Deterministic Generation of All-Photonic Quantum Repeaters from Solid-State Emitters

Quantum repeaters are nodes in a quantum communication network that allow reliable transmission of entanglement over large distances. It was recently shown that highly entangled photons in so-called graph states can be used for all-photonic quantum repeaters, which require substantially fewer resources compared to atomic-memory-based repeaters. However, standard approaches to building multiphoton entangled states through pairwise probabilistic entanglement generation severely limit the size of the state that can be created. Here, we present a protocol for the deterministic generation of large photonic repeater states using quantum emitters such as semiconductor quantum dots and defect centers in solids. We show that arbitrarily large repeater states can be generated using only one emitter coupled to a single qubit, potentially reducing the necessary number of photon sources by many orders of magnitude. Our protocol includes a built-in redundancy, which makes it resilient to photon loss.

Popular Summary

Quantum communication relies on the properties of quantum mechanics to provide inherent security to transmitted information. This information will be carried by quantum states of photons traveling via optical fibers. In classical telecommunications, repeaters are used to amplify signals at intermediate points so that the information can cover longer distances than what is possible with only optical fibers. Quantum repeaters have been suggested to play a similar role in quantum communication, but the nature of quantum states requires a distinct approach. It was recently shown that states of many photons with a specific type of entanglement can be used for all-photonic quantum repeaters. The generation of such states, however, remains probabilistic even in principle, limiting practical implementations. We provide a deterministic approach based on solid-state emitters which, when controlled appropriately, can generate photons readily in the required highly entangled “repeater” state.

We show that with only a single emitter coupled to one qubit, it is possible to generate repeater states with arbitrarily many photons. This is achieved by applying a particular sequence of operations between each photon emission event, including rotations and measurements on the emitter, and photon polarizations and entanglement operations between the emitter and qubit. These operations ensure that the emitted photons already carry the correct entanglement structure, bypassing the need for probabilistic photon manipulations.

Communication fidelity grows as the number of photons in the repeater state is increased, so the fact that only a single emitter is needed, regardless of photon number, is promising for scalability. Our approach thus constitutes a paradigm shift that could potentially reduce the resources needed to build a quantum communication network by orders of magnitude.

Figure 1

Graphical representation of $N=4$ and $N=6$ repeater states proposed in Ref. [16]. States consist of a complete subgraph of $N$ core photons each connected to an additional photon forming $N$ external arms.

Figure 2

(a) Level structure required for the emitter to emit entangled photons. Each of two ground states couples to its own excited state. Cross transitions are forbidden by selection rules. (b) Linear photonic cluster state. Photons are blue circles, while the red circle is the emitter. Each line represents entanglement between the qubits it connects. (c) Partial $N=4$ repeater state. All but 2 of the 8 entangled photons comprising this repeater state can be produced from a single emitter.

Figure 3

Generation of the $N=6$ repeater state proposed in Ref. [16]: (a) Top: Emitter $B$ is connected to ancilla $A$ with a CZ gate and pumped twice, creating photons 1 and 2. Bottom: Hadamard gates are applied and emitter $B$ is measured, detaching it from the graph. (b) This process is repeated (creating photons 3 and 4), generating another arm. (c) After $N$ arms have been generated, local complementation is applied about ancilla $A$, and ancilla $A$ is then measured. The exact sequence of gates for this process is given in the Appendix.

Figure 4

A tree of depth $d=2$ with $k=6$ arms. Blue edges represent entanglement created by pumping an emitter, while red edges represent entanglement created with a CZ gate between an emitter and another emitter or ancilla.

Figure 5

Encoded RGS with (a) depth-one and (b) depth-two tree structures. Both of these can be generated by pumping a single emitter, which is coupled to an ancilla qubit via CZ gates.

Figure 6

A large repeater state with $N=6$ (logical qubits) proposed in Ref. [20], which includes subtrees in order to make the state more robust against errors.

Figure 7

(a) The fidelity of the $N=6$ RGS shown in Fig. 1 as a function of the infidelities of the two-qubit CZ gate and the individual single-qubit gates applied to emitters and ancillas (which are assumed to all have the same infidelity). (b) The fidelity of the large repeater state shown in Fig. 6.

Figure 8

The fidelity of the $N=6$ RGS shown in Fig. 1 as a function of the infidelity of the two-qubit CZ gate and the optical pumping infidelity. (The fidelity of single-qubit gates is taken to be 99.9%.)

Figure 9

The single-qubit gate and two-qubit CZ-gate infidelities needed to create a RGS of size $N$ with 90% fidelity. The fidelity of the RGS is given by ${\mathrm{CZ}}^N{U}^{2N+2}{P}^{2N}$, where CZ, $U$, and $P$ are the fidelities of the CZ gates, single-qubit gates on the emitters and ancillas, and pumping operations, respectively.