicolai ten Brinke, Andreas Osterloh, Ralf Schützhold

Published Aug 10, 2011• 5 citations
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Abstract

We propose a scheme for entangling two photons via the quantum Zeno effect, which describes the inhibition of quantum evolution by frequent measurements and is based on the difference between summing amplitudes and probabilities. For a given error probability ${P}_{\mathrm{error}}$, our scheme requires that the one-photon loss rate ${\ensuremath{\xi}}_{1\ensuremath{\gamma}}$ and the two-photon absorption rate ${\ensuremath{\xi}}_{2\ensuremath{\gamma}}$ in some medium satisfy ${\ensuremath{\xi}}_{1\ensuremath{\gamma}}/{\ensuremath{\xi}}_{2\ensuremath{\gamma}}=2{P}_{\mathrm{error}}^{2}/{\ensuremath{\pi}}^{2}$, which is significantly improved compared to previous approaches. Again based on the quantum Zeno effect, as well as coherent excitations, we present a possibility to fulfill this requirement in an otherwise linear optics setup.

DOI
10.1103/physreva.84.022317

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We propose a scheme for entangling two photons via the quantum Zeno effect, which describes the inhibition of quantum evolution by frequent measurements and is based on the difference between summing amplitudes and probabilities. For a given error probability Perror{P}_{\mathrm{error}}Perror​, our scheme requires that the one-photon loss rate \ensuremathξ1\ensuremathγ{\ensuremath{\xi}}_{1\ensuremath{\gamma}}\ensuremathξ1\ensuremathγ​ and the two-photon absorption rate \ensuremathξ2\ensuremathγ{\ensuremath{\xi}}_{2\ensuremath{\gamma}}\ensuremathξ2\ensuremathγ​ in some medium satisfy \ensuremathξ1\ensuremathγ/\ensuremathξ2\ensuremathγ=2Perror2/\ensuremathπ2{\ensuremath{\xi}}_{1\ensuremath{\gamma}}/{\ensuremath{\xi}}_{2\ensuremath{\gamma}}=2{P}_{\mathrm{error}}^{2}/{\ensuremath{\pi}}^{2}\ensuremathξ1\ensuremathγ​/\ensuremathξ2\ensuremathγ​=2Perror2​/\ensuremathπ2, which is significantly improved compared to previous approaches. Again based on the quantum Zeno effect, as well as coherent excitations, we present a possibility to fulfill this requirement in an otherwise linear optics setup.
The quantum Zeno effect describes the inhibition of quantum evolution by frequent measurements. Here, we propose a scheme for entangling two given photons based on this effect. We consider a linear-optics set-up with an absorber medium whose two-photon absorption rate ξ2γξ_{2γ}ξ2γ​ exceeds the one-photon loss rate ξ1γξ_{1γ}ξ1γ​. In order to reach an error probability PerrorP_{\rm error}Perror​, we need ξ1γ/ξ2γ<2Perror2/π2ξ_{1γ}/ξ_{2γ}<2P_{\rm error}^2/π^2ξ1γ​/ξ2γ​<2Perror2​/π2, which is a factor of 64 better than previous approaches (e.g., by Franson et al). Since typical media have $ξ_{2γ}
The phenomenon of quantum interrogation allows one to optically detect the presence of an absorbing object, without the measuring light interacting with it. In an application of the quantum Zeno effect, the object inhibits the otherwise coherent evolution of the light, such that the probability that an interrogating photon is absorbed can in principle be arbitrarily small. We have implemented this technique, achieving efficiencies of up to 7373%73, and consequently exceeding the 5050%50 theoretical maximum of the original ``interaction-free'' measurement proposal. We have also predicted and experimentally verified a previously unsuspected dependence on loss.
In this work we theoretically consider quantum Zeno effect for entangled (correlated) quantum states. (Our physical systems and calculations are simpler than it is case in remarkable work on entanglement protection via Zeno effect by Maniscalco et all. But Maniscalco et all and our final conclusions are the same.) Firstly, we demonstrate well-known quantum Zeno effect by frequent decay detection for single, simple, two-level quantum system, with stable, ground quantum state and one non-stable, excited quantum state which can decay, by photon emission, in the ground state. (In this case, by frequent decay detections, system stands in the excited state.) Further, we consider single photon with energy equivalent to energy difference between excited and ground energy level of mentioned system. After interaction with a half-silvered mirror, mentioned photon is in a quantum superposition of the reflected and transmitted quantum state or trajectory. Mentioned trajectories are directed toward two identical, but distant, mentioned simple two-level systems both of which are initially (before interaction with photon) in ground state. Immediately after interaction with photon (photon absorption) two two-level systems are described by entangled (correlated) quantum state ( (excited, ground) + (ground, excited) , symbolically). We prove that in this case, by frequent decay detections on both systems, mentioned two two-level systems are described by initial entangled (correlated) quantum state ( (excited, ground) +(ground, excited)).
Quantum logic gates for photonic qubits can be implemented using the quantum Zeno effect based on strong two-photon absorption. The fidelity of quantum Zeno gates of this kind may be substantially reduced by photon loss. Heralding on those outcomes in which both of the logical qubits emerge from the Zeno gate can increase the fidelity at the expense of a limited success rate (P.M. Leung et al., Phys. Rev. A 74, 062325 (2006)). We analyze the performance of heralded quantum Zeno gates by solving Schrodinger's equation for a system of photons coupled to three-level atoms. This approach identifies several potential error sources that are not described by earlier models that assumed a fixed rate of single-photon loss and two-photon absorption.
The quantum Zeno effect is a distinctive phenomenon in quantum mechanics, describing the nontrivial effect of frequent projective measurements on hindering the evolution of a quantum system. However, when subjected to environmental noise, the quantum system may dissipate, and the quantum Zeno effect no longer works. This research starts from the physical mechanism for the decay of the quantum Zeno effect in the presence of noise and investigates the effect of coherent quantum controls on mitigating the decrease of the survival probability that the system stays in the initial state induced by the noise. We derive the decay rate of the survival probability with and without coherent quantum controls in general, and show that when the frequency of the projective measurements is large but finite, proper coherent controls by sufficiently strong Hamiltonians can be designed to decrease the decay rate of the survival probability. A two-level quantum system suffering from typical unitary and nonunitary noise is then considered to demonstrate the effect of the proposed coherent quantum control scheme in protecting the quantum Zeno effect against the noise. The decay rate of the survival probability is obtained in the presence of noise, and the control Hamiltonian is further optimized analytically to minimize the decay rate by a variational approach. The evolution paths of the quantum system with the optimal coherent controls are illustrated numerically for different scenarios to explicitly show how the coherent control scheme works in lowering the decay of survival probability.
The quantum Zeno effect reveals that continuous observation of a quantum system can significantly alter its evolution. Here, we present a method for establishing polarization entanglement between two initially unentangled photons in coupled waveguides via the quantum Zeno effect. We support our analytical investigation with numerical simulations of the underlying Schrodinger equation describing the system. Further, we extend our technique to three coupled waveguides in a planar configuration and determine the parameters required to generate three-qubit W-states. In contrast to existing schemes based on a vacuum and single-photon encoding, the polarization encoding in our approach is compatible with quantum information protocols that remove photon loss through post-selection. Our findings offer a powerful quantum state engineering approach for photonic quantum information technologies.