Graphic presentations of isotropic systems
Journal of Combinatorial Theory Series A
Quantum computation and quantum information
Quantum computation and quantum information
Aperiodic propagation criteria for Boolean functions
Information and Computation
On the classification of all self-dual additive codes over GF(4) of length up to 12
Journal of Combinatorial Theory Series A
Edge local complementation and equivalence of binary linear codes
Designs, Codes and Cryptography
Connections between relative entropy of entanglement and geometric measure of entanglement
Quantum Information & Computation
One and two-variable interlace polynomials: a spectral interpretation
WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
Univariate and multivariate merit factors
SETA'04 Proceedings of the Third international conference on Sequences and Their Applications
SETA'04 Proceedings of the Third international conference on Sequences and Their Applications
Quantum error correction via codes over GF(4)
IEEE Transactions on Information Theory
Generalized Bent Criteria for Boolean Functions (I)
IEEE Transactions on Information Theory
A complementary construction using mutually unbiased bases
Cryptography and Communications
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The name `graph state' is used to describe a certain class of pure quantum state which models a physical structure on which one can perform measurement-based quantum computing, and which has a natural graphical description. We present the two-graph state, this being a generalisation of the graph state and a two-graph representation of a stabilizer state. Mathematically, the two-graph state can be viewed as a simultaneous generalisation of a binary linear code and quadratic Boolean function. It describes precisely the coefficients of the pure quantum state vector resulting from the action of a member of the local Clifford group on a graph state, and comprises a graph which encodes the magnitude properties of the state, and a graph encoding its phase properties. This description facilitates a computationally efficient spectral analysis of the graph state with respect to operations from the local Clifford group on the state, as all operations can be realised graphically. By focusing on the so-called local transform group, which is a size 3 cyclic subgroup of the local Clifford group over one qubit, and over n qubits is of size 3 n , we can efficiently compute spectral properties of the graph state.