arXiv:quant-ph/0409014v1 2 Sep 2004 Kochen-Specker Qubits Mladen Paviˇ ci´ c†¶, Jean-Pierre Merlet‡♯, Brendan McKay§‖, and Norman D. Megill* + † University of Zagreb, Gradjevinski fakultet, POB 217, HR-10001 Zagreb, Croatia. ‡ INRIA, projet COPRIN: 06902 Sophia Antipolis Cedex, France § Department of Computer Science, Australian National University, Canberra, ACT, 0200, Australia * Boston Information Group, 30 Church St., Belmont MA 02478, U. S. A. Abstract. We give a constructive and exhaustive definition of Kochen-Specker (KS) qubits in the Hilbert space of any dimension as well as all the remaining vectors of the space. KS qubits are orthonormal states, i.e., vectors in n-dim Hilbert space, H n , n ≥ 3 to which it is impossible to assign 1s and 0s in such a way that no two of mutually orthogonal vectors are both assigned 1. Our constructive definition of such KS vectors is based on the algorithms that generate linear MMP diagrams corresponding to blocks of orthogonal vectors in R n , on algorithms that filter out diagrams on which algebraic 0-1 states cannot be defined, and on algorithms that solve nonlinear equations describing the orthogonalities of the vectors by means of polynomially complex interval analysis and self-teaching programs. To demonstrate the power of the algorithms, all 4-dim KS vector systems containing up to 24 vectors are generated and described, all 3-dim vector systems containing up to 30 vectors are scanned, and several general properties of KS vectors are found. PACS numbers: 03.65.Ta, 03.65.Ud Submitted to: J. Phys. A: Math. Gen. ¶ E-mail: pavicic@grad.hr ♯ E-mail: Jean-Pierre.Merlet@sophia.inria.fr ‖ E-mail: bdm@cs.anu.edu.au + E-mail: nm@alum.mit.edu