Dual objects are abstract categorical structures that represent the quantum notion of entanglement. We prove a range of important results about dual objects and show how to use them to model quantum teleportation. Dual objects have an important topological representation, in terms of wires bending ‘backwards in time’, and we use this to characterize different sorts of duality structures, including pivotal, ribbon and compact structures. Dual objects interact well with any linear structure available, allowing us to capture linear-algebraic properties such as trace and dimension.
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