One-shot entanglement generation over long distances in noisy quantum networks

Abstract

We consider the problem of creating a long-distance entangled state between two stations of a network, where neighboring nodes are connected by noisy quantum channels. We show that any two stations can share an entangled pair if the effective probability for the quantum errors is below a certain threshold, which is achieved by a local encoding of the qubits and a global bit-flip correction. In contrast to the conventional quantum-repeater schemes, we do not need to store the qubits in quantum memory for a long time: our protocol is a one-shot process ͑i.e., the elementary entangled pairs are used only once͒ involving one-way classical communication. Furthermore, the overhead of local resources increases only logarithmically with the size of the network, making our proposal favorable to long-distance quantum communication.

Long-distance entanglement generation in two-dimensional networks

“…Previously, entangled states could only be generated over an arbitrarily long distance from rank two states, or less, in regular 2D networks [11,[19][20][21]. Here we have devised a global error correction scheme that enables a highly entangled state to be generated over an arbitrary distance.…”

“…Our previous protocol [19], as well as the scheme described in Ref. [21], requires states of rank two, or less, for long distance entanglement generation using constant resources. So far no protocol has been able to transform a 2D network of full rank states into a highly entangled two qubit state with no dependence on the qubit separation, although this is possible in infinite 3D networks [22].…”

“…All of the qubits are then replaced with encoded qubits and all operations are replaced with their encoded versions. This technique was looked at in [21] for a square network using a majority voting CSS code. In this case for bonds containing 2t + 1 edges the phase error probability on each encoded edge can be suppressed to ≈ 2t+1 t+1 p t+1 z .…”

“…Other schemes have also been shown to generate highly entangled states from a regular 2D square network made of 'binary states' [3,21]. Here, if the amount of entanglement in the binary states exceeds a threshold, the network is transformed into an entangled state that can stretch over an arbitrary distance, while maintaining a non-maximal but constant entanglement.…”

Area law for random graph states

“…This issue is relevant in studies on generating entanglement between given nodes of a graph [15], entanglement swapping and quantum repeater systems [1] and quantum communications in noisy networks [16].…”