Conversion of a General Quantum Stabilizer Code to an Entanglement Distillation Protocol

友彦 植松, Tomohiko Uyematsu

峻 渡辺, Shun N. Watanabe, 隆太郎 松本 +3 more

M. Yoshida, Manabu Hagiwara, Takayuki Miyadera +1 more

Ryutaroh Matsumoto

We show how to convert a quantum stabilizer code to a one- or two-way entanglement distillation protocol. The proposed conversion method is a generalization of those of Shor–Preskill and Nielsen–Chuang. The recurrence protocol and the quantum privacy amplification protocol are equivalent to the protocols converted from [[2, 1]] stabilizer codes. We also give an example of a two-way protocol converted from a stabilizer better than the recurrence protocol and the quantum privacy amplification protocol. The distillable entanglement by the class of one-way protocols converted from stabilizer codes for a certain class of states is equal to or greater than the achievable rate of stabilizer codes over the channel corresponding to the distilled state, and they can distill asymptotically more entanglement from a very noisy Werner state than the hashing protocol.

Theodore M. Mahaffey, Chaohan Cui, Saikat Guha +1 more

We introduce an entanglement distillation protocol that utilizes an arbitrary $[[n,k,d]]$ stabilizer code to convert $n$ raw copies of an $N$-qubit Greenberger-Horne-Zeilinger (GHZ) state into $k$ logical copies in the presence of Pauli noise. Our explicit formulation of the scheme on a star network topology is efficiently scalable to arbitrary $N$, requires only local operations, and minimizes the impact of errors on idle physical qubits, enabling the distribution of high-fidelity entangled logical states between any number of quantum processors. We report the results of numerical experiments using the 5-qubit code, toric code, and $[[144,12,12]]$ bivariate bicyle code to protect against independent single-qubit depolarizing noise on all qubits. Our encoding scheme improves the final GHZ state fidelity relative to a single bare GHZ state sent over the same noisy channel for depolarizing rates up to or above $6 \%$ for all codes tested. Additionally, we use the stabilizer formalism to prove that our protocol can be applied to any $N$-qubit Calderbank-Shor-Steane (CSS) stabilizer state, from which the GHZ state emerges as a special case. This result explicitly establishes the working principle of previous stabilizer-based Bell pair and GHZ state distillation schemes, and generalizes such protocols beyond the traditionally considered states. We also show that some stabilizer codes can distill any stabilizer state with our protocol.

Ryutaroh Matsumoto

We show how to convert a quantum stabilizer code to a one-way or two-way entanglement distillation protocol, and give an example of a converted two-way protocol better than the recurrence protocol and the quantum privacy amplification protocol.