This work is concerned with multi-party stabilizer states in the sense of quantum information theory. We investigate the homological invariants for states of which each party holds a large equal number N of quantum bits. We show that in many cases there is a generic expected value of the invariants : for large N it is approximated with arbitrarily high probability if a stabilizer state is chose...

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We consider the transformation of Hamilton operators under various sets of quantum operations acting simultaneously on all adjacent pairs of particles. We find mappings between Hamilton operators analogous to duality transformations as well as exact characterizations of ground states employing non-Hermitean eigenvalue equations and use this to motivate a generalization of the stabilizer formali...

We suggest concrete models for self-correcting quantum memory by reporting examples of local stabilizer codes in 3D that have no string logical operators. Previously known local stabilizer codes in 3D all have stringlike logical operators, which make the codes non-self-correcting. We introduce a notion of “logical string segments” to avoid difficulties in defining one-dimensional objects in dis...

In order to use quantum error-correcting codes to improve the performance of a quantum computer, it is necessary to be able to perform operations fault-tolerantly on encoded states. I present a theory of fault-tolerant operations on stabilizer codes based on symmetries of the code stabilizer. This allows a straightforward determination of which operations can be performed fault-tolerantly on a ...

The stabilizer code is the most general algebraic construction of quantum error-correcting codes proposed so far. A stabilizer code can be constructed from a self-orthogonal subspace of a symplectic space over a finite field. We propose a construction method of such a selforthogonal space using an algebraic curve. By using the proposed method we construct an asymptotically good sequence of bina...

We show the equivalence of two approaches to the design of entanglement distillation protocols. The first approach is based on local unitary operations that yield permutations of tensor products of Bell states. The second approach is based on stabilizer codes.

Group Operations Definition. Let G be a group and S a set. An operation of G on S is a rule for combining elements g ∈ G and s ∈ S so that gs ∈ S, such that 1s = s for all s, and (gg’)s = g(g’s) for all g, g’, and s. With this operation, S is called a G-set. Definition. Let s ∈ S, with S a G-set. The orbit of s is the set Os = {s’ ∈ S | s’ = gs for some g ∈ G}. Proposition. S is a union of disj...

We study the nucleation and propagation of the normal zone in large composite superconductors, considering the relatively long time of current redistribution in the stabilizer. We propose a model treating the composite as an effective electrical circuit, which yields two diffusion equations for the electric current and temperature distributions along the conductor. Numerical simulations are per...