The ZX-calculus is incomplete for quantum mechanics

Abstract

We prove that the ZX-calculus is incomplete for quantum mechanics. We suggest the addition of a new 'color-swap' rule, of which currently no analytical formulation is known and which we suspect may be necessary, but not sufficient to make the ZX-calculus complete.

In Proceedings QPL 2014, arXiv:1412.8102

References in corpus (2)

• Multi-party entanglement in graph states
• Superdense Coding with GHZ and Quantum Key Distribution with W in the ZX-calculus

Cited by in corpus (5)

• A universal completion of the ZX-calculus
• The ZX-calculus is complete for the single-qubit Clifford+T group
• The algebra of entanglement and the geometry of composition
• ZX-calculus for the working quantum computer scientist
• Kindergarden quantum mechanics graduates (...or how I learned to stop gluing LEGO together and love the ZX-calculus)