## Experimental circular quantum secret sharing over telecom fiber networkPublished in Optics Express, Vol. 21 Issue 14, pp.16663-16669 (2013) |

**Spotlight summary:**Imagine a padlock with two keyholes that can be opened only if the two correct keys are used. We can say that the two owners of the keys “share the secret” that the padlock is protecting. If we generalised this example to a padlock with n keyholes and that can be opened by k < n keys we would have an example of a "(k,n) – classical secret sharing scheme", i.e. a scheme where the secret is shared amongst n parties, and that any k of them can access.

In a world where, very likely, quantum technologies are going to become the backbone of communication, criptography and security, quantum secret sharing (QSS) will be used to distribute information between parties that do not completely trust each other.

Some QSS protocols involve multipartite entangled states, which are notoriously difficult to create and manipulate efficiently. However, it is possible to implement a simple (2,3) - QSS protocol (i.e. three parties sharing a secret that can be reconstructed by any two of them) using single photons and operations on their polarisation. There are advantages of working with unentangled photons and operating on polarisation: these photons can be produced at a high rate, the operations can be carried out very efficiently, and most importantly it is possible to transmit them in optical fibres over considerable distances.

In this work, Wei, Ma and Yang show the reliability of a protocol proposed a few years ago over 50 km of fibre, with a birefringence compensation mechanism that can maintain the polarisation basis fixed virtually perpetually. The idea behind this (2,3)-QSS scheme is simple: Alice sends a quantum coin to Bob, which can decide to flip it or not. After his operation he hands it over to Charlie, who can as well decide to flip it or not. When Charlie is done he hands it back to Alice, who can check if the coin is still facing the same way as it started. If it is, all Alice knows is that Bob and Charlie performed the same operation, but she cannot know which of the two possibilities (flip - flip or no flip - no flip). If she receives a flipped coin, all she knows is that the operations were different (flip-no flip or no flip – flip). Hence, the information that she has is only the parity of the joint operation. Similarly, neither Bob nor Charlie hold enough information to reconstruct the sequence of the two operations. However, if any party shared his information with any of the others, they could reconstruct the joint operation.

The security of this scheme is enforced by the quantum properties of the state that Alice sends out, which in the implementation by Wei, Ma and Yang is a photon in an eigenstate either of the horizontal/vertical basis or of the antidiagonal/diagonal basis. The flipping operation that Bob and Charlie implement (mathematically described by the Pauli x operator), works on the eigenstates of either, and this prevents them to measure with certainty the initial state of the photon. Also, an eventual eavesdropper faces the same problem, and Alice, Bob and Charlie can apply similar security checks of quantum key distribution protocols on random subsets of the stream of photons.

--Filippo Miatto

**Technical Division:**Light–Matter Interactions

**ToC Category:**Quantum Optics

OCIS Codes:
| (270.0270) Quantum optics : Quantum optics |

(270.5565) Quantum optics : Quantum communications | |

(270.5568) Quantum optics : Quantum cryptography |

Posted on August 06, 2013

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