Quantum Gates, MixedState Entanglement and Error  Codes.
Abstract
I give an overview of quantum information and existing results. I present a new view of of locality and argue that the criterion for nonlocality of a mixed state M is nonzero E(M), the entanglement required to prepare M by local actions. I compare E(M) with the amounts D_1(M) and D_2(M) that can be locally distilled from M by entanglement purification protocols (EPPs) using one and twoway classical communication respectively, and give an exact expression for E(M) when M is Belldiagonal. I show the relationship between EPPs and quantum errorcorrecting codes (QECCs). In an EPP perfectly entangled pure states are extracted with yield D from bipartite mixed states M; in a QECC arbitrary quantum states are reliably transmitted at rate Q through a noisy channel chi. I prove an EPP involving oneway classical communication and acting on mixed state M(chi) (obtained by sharing EPR pairs through chi) yields a QECC on chi with rate Q = D, and vice versa. While EPPs require classical communication, QECCs do not; I prove Q is not increased by adding oneway classical communication. However, both D and Q can be increased by adding twoway communication. I show that certain noisy channels can be used for reliable quantum transmission iff twoway communication is available. I exhibit a family of codes based on universal hashing able to achieve an asymptotic Q (or D) of 1S for independent noise models, where S is the error entropy. I obtain a 5bit singleerrorcorrecting quantum block code. I prove that iff a QECC results in high fidelity for the case of no error the QECC can be recast with the encoder as the matrix inverse of the decoder. I discuss quantum gate arrays for quantum computation and present numerical results indicating that six twobit quantum gates are enough to implement any threebit quantum gate, and results for implementing specific gates. An analytic argument and numerical results are given for why a twobit gate adds nine, twelve, fifteen, or zero parameters to the space accessible by a gate array, depending on the topology.
 Publication:

Ph.D. Thesis
 Pub Date:
 1996
 Bibcode:
 1996PhDT........77S
 Keywords:

 Physics: General; Engineering: Electronics and Electrical