A Novel Quantum Visual Secret Sharing Scheme

Inspired by Naor et al.'s visual secret sharing (VSS) scheme, a novel n out of n quantum visual secret sharing (QVSS) scheme is proposed, which consists of two phases: sharing process and recovering process. In the first process, the color information of each pixel from the original secret image is encoded into an n-qubit superposition state by using the strategy of quantum expansion instead of classical pixel expansion, and then these n qubits are distributed as shares to n participants, respectively. During the recovering process, all participants cooperate to collect these n shares of each pixel together, then perform the corresponding measurement on them, and execute the n-qubit XOR operation to recover each pixel of the secret image. The proposed scheme has the advantage of single-pixel parallel processing that is not available in the existing analogous quantum schemes and perfectly solves the problem that in the classic VSS schemes the recovered image has the loss in resolution. Moreover, its experiment implementation with the IBM Q is conducted to demonstrate the practical feasibility.Comment: 19 pages, 13 figure

Quantum Coding with Entanglement

Quantum error-correcting codes will be the ultimate enabler of a future quantum computing or quantum communication device. This theory forms the cornerstone of practical quantum information theory. We provide several contributions to the theory of quantum error correction--mainly to the theory of "entanglement-assisted" quantum error correction where the sender and receiver share entanglement in the form of entangled bits (ebits) before quantum communication begins. Our first contribution is an algorithm for encoding and decoding an entanglement-assisted quantum block code. We then give several formulas that determine the optimal number of ebits for an entanglement-assisted code. The major contribution of this thesis is the development of the theory of entanglement-assisted quantum convolutional coding. A convolutional code is one that has memory and acts on an incoming stream of qubits. We explicitly show how to encode and decode a stream of information qubits with the help of ancilla qubits and ebits. Our entanglement-assisted convolutional codes include those with a Calderbank-Shor-Steane structure and those with a more general structure. We then formulate convolutional protocols that correct errors in noisy entanglement. Our final contribution is a unification of the theory of quantum error correction--these unified convolutional codes exploit all of the known resources for quantum redundancy.Comment: Ph.D. Thesis, University of Southern California, 2008, 193 pages, 2 tables, 12 figures, 9 limericks; Available at http://digitallibrary.usc.edu/search/controller/view/usctheses-m1491.htm