Complete Bell state measurement of diamond nuclear spins under a complete spatial symmetry at zero magnetic field

Abstract

The symmetry of the space where a spin qubit resides plays an essential role in the manipulation of quantum entanglement, which governs the performance of quantum information systems. Application of a magnetic field, which is usually necessary for spin manipulation and readout, inevitably breaks the spatial symmetry to induce competition among quantization axes between internal and external fields, thus limiting the purity of the entanglement. If we could manipulate and readout entanglement under a zero magnetic field, we would be able to avoid the competition among quantization axes to achieve ideally high fidelity. We here demonstrate the complete Bell state measurement, which is a core element of quantum processing, of two carbon nuclear spins in the vicinity of a diamond nitrogen-vacancy center. The demonstration was made possible by holonomic entanglement manipulations based on the geometric phase with a polarized microwave under a zero magnetic field, where the quantization axis is uniquely defined by the hyperfine field. The demonstrated scheme allows high-fidelity entanglement processing even when magnetic fields cannot be applied to the integration of superconducting and spin qubits, thereby paving the way for building fault-tolerant distributed quantum computers and quantum repeater networks.

Deterministic Bell state measurement with a single quantum memory

“…The development of large-scale distributed quantum computers requires quantum networks [1][2][3] based on remote entanglement to connect the computers [4][5][6][7][8][9][10] and thus requires quantum repeaters [11][12][13][14] or quantum interfaces 15 that can perform a deterministic and complete Bell state measurement (BSM) [16][17][18][19] not only to extend the distance of photon transmission and to route photons over the networks but also to interface the quantum state between photons and qubits in quantum computers 15,[20][21][22] . A complete BSM allows us to project any two-qubit states into one of the four Bell states deterministically, which typically requires quantum nondemolition measurement known as single-shot measurement [23][24][25][26][27][28] .…”

“…1d. The Bell states are composed of inherently degenerate qubits, which we call geometric spin qubits 19,28,32,34,[49][50][51][52][53][54][55][56] , according to the computational basis states | ± 1⟩ e for the electron and | ± 1⟩ N for the nitrogen (dashed area in Fig. 1d), and are operated by the universal holonomic quantum gate with polarized MW and RF pulses via the ancilla states |0⟩ e and |0⟩ N 55 .…”

Bell-state measurement exceeding 50% success probability with linear optics

“…However, these require intricate experimental setups that are challenging to scale up. Complete BSMs on spin qubits are possible in solid-state systems ( 34 ), but thermal effects typically prevent operations at room temperature. In general, nonoptical approaches suffer from limited intrinsic clock rates of the order of megahertz.…”

Bell-state measurement exceeding 50% success probability with linear optics

“…However, these require intricate experimental set-ups that are challenging to scale up. Complete BSMs on spin qubits are possible in solid-state systems [33], but thermal effects typically prevent operations at room temperature. Generally, non-optical approaches suffer from limited intrinsic clock rates of the order of MHz.…”