Frequency subspace encoding for multiplexed quantum secret sharing

The gist The authors present a variant of Quantum Secret Sharing (QSS) that leverages frequency correlations in wavelength-multiplexed networks to connect multiple users with a single source, offering a resource-efficient path for multi-user secret sharing over such networks.

How it works

The protocol utilizes a broadband polarization-entangled photon pair source where the secret owner encodes classical information by applying frequency-dependent phase modulation to this pair, allowing each frequency channel to provide an independent QSS session among the secret owner and a pair of users The dealer encodes classical information in a two-photon entangled state For the information to remain secret, the encoding must utilize sets of states that are mutually unbiased, which is achieved by choosing phase sets such as ϕ±⟩ or φ±⟩ Each user needs to measure their photon either in the X or Y basis and then compare their measurement result with the other participants in the protocol The dealer shares the encoding basis C ∈ ϕ, whereas Alice and Bob communicate the measurement basis A, B ∈ X, Y

Frequency-Subspace Encoding

The approach addresses each wavelength channel pair or subspace independently This is achieved by manipulating the relative spectral phase θj between the two polarization components, and a pulse shaper The overall state is expressed as ψ(θj)⟩j = 1/√2 HH⟩ ⊗ j, j⟩ + e(iθj) VV⟩ ⊗ j, j> This can be accomplished with a balanced polarization-dependent Mach-Zehnder interferometer (MZI), and a pulse shaper The MZI is stabilized with the quantum bit error rate of a pair of correlated frequency channels

Experimental Setup and Results

The experiment uses a polarization-entangled photon source based on spontaneous parametric down-conversion (SPDC) integrated into an all-fiber Sagnac interferometer The source generates photon pairs centered at λ0 = 1548.1 nm, and extends over 70 nm of bandwidth The experimental fidelities for the ϕ±⟩ states are reported in Table I The correlation parameter is obtained as ⟨ϵ⟩ = 1/2 Vc=+−Vc=−, assuming that Charlie chooses his private bit with equal probability The experimental results show an average correlation parameter of ⟨ϵexp⟩ = 0.894 on average This translates to an average QBER of 5.3 % and a key fraction of 0.4 bits/photon

Performance and Optimization

The obtained correlation parameters are lower than the reported fidelities because ⟨ϵ⟩exp only depends on the visibilities in the X and Y bases, which are highly influenced by the noise of the MZI stabilization The asymptotic key fraction per coincidence detection can then be obtained with the standard Koashi-Preskill formula, r∞ = 1 − 2h(QBER) Simple improvements, such as an optimized active stabilization that achieves 98 % visibility would double the QSS key fraction at the same photon rate Reducing a loss reduction of 7 dB for each photon would increase ×5 the heralding efficiency and ×50 the total key rate

Conclusion

In conclusion, in this work we have demonstrated a proof-of-principle implementation of QSS in a wavelength-multiplexed quantum network The main idea relies on spectral phase modulation performed by the quantum server as supplier of entanglement It achieves independent state modulation for each pair of correlated frequency channels, while the entanglement in another DOF is used to perform and track the security of the protocol Our methods extend the capabilities of standard wavelength-multiplexed networks beyond QKD and could pave the way for further advances in quantum cryptography.

How it works

The paper demonstrates that a single source of bipartite entanglement can also be used to extend QSS to multi-user networks This scheme enables independent and parallel realization of polarization-encoded QSS between the dealer, the secret owner, and multiple pairs of users, while requiring a single source at the center of the network The source provides a bandwidth of 70 nm that is aligned to the ITU frequency grid This enables the discretization of its spectrum into multiple channels, according to the spectral filters of choice A number of NMUX(NMUX − 1)/2 channel pairs enables the full connectivity of NMUX users Active routers allow the reconfigurability of allocated spectral channels and their bandwidth While our source meets the QKD requirements in these networks, our proposed scheme further enhances the network services by also offering the possibility of QSS The dealer is positioned at the center of the network to implement QSS with multiple user pairs, and other users with access to spectral phase control may also actively participate in the protocol The experimental system uses only COTS components, including an all-fiber polarization-entangled photon source Our methods extend the capabilities of standard wavelength-multiplexed networks beyond QKD and could pave the way for further advances in quantum cryptography.

1. Bold header: Spectral Phase Modulation for Independent QSS Channels

The system can implement independent and parallel realization of polarization-encoded QSS between the dealer, the secret owner, and multiple pairs of users by applying a unique relative spectral phase modulation to each frequency channel using a pulse shaper.

2. Bold header: Wavelength-Multiplexed Scalability

The improved AI system can achieve wavelengthmultiplexed scalability by addressing each wavelength channel pair or subspace independently, supporting the realization of QSS over networks utilizing WDM schemes.

3. Bold header: Resource-Efficient Multi-User Secret Sharing

The system eliminates the need for multiple sources by leveraging frequency correlations to connect multiple users with a single source, providing a resource-efficient path toward multi-user secret sharing over wavelength-multiplexed networks, eliminating the need for multiple two-photon or multi-photon sources.

4. Bold header: Enhanced Security via Basis Tracking

The system can track security by allowing participants to monitor the quantum bit error rate (QBER), which enables them to test, in pairs, whether the other participant may be dishonest by analyzing correlations across different measurement bases.

Quantum secret sharing (QSS) is a multi-party quantum communication protocol that can be realized with bipartite entanglement and relative phase encoding. Previous implementations typically encoded the phase in the pump, applying it across the entire source bandwidth, thereby limiting scalability via wavelength multiplexing. In contrast, we present a variant of the standard QSS protocol that leverages frequency correlations to connect multiple users with a single source. The secret owner, who has access to the source, encodes classical information by applying frequency-dependent phase modulation to a broadband polarization-entangled photon pair. Each frequency channel therefore provides an independent QSS session among the secret owner and a pair of users. We demonstrate state fidelities of at least 90% for a channel pair of the 200 GHz ITU grid, which could be extended to more than 40 frequency bins with adequate dense-wavelength division multiplexed filters. Our results provide a resource-efficient path toward multi-user secret sharing over wavelength-multiplexed networks, eliminating the need for multiple two-photon or multi-photon sources.