PPubMed24 Apr 2023

Entanglement Purification for Logic-Qubit of Photon System Based on Parity Check Measurement Gate

Chunyan Li, Rong Kong, Baocang Ren, Meiqiu Deng, Fuguo Deng, Osamu Hirota

Abstract

'Osamu Hirota'] It has been found that logic-qubit entanglement has great potential for applications in quantum communication and quantum networks in recent years. However, along with the effects of noise and decoherence, the fidelity of the communication transmission can be greatly reduced. In this paper, we investigate the entanglement purification of logic bit-flip error and phase-flip error in polarization logic-qubit entanglement based on the parity-check measurement (PCM) gate, which is constructed by the cross-Kerr nonlinearity and used to distinguish the parity information of two-photon polarization states. The probability of entanglement purification is higher than the scheme using the linear optical method. Moreover, the quality of logic-qubit entangled states can be improved by a cyclic purification process. This entanglement purification protocol will be useful in the future when faced with long-distance communication with logic-qubit entanglement states.

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A parity‑check measurement gate using cross‑Kerr nonlinearity enables higher‑probability purification of logic‑qubit photon entanglement, achieving near‑unit fidelity after iterative cycles.

What’s new

i.Proposed entanglement purification protocols for logic‑qubit photon states using a parity‑check measurement (PCM) gate built from cross‑Kerr nonlinearity.
ii.Showed that the PCM‑based scheme has a higher purification probability than linear‑optical methods.
iii.Introduced a cyclic (iterative) purification process that can raise the fidelity of the entangled state toward unity.
iv.Addressed both logic bit‑flip and phase‑flip errors in concatenated GHZ (C‑GHZ) states.
v.Demonstrated the protocol’s suitability for long‑distance quantum communication and networks.

How they did it

The authors construct a PCM gate with weak cross‑Kerr nonlinearity to measure the parity of two‑photon polarization states. Half‑wave plates, PCM gates, and homodyne X‑quadrature measurements are applied to pairs of mixed C‑GHZ states to detect and discard error‑containing copies. The purification steps are iterated to progressively increase the fidelity of the remaining logic‑qubit entanglement.

What they found

Purification probability is higher than schemes using linear optical methods.
Fidelity after n purification cycles follows F(n)=F^{2n}/[F^{2n}+(1-F)^{2n}].
With an initial fidelity of 0.61, four purification cycles raise the fidelity to 0.999.
Error probability of distinguishing phase shifts is <10^{-5} when αθ^{2}>9.

Caveats

✕In practice only a finite number of purification iterations can be performed, limiting the achievable fidelity.
✕The scheme requires a cross‑Kerr nonlinearity strong enough that αθ^{2}>9 to keep the error probability below 10^{-5}.

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