### Abstract

In single-qubit quantum secret sharing, a secret is shared between *N* parties via manipulation and measurement of one qubit at a time. Each qubit is sent to all *N* parties in sequence; the secret is encoded in the first participant’s preparation of the qubit state and the subsequent participants’ choices of state rotation or measurement basis. We present a protocol for single-qubit quantum secret sharing using polarization entanglement of photon pairs produced in type-I spontaneous parametric downconversion. We investigate the protocol’s security against eavesdropping attack under common experimental conditions: a lossy channel for photon transmission, and imperfect preparation of the initial qubit state. A protocol which exploits *entanglement* between photons, rather than simply polarization *correlation*, is more robustly secure. We implement the entanglement-based secret-sharing protocol with 87% secret-sharing fidelity, limited by the purity of the entangled state produced by our present apparatus. We demonstrate a photon-number splitting eavesdropping attack, which achieves no success against the entanglement-based protocol while showing the predicted rate of success against a correlation-based protocol.

### Abstract

Measuring an entangled state of two particles is crucial to many quantum communication protocols. Yet Bell- state distinguishability using a finite apparatus obeying linear evolution and local measurement is theoretically limited. We extend known bounds for Bell-state distinguishability in one and two variables to the general case of entanglement in *n* two-state variables. We show that at most :mil:2^{n+1} - 1 classes out of :mil:4^{n} hyper-Bell states can be distinguished with one copy of the input state. With two copies, complete distinguishability is possible. We present optimal schemes in each case.

### Theresa W. Lynn

Student authorFaculty author

1. David A. Berryrieser, Peter J. Scherpelz, Rudolph W. Resch, and Theresa W. Lynn Entanglement-secured single-qubit quantum secret sharing Physical Review A 84 (2011) 032303. Neal C. Pisenti, Carl Philipp E. Gaebler, and Theresa W. Lynn Distinguishability of hyperentangled Bell states by linear evolution and local projective measurement Physical Review A 84 (2011) 022340. Theresa W. Lynn, E. Brobeck, B. E. Carlson, C. J. Jilings, M. B. Larson, R. D. McKeown, J. E. Hill, B. J. Falkowski, R. Seki, J. Sepikas, G. B. Yodh, D. Wells, and K. C. Chan Studies of air showers above 1018 eV with the CHICOS array Proceedings of the International Cosmic Ray Conference 29 (2005) NULL. Theresa W. Lynn, K. Birnbaum, and H. J. Kimble Strategies for real-time position control of a single atom in cavity QED Journal of Optics B - Quantum and Semiclassical Optics 7 (2005) S215-S225. R. D. McKeown, B. E. Carlson, E. Brobeck, Nathan Jones, M. B. Larson, Theresa W. Lynn, J. E. Hill, B. J. Falkowski, R. Seki, J. Sepikas, and G. B. Yodh Search for correlated high energy cosmic ray events with CHICOS (update) Proceedings of the International Cosmic Ray Conference 29 (2005) NULL. R. D. McKeown, B. E. Carlson, E. Brobeck, Nathan Jones, M. B. Larson, Theresa W. Lynn, J. E. Hill, B. J. Falkowski, R. Seki, J. Sepikas, and G. B. Yodh Search for correlated high energy cosmic ray events with CHICOS Proceedings of the International Cosmic Ray Conference 31 (2005) 409-416. J. Ye and Theresa W. Lynn Applications of optical cavities in modern atomic, molecular, and optical physics Advances in Atomic Molecular and Optical Physics 49 (2003) 1-83. H. J. Kimble and Theresa W. Lynn Cavity QED with strong coupling: toward the deterministic control of quantum dynamics Coherence and Quantum Optics 8 (2002) NULL.