The Quantum Entanglement of Binary and Bipolar Sequences [chapter]

Matthew G. Parker, V. Rijmen
2002 Sequences and their Applications  
Classification of different forms of quantum entanglement is an active area of research, central to development of effective quantum computers, and similar to classification of error-correction codes, where code duality is broadened to equivalence under all 'local' unitary transforms. We explore links between entanglement, coding theory, and sequence design, by examining multi-spectra of quantum states under local unitary action, and show that optimal error-correcting codes and sequences
more » ... nt states with high multiparticle entanglement. Entanglement and Measurement Definitions and Partial Quantification A qubit is a two-state particle, (s 0 , s 1 ), meaning it is in state 0 with complex probability s 0 , and state 1 with complex probability s 1 , such that |s 0 | 2 + |s 1 | 2 = 1. Definition 1 Let l n be the infinite set of normalised linear vectors which can be written in the form (a 0 , b 0 ) ⊗ (a 1 , b 1 ) ⊗ . . . ⊗ (a n−1 , b n−1 ) Entanglement exists between two or more particles if their joint probability state cannot be factorised using the tensor product. More formally, Definition 2 Let s be an n-qubit state. s is a pure entangled state if s ∈ l n . s is not entangled if s ∈ l n .
doi:10.1007/978-1-4471-0673-9_22 dblp:conf/seta/ParkerR01 fatcat:dqznbprnifedbgs7o7xyraqiwi