# Generalised Proof-Nets for Compact Categories with Biproducts

@article{Duncan2009GeneralisedPF, title={Generalised Proof-Nets for Compact Categories with Biproducts}, author={Ross Duncan}, journal={ArXiv}, year={2009}, volume={abs/0903.5154} }

Just as conventional functional programs may be understood as proofs in an intuitionistic logic, so quantum processes can also be viewed as proofs in a suitable logic. We describe such a logic, the logic of compact closed categories and biproducts, presented both as a sequent calculus and as a system of proof-nets. This logic captures much of the necessary structure needed to represent quantum processes under classical control, while remaining agnostic to the fine details. We demonstrate how to… CONTINUE READING

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#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 92 REFERENCES

De-linearizing Linearity: Projective Quantum Axiomatics From Strong Compact Closure

- Mathematics, Computer Science
- 2007

52

Models of Lambda Calculi and Linear Logic: Structural, Equational and Proof-Theoretic Characterisati

- Mathematics
- 1994

17

A topos foundation for theories of physics: I. Formal languages for physics

- Mathematics, Physics
- 2008

134