[PPT] - Picturing Quantum Processes Aleks Kissinger QTFT, V axj o 2015 PowerPoint Presentation

SLIDE 1

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Picturing Quantum Processes

Aleks Kissinger

QTFT, V¨ axj¨

2015

June 10, 2015

SLIDE 2

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Quantum Picturalism: what it is, what it isn’t

‘QPism’ ☺ is a methodology for expressing, teaching, and reasoning

about quantum processes

SLIDE 3

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Quantum Picturalism: what it is, what it isn’t

‘QPism’ ☺ is a methodology for expressing, teaching, and reasoning

about quantum processes

Diagrams live at the centre, thus composition and interaction

SLIDE 4

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Quantum Picturalism: what it is, what it isn’t

‘QPism’ ☺ is a methodology for expressing, teaching, and reasoning

about quantum processes

Diagrams live at the centre, thus composition and interaction
QP is not a reconstruction, but some ideas from operational reconstructions

play a major role, e.g.

ρ′ µ ρ ρ Φ ρ′

local/process tomography

Φ =

f

purification

SLIDE 5

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Quantum Picturalism: what it is, what it isn’t

‘QPism’ ☺ is a methodology for expressing, teaching, and reasoning

about quantum processes

Diagrams live at the centre, thus composition and interaction
QP is not a reconstruction, but some ideas from operational reconstructions

play a major role, e.g.

ρ′ µ ρ ρ Φ ρ′

local/process tomography

Φ =

f

purification

...and relationship between operational setups and theoretical models:
=

ρ

U
U

SLIDE 6

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Picturing Quantum Processes

A first course in quantum theory and diagrammatic reasoning Bob Coecke & Aleks Kissinger CUP 2015

SLIDE 7

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Outline

Picturing Quantum Processes chapters 4-9 (roughly)

SLIDE 8

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Outline

Picturing Quantum Processes chapters 4-9 (roughly)

1. Process theory of linear maps

SLIDE 9

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Outline

Picturing Quantum Processes chapters 4-9 (roughly)

1. Process theory of linear maps
2. quantum maps via ‘doubling’ construction

SLIDE 10

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Outline

Picturing Quantum Processes chapters 4-9 (roughly)

1. Process theory of linear maps
2. quantum maps via ‘doubling’ construction
3. Consequences: purification, causality, no-signalling, no-broadcasting

SLIDE 11

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Outline

Picturing Quantum Processes chapters 4-9 (roughly)

1. Process theory of linear maps
2. quantum maps via ‘doubling’ construction
3. Consequences: purification, causality, no-signalling, no-broadcasting
4. Classical/quantum interaction

SLIDE 12

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Outline

Picturing Quantum Processes chapters 4-9 (roughly)

1. Process theory of linear maps
2. quantum maps via ‘doubling’ construction
3. Consequences: purification, causality, no-signalling, no-broadcasting
4. Classical/quantum interaction
5. Complementarity

SLIDE 13

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Recap

Wires represent systems, boxes represent processes

quicksort

lists lists

cooking

bacon breakfast eggs food

baby

love poo noise

SLIDE 14

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Recap

Wires represent systems, boxes represent processes

quicksort

lists lists

cooking

bacon breakfast eggs food

baby

love poo noise

The world is organised into process theories, collections of processes that

make sense to combine into diagrams

g

A

ψ

h

B C A D A

processes systems

SLIDE 15

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Recap

Certain processes play a special role:

states: ψ effects: φ numbers:

λ

SLIDE 16

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Recap

Certain processes play a special role:

states: ψ effects: φ numbers:

λ

State + effect = number, interpreted as:

ψ φ test state probability

this is called the Born rule.

SLIDE 17

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

linear maps

In the process theory of linear maps:

SLIDE 18

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

linear maps

In the process theory of linear maps: (L1) Every type has a (finite) basis:    for all i : i f = i g     = ⇒ f = g

SLIDE 19

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

linear maps

In the process theory of linear maps: (L1) Every type has a (finite) basis:    for all i : i f = i g     = ⇒ f = g (L2) Processes can be summed:

i

fi where

i
f

hi g g =

i

            f g hi g            

SLIDE 20

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

linear maps

In the process theory of linear maps: (L1) Every type has a (finite) basis:    for all i : i f = i g     = ⇒ f = g (L2) Processes can be summed:

i

fi where

i
f

hi g g =

i

            f g hi g            

(L3) Numbers are the complex numbers:

λ

∈ C

SLIDE 21

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Bases ⇔ process tomography

Theorem

      for all i , j : i f j = i g j       = ⇒ f = g

SLIDE 22

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Bases ⇔ process tomography

Theorem

      for all i , j : i f j = i g j       = ⇒ f = g

Proof.

i f j = i g j

SLIDE 23

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Bases ⇔ process tomography

Theorem

      for all i , j : i f j = i g j       = ⇒ f = g

Proof.

f j = g j

SLIDE 24

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Bases ⇔ process tomography

Theorem

      for all i , j : i f j = i g j       = ⇒ f = g

Proof.

j f = j g

SLIDE 25

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Bases ⇔ process tomography

Theorem

      for all i , j : i f j = i g j       = ⇒ f = g

Proof.

f = g

SLIDE 26

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Bases ⇔ process tomography

Theorem

      for all i , j : i f j = i g j       = ⇒ f = g

Proof.

f = g

SLIDE 27

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Bases ⇔ process tomography

Theorem

      for all i , j : i f j = i g j       = ⇒ f = g

In other words, f is uniquely fixed by its matrix:

       f 1

1

f 1

2

· · · f 1

m

f 2

1

f 2

2

· · · f 2

m

. . . . . . ... . . . f n

1

f n

2

· · · f n

m

       where f j

i

:= i f j

SLIDE 28

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

What about the Born rule?

