Quantum Secret Sharing

Short answer: Quantum secret sharing splits a secret among several parties so that it can be reconstructed only when enough of them cooperate, using quantum states to protect the process against eavesdroppers. Experiments have used entangled photons, a five-qubit graph state, and continuous-variable light over optical fibre. These are laboratory demonstrations of protocols for multi-party quantum communication, and the papers describe them as components of future quantum networks.

The idea

A 2006 paper in Fortschritte der Physik describes secret sharing as the task in which a secret message is split among several parties so that its reconstruction requires their mutual collaboration. It explains that a protocol using ideas from quantum cryptography was proposed in which a shared GHZ state allows information splitting and eavesdropper protection at once. For a long time an experimental demonstration was missing for lack of efficient multi-photon sources, with only in-principle feasibility shown using pseudo-GHZ states and, very recently at the time, a three-party GHZ-protocol.

The paper presents two protocols and their experimental realization. The first uses a multiqubit entangled state as the resource and needs no interferometric setup, unlike earlier GHZ-based schemes, so the authors say the implementation is simpler and more stable. The second uses only sequential transformations on a single qubit. The authors say this simplifies the method further, makes it scalable with the number of participants and makes it technologically comparable to quantum key distribution.

Graph states

A paper in Nature Communications reports an experimental demonstration of graph state-based quantum secret sharing, which it calls an important primitive for a quantum network. Graph states are a class of entangled states described as versatile quantum resources for networking tasks. The authors use an all-optical setup encoding quantum information into photons that represent a five-qubit graph state. They show that the same state can share a classical secret among four players using quantum channels, secure against a distrusted channel between the dealer and the players, and that it can share a quantum secret with quantum channels. They find one can reliably encode, distribute and share quantum information among four parties with various access structures based on the graph's connectivity. They conclude graph states are a promising route to multi-layered communication protocols in quantum networks.

Continuous variables over fibre

A 2023 paper in npj Quantum Information proposes and demonstrates a (k, n) threshold continuous-variable secret sharing protocol which they describe as practical, scalable and verifiable, and secure against eavesdroppers and dishonest players. It does not require each player to prepare a laser source or phase lock independent lasers, and multiple sideband modulation lets a single heterodyne detector extract the information of several players. The same system can support conference key agreement with only changes to classical post-processing. With five parties over 25 km of single-mode fibre the authors observe a key rate of 0.0061 bits per pulse, and over 55 km a rate of 7.14 times 10 to the minus 4 bits per pulse. They say the results reduce system complexity and pave the way for practical applications. The paper notes two broad routes for such protocols: multipartite entangled states, and bipartite QKD-based schemes that can use mature QKD security proofs.

What this does not tell you

These are demonstrations in the laboratory with a few parties. They do not show a deployed secret sharing service, and the key rates apply to the authors' setup and distances.

FAQ

What is quantum secret sharing?

Splitting a secret among parties so it can be rebuilt only when enough of them cooperate, with quantum states protecting the exchange.

What states have been used?

Multiqubit entangled photon states, a five-qubit graph state, and continuous-variable light.

How many parties have been shown?

Four in the graph-state experiment and five in the 2023 fibre experiment.

How far has it worked?

The 2023 paper reports operation over 25 km and 55 km of fibre.

Is it used in products?

The papers describe laboratory demonstrations, not products.