Subject B : Entanglement purification between distant nodes

158B-T01Quantum repeater based on diamond NV centers

Tohoku University (Hideo Kosaka)
Osaka University
Nippon Telegraph and Telephone Corporation
National Institute of Informatics

To make a practical quantum repeater, a long-lived quantum memory is highly desirable device at the nodes. Our target is to make an interface between a photon as a transmission qubit and a nuclear spin as a memory qubit intermediated by an electron spin as a gate qubit.

Toward this purpose, we have several candidates such as semiconductor quantum dots, NV centers in diamond, and rare-earth impurities in non-linear crystal. Among those candidates this project focuses on NV centers in diamond which provide longest memory time together with reasonable optical activity.

The project consists of four groups – Tohoku univ., Osaka univ., NTT, and NII. Each of them contributes different aspects as summarized below.

Subtheme 1: Quantum media conversion from a photon into a nuclear spin (Tohoku univ.)

The main task of Tohoku university group is to transfer the quantum state of a photon into a nuclear spin via an adjacent electron spin at an NV

Subtheme 2: Enhancing application platform (Osaka univ.)

Osaka university group try to detect the entangled state stored in multiple nuclear spins.

Subtheme 3-1: Next generation quantum key distribution system technology (NTT)

NTT group theoretically supports this entanglement detection by solving the decoupling problem between an electron spin and nuclear spins during the state transfer and gate operation.

Subtheme 3-2: Long-term operational testing (NII)

NII group theoretically supports the cavity design which is ideal for a practical quantum repeater which consists of hybrid systems.

For quantum entanglement purification between remote nodes, gate operation and entanglement detection between nuclear spins intermediated by an electron spin are needed besides the quantum media conversion. Furthermore, we have to solve the issue of fidelity degradation upon the system operation when we combine the quantum media conversion, gate operation, and entanglement detection.

Interim results for Team 158B-T01

Task title	Outcome	Date	Note
1: Hybrid quantum repeater fundamental technology	a) Experimental demonstration of entanglement detection between a photon and an electron spin	Aug. 2013	MRS2013
	b) Preliminary experiments for quantum state tomography of a nuclear spin via photon absorption	Aug. 2013	MRS2013
2: Hybrid quantum repeater purification technology	a) Demonstration of fast quantum gate operation of electron spin (< 10 ns)	Sep. 2013
	b) Demonstration of detection of entangled state stored in multiple nuclear spins. (F > 75%)	Mar. 2013	SEST2013
3: Hybrid gate and optical module design	1a) Protocol for gate operation between ele. and nuc. spin with F>90% within ∼ 4 ms	Apr. 2012
	1b) Optimized protocol with phase gate fidelity > 99% within ∼ 4 ms	Apr. 2013
	2a) One-side cavity design with a single NV	Mar. 2012	QCMC2012
	2b) Numerical analysis on N-V-C system	Oct. 2013	CLEO-PR2013 MRS2013

Task 1: Entanglement detection between a photon and an electron spin has been demonstrated by utilizing the inherent spin-orbit entanglement of an electron via the degenerate Λ-V system in an NV center in diamond (Fig. 1). We also showed the possibility of entanglement detection between a photon and a nuclear spin by utilizing the hyperfine interaction. These demonstrations enable quantum state tomography of an electron and a nuclear spin via photon absorption heralded by the phonon-sideband emission, and supplies building blocks for a long-distance quantum repeater.

Task 2: Detection of entangled states (= four Bell states, Φ^-,Φ⁺,Ψ^-,Ψ⁺) stored in multiple nuclear spins has been demonstrated (Fig. 2). The four Bell states were generated and detected in NV center which couples with three ¹³C nuclear spins. The fidelities of the detection of the four Bell states are shown in figure. The smallest one was larger than 75%.

Task 3-1: Our task was to design a simple and efficient protocol that would allow for the transfer of the state of the electron spin to the nuclear spin. We have designed set of operations that allow this to be achieved without the need for complicated composite pulse sequences. These operations include both the electron and nuclear spin rotations, as well as an entangling gate between them. These are experimentally realizable gates with current technology of sufficiently high fidelities that they can be used to build graph states for quantum information processing tasks

Task 3-2: NVC system has been analyzed in details. We numerically solved the three body problem, and determined the gate fidelity for single qubit operations for each component. This analysis is a basis for optical control for optical modules for single diamond NV center. More than 99% fidelity can be achieved by square pulse driving, which can be sufficient for quantum repeater protocol. The direction of further improvement needs to be discussed jointly with the quantum repeater system development.

Targets for Team 158B-T01

Task title	Work/Milestone	Due Date	Note
1: Hybrid quantum repeater fundamental technology	a) High fidelity entanglement detection between a photon and an electron	Apr. 2014	Target fidelity >90%
	b) Entanglement detection between a photon and a nuclear spin	Aug. 2014	Target fidelity >80%
	c) Teleportation-based quantum media conversion from a photon to an nuclear spin	Apr. 2015	Target fidelity >80%
2: Hybrid quantum repeater purification technology	a) Fast quantum gate operation of electron spin	Aug. 2014	105 gate operations within T2
	b) Demonstration of complete entangled states (Bell states) measurement in multiple nuclear spins	Dec. 2015	Target fidelity > 90 %
	c) Practical decoupling technique for quantum memory of nuclear spin	Dec. 2015	T2 > 1 ms
3: Hybrid gate and optical module design	1a) Realistic parameters with phase gate fidelity > 90%	Apr. 2014	Operation time ∼1µs
	1b) Comparison with other donor systems	Apr. 2015	ErYSO : Bandwidth ∼10MHz
	2a) Quantum repeater unit design	Oct. 2014	Scalable design
	2b) Quantum repeater system design	Oct. 2015	Scalable design