Diagram graph

Extract diagram as a Graph:

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Special processes

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Dual types

Dual types (SuperStar) go in reverse direction (top→bottom):

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Transposition

Transposition rotates diagram 180°:

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Adjoint

Adjoint (SuperDagger) flips digram vertically:

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Conjugate

Conjugate (OverBar) flips diagram horizontally:

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Trace

Trace creates a loop using cup and cap processes:

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Specify indices to be traced:

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Smart composition

Permutation and identity processes are added automatically to complete composition:

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Simplify diagram

Simplification drops all topological processes from a diagram:

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Summation

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Doubling

Doubling process parallel composes it with its dual conjugate currying inputs and outputs, then wrapping it in a special bold border process:

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Execution

Sequential and parallel process execution:

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Tensor notation

Overscript \[Breve] and \[DownBreve] indicate input and output respectively:

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Matrix and tensor interpretation

Perform tensor products and contractions of a tensor process:

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Circuits

There is a way to build circuit like diagrams using empty types and some hackery (parallel composition: NW→SE, composition: SW→NW):

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Outline

Some special processes render differently than generic ones, "OutlineProcess" draws an additional dashed outline around all processes:

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AddTerminals

Terminal processes are added by default on top and bottom of a diagram's summary box to make ingoing and outgoing wires visible, specify "AddTerminals" → False to turn it off:

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ShowProcessLabels

Show or hide process labels:

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ShowWireLabels

Summary box doesn't include wire labels by default, "ShowWireLabels"→True to show them:

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ShowArrowLabels

Show or hide composition arrow labels:

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Size

Size of a digram can be controlled:

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ComposeDistance

Specify vertical distance between processes:

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ParallelComposeDistance

Specify horizontal distance between processes:

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ArrowPosition

Specify relative position of wire arrows:

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ThickDoubleWire

Thicken double wires:

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ShowComposites

Reveal composit processes:

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ShowProcessArrows

There is no arrows draws inside topological processes by default:

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Show them:

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Quantum Teleportation

A diagram of quantum teleportation protocol teleporting state ρ with simplest quantum isometry map U that realizes it and classical channel between them, with its matrix interpretation:

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Which is equivalent to:

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Dense coding

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Entanglement swapping

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Quantum teleportation spider circuit

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