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arXiv:0801.2873 · Physical Review B

Measurement-based approach to entanglement generation in coupled quantum dots

Avinash Kolli, Brendon W. Lovett, Simon C. Benjamin, Thomas M. Stace

Published Jan 15, 2009• 6 citations
arXivHTMLPDF

Abstract

The remarkable phenomenon of measurement-induced quantum entanglement has recently been demonstrated between noninteracting atomic systems [D. L. Moehring et al., Nature (London) 449, 68 (2007)]. In the solid state, the technique may offer a new means of harnessing the strong interactions between neighboring units without the need for precise control over interactions. Recently, we proposed a method for optical parity measurements in a coupled quantum dot system [A. Kolli et al., Phys. Rev. Lett. 97, 250504 (2006)]. Here we perform a comprehensive analytic and numerical study to determine the feasibility of realizing this method using existing technology. We calculate the effects of possible error sources including nonideal photon detectors, ineffective spin-selective excitation, and dot distinguishability (both spatial and spectral). Furthermore, we present an experimental approach for verifying the success of the parity measurement. We conclude that experimental realization of the process should be feasible immediately.

DOI
10.1103/physrevb.79.035315

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The remarkable phenomenon of measurement-induced quantum entanglement has recently been demonstrated between noninteracting atomic systems [D. L. Moehring et al., Nature (London) 449, 68 (2007)]. In the solid state, the technique may offer a new means of harnessing the strong interactions between neighboring units without the need for precise control over interactions. Recently, we proposed a method for optical parity measurements in a coupled quantum dot system [A. Kolli et al., Phys. Rev. Lett. 97, 250504 (2006)]. Here we perform a comprehensive analytic and numerical study to determine the feasibility of realizing this method using existing technology. We calculate the effects of possible error sources including nonideal photon detectors, ineffective spin-selective excitation, and dot distinguishability (both spatial and spectral). Furthermore, we present an experimental approach for verifying the success of the parity measurement. We conclude that experimental realization of the process should be feasible immediately.
Parity measurements on qubits can generate the entanglement resource necessary for scalable quantum computation. Here we describe a method for fast optical parity measurements on electron spin qubits within coupled quantum dots. The measurement scheme, which can be realized with existing technology, consists of the optical excitation of excitonic states followed by monitored relaxation. Conditional on the observation of a photon, the system is projected into the odd/even-parity subspaces. Our model incorporates all the primary sources of error, including detector inefficiency, effects of spatial separation and nonresonance of the dots, and also unwanted excitations. Through an analytical treatment we establish that the scheme is robust to such effects. Two applications are presented: a realization of a controlled-NOT gate, and a technique for growing large scale graph states.
Entanglement between particles is a crucial resource in quantum information processing, an important example of which is the exploitation of entangled photons in quantum communication protocols. Among the different available sources of entangled photons, semiconductor quantum dots (QDs) excel owing to their deterministic emission properties, potential for electrical injections, and direct compatibility with semiconductor manufacturing techniques. Despite the great promises, QD-based sources are far from being ideal. In particular, such sources present several critical issues, which require the overcoming of challenges pertaining to spectral tunability, entanglement fidelity, photon indistinguishability and brightness. In this article, we will discuss the potential solutions to these problems and review the recent progress in the field.
We introduce an architecture for robust and scalable quantum computation using both stationary qubits (e.g., single photon sources made out of trapped atoms, molecules, ions, quantum dots, or defect centers in solids) and flying qubits (e.g., photons). Our scheme solves some of the most pressing problems in existing nonhybrid proposals, which include the difficulty of scaling conventional stationary qubit approaches, and the lack of practical means for storing single photons in linear optics setups. We combine elements of two previous proposals for distributed quantum computing, namely the efficient photon-loss tolerant build up of cluster states by Barrett and Kok [Phys. Rev. A 71, 060310(R) (2005)] with the idea of repeat-until-success (RUS) quantum computing by Lim et al. [Phys. Rev. Lett. 95, 030505 (2005)]. This idea can be used to perform eventually deterministic two qubit logic gates on spatially separated stationary qubits via photon pair measurements. Under nonideal conditions, where photon loss is a possibility, the resulting gates can still be used to build graph states for one-way quantum computing. In this paper, we describe the RUS method, present possible experimental realizations, and analyze the generation of graph states.
Measurement-based entanglement (MBE) is a method for entangling quantum systems through the state projection that accompanies a parity measurement. We derive a stochastic master equation describing measurement-based entanglement of a pair of silicon double-dot flopping-mode spin qubits, develop numerical simulations to model this process, and explore what modifications could enable an experimental implementation of such a protocol. With device parameters corresponding to current qubit and cavity designs, we predict an overlap of the final state of the MBE protocol with the target Bell state $|{\mathrm{\ensuremath{\Psi}}}_{+}\ensuremath{\rangle}$ of $\ensuremath{\approx}61%$. By increasing the cavity outcoupling rate by a factor of 10, we are able to obtain an improvement of this metric to $\ensuremath{\approx}81%$ while maintaining a yield of 33%.
Self-assembled quantum dots can act as an interface between single spins and photons. They combine the flexibility and scalability of semiconductor systems with near-perfect two level systems, emitting highly coherent single photons. In potential quantum information processing architectures based upon optical networks, quantum dots permit light-matter coupling between matter qubits and photonic links. Single trapped charge carriers in quantum dots can be addressed optically, generating spin-photon entanglement between the matter qubits and \lq flying' photon qubits, a key first step in creation of a network. Such an optically linked network of spins in quantum dots has yet to be realized. The semiconductor environment presents a key challenge; it broadens the spectrum of the emitted light, which reduces the fidelity of schemes based upon photon exchange or interference. In addition, these quantum dots are subject to hyperfine coupling to a bath of >>> 105^{5}5 nuclear spins. While this presents an opportunity to study the physics of a central spin in a spin bath, it degrades the spin coherence of a trapped electron or hole. The suggested gate operations to generate entanglement, and the spin measurements to verify a created state, rely upon photon detection. Thus a second limitation occurs due to low efficiency of detectors and photon collection probability. Recent developments in detector technology have enabled us to bring generation and verification of entangled states with quantum dots into the realm of possibility. This dissertation begins with a detailed study of the interaction of a single electron spin with the solid state environment of the quantum dot, analysing the intensity noise of scattered light under resonant excitation to uncover the timescales and relative amplitudes of identified noise sources. A technique for rapid characterization of samples is presented, focusing in particular upon comparison of spectral broadening of the optical transitions relevant to a spin-photon interface. Having identified the extent of environmental factors acting upon the quantum dots, we turn to a demonstration of photon-mediated entanglement between two distant electron spins using a probabilistic scheme. We are able to generate entangled states at 7 kHz, the fastest yet reported for photon-mediated protocols. The average state fidelity of the created Bell states is 63.5 ±\pm± 3.0 \%., violating the classical limit by over 4 standard deviations of the mean. In addition, we demonstrate full optical phase tuning of the Bell state ∣Ψ=12(∣↑∣↓+eiϕ∣↓∣↑)|{\Psi} = \frac{1}{\sqrt{2}}\left(|{\uparrow}|{\downarrow} + e^{i\phi}|{\downarrow}|{\uparrow} \right)∣Ψ=2​1​(∣↑∣↓+eiϕ∣↓∣↑). This is a proof of principle experiment, and sets a fidelity benchmark upon which gains can be made by mitigation of environmental dynamics.