ψ φ test state probability

SLIDE 29

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

The Born rule for relations

ψ φ test state B := {0, 1}

SLIDE 30

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

The Born rule for relations

ψ φ test state B := {0, 1} possibility

SLIDE 31

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

The Born rule for linear maps

ψ φ test state C ???

SLIDE 32

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Fixing the problem

ψ φ test state R≥0 probability ψ φ

SLIDE 33

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Doubled states and effects

Letting: ψ ψ :=

ψ

and φ φ :=

φ

SLIDE 34

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Doubled states and effects

Letting: ψ ψ :=

ψ

and φ φ :=

φ

yields... test state probability ψ ψ φ φ := :=

ψ
φ

SLIDE 35

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

A new process theory from an old one...

The theory of pure quantum maps has types:

:=

A

SLIDE 36

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

A new process theory from an old one...

The theory of pure quantum maps has types:

:=

A
and processes:

=

f

f f for all processes f from linear maps.

SLIDE 37

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Embedding the old theory

linear maps embed in quantum maps, and this embedding preserves

diagrams: double         f g h         =

g
h
f

SLIDE 38

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Embedding the old theory

linear maps embed in quantum maps, and this embedding preserves

diagrams: double         f g h         =

g
h
f
But now we’re in a bigger space, so there is room for something new

SLIDE 39

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Embedding the old theory

linear maps embed in quantum maps, and this embedding preserves

diagrams: double         f g h         =

g
h
f
But now we’re in a bigger space, so there is room for something new,

discarding:

ψ

=

SLIDE 40

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

What is discarding?

ψ

= ψ ψ ???

SLIDE 41

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

What is discarding?

ψ

= ψ ψ

SLIDE 42

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

What is discarding?

ψ

= ψ ψ = ψ ψ =

SLIDE 43

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

What is discarding?

ψ

= ψ ψ = ψ ψ =

So discarding is defined as the effect:

:=

SLIDE 44

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

What is discarding?

ψ

= ψ ψ = ψ ψ =

So discarding is defined as the effect:

:=

In fact, this is the unique map with this property. Let {

ψi}i be a basis of pure states (e.g. z+, z−, x+, y+), then:

ψi

= d

ψi

=

SLIDE 45

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

What is discarding?

ψ

= ψ ψ = ψ ψ =

So discarding is defined as the effect:

:=

In fact, this is the unique map with this property. Let {

ψi}i be a basis of pure states (e.g. z+, z−, x+, y+), then:

ψi

= d

ψi

= = ⇒ = d

SLIDE 46

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

quantum maps

Definition

The process theory of quantum maps consists of all processes obtained from pure quantum maps and discarding:

f

. . .

. . .

SLIDE 47

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

quantum maps

Definition

The process theory of quantum maps consists of all processes obtained from pure quantum maps and discarding:

f

. . .

. . .
e.g.

ρ :=

ψ

and Φ :=

f
g
h

SLIDE 48

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Causality

This gives all quantum processes, including post-selected ones

SLIDE 49

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Causality

This gives all quantum processes, including post-selected ones
To get all of the deterministically realisable processes, we additionally

require causality: Φ =

SLIDE 50

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Causality

This gives all quantum processes, including post-selected ones
To get all of the deterministically realisable processes, we additionally

require causality: Φ =

Causality =

⇒ no-signalling: Ψ Φ ρ Alice Bob

SLIDE 51

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Causality

This gives all quantum processes, including post-selected ones
To get all of the deterministically realisable processes, we additionally

require causality: Φ =

Causality =

⇒ no-signalling: Ψ Φ ρ Alice Bob

SLIDE 52

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Causality

This gives all quantum processes, including post-selected ones
To get all of the deterministically realisable processes, we additionally

require causality: Φ =

Causality =

⇒ no-signalling: Ψ Φ ρ Alice Bob = Bob Ψ Alice ρ

SLIDE 53

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Causality

This gives all quantum processes, including post-selected ones
To get all of the deterministically realisable processes, we additionally

require causality: Φ =

Causality =

⇒ no-signalling: Ψ Φ ρ Alice Bob = Bob Ψ Alice ρ Alice = Ψ′ Bob

SLIDE 54

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Purification

Any quantum map extends to a pure quantum map on an extended system:

Φ =

f

SLIDE 55

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Purification

Any quantum map extends to a pure quantum map on an extended system:

Φ =

f
This is built-in to our definition of quantum maps:
f
g
h

→

g
f
h

SLIDE 56

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Purification

Any quantum map extends to a pure quantum map on an extended system:

Φ =

f
This is built-in to our definition of quantum maps:
f
g
h

→

g
f
h
If Ψ causal,

f must be isometry: Stinespring dilation.

SLIDE 57

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

No-broadcasting from pure extension

Theorem

A state is pure if and only if any extension separates:

ψ

= ρ = ⇒ ρ =

ψ

ρ′

SLIDE 58

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

No-broadcasting from pure extension

Theorem

A state is pure if and only if any extension separates:

ψ

= ρ = ⇒ ρ =

ψ

ρ′

Corollary

There exists no quantum map ∆ such that: ∆ = ∆ =

SLIDE 59

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

No-broadcasting from pure extension - proof

Broadcast to the left: = ∆

SLIDE 60

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

No-broadcasting from pure extension - proof

Broadcast to the left: = ∆ Bend the wire: ∆ =

SLIDE 61

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

No-broadcasting from pure extension - proof

Broadcast to the left: = ∆ Bend the wire: ∆ = = ⇒ ∆ = ρ

SLIDE 62

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

No-broadcasting from pure extension - proof

Broadcast to the left: = ∆ Bend