Entangling spins by measuring charge: A parity-gate toolbox

Abstract

The parity gate emerged recently as a promising resource for performing universal quantum computation with fermions using only linear interactions. Here we analyse the parity gate (P -gate) from a theoretical point of view in the context of quantum networks. We present several schemes for entanglement generation with P -gates and show that native networks simplify considerably the resources required for producing multi-qubit entanglement, like n-GHZ states. Other applications include a Bell-state analyser and teleportation. We also show that cluster state fusion can be performed deterministically with parity measurements. We then extend this analysis to hybrid quantum networks containing spin and mode qubits. Starting from an easy-to-prepare resource (spin-mode entanglement of single electrons) we show how to produce a spin n-GHZ state with linear elements (beam-splitters and local spin-flips) and charge-parity detectors; this state can be used as a resource in a spin quantum computer or as a precursor for constructing cluster states. Finally, we construct a novel spin CZ-gate by using the mode degrees of freedom as ancillae.

Generalized parity measurements

“…Standard resources for preparing stabilizer and cluster states are parity gates [10] and photonic modules [12,33]. In this article we introduced a generalized parity module and studied its use in preparing several families of entangled states.…”

“…It is worth emphasising that W -states are not stabilizer/graph states, hence they cannot be described in the stabilizer formalism. As such they cannot be prepared systematically, in one-shot, using the photonic module or Pgates [10,12] as described above (they require extra resources/ancillae). It is known that W -states belong to a different entanglement class than GHZ-states, and the two families cannot be interconverted through local operations and classical communications (LOCC) [35]; thus they represent different entanglement resources.…”

“…A core primitive used in building the cluster state is the parity gate [8,9]. As shown previously, the parity gate [10,11] and the related photonic module [12] can be used to prepare deterministically arbitrary stabilizer/graph states, hence any cluster state used as a resource in the oneway quantum computing model [7].…”

“…A standard quantum network for the parity gate uses a qubit ancilla [10]. The new feature of our work here is that we relax this constraint and instead use a qudit ancilla [42].…”

Optimal multipartite entanglement concentration of electron-spin states based on charge detection and projection measurements

“…For example, Beenakker et al [46] exploited the charge detection [47] to construct a CNOT gate based on both the charge and the spin degrees of freedom of electrons in 2004. In 2007, Ionicioiu [48] used charge detection to complete the generation of the entangled spins. In 2006, Zhang, Feng, and Gao [49] presented a scheme for the multipartite entanglement analyzer.…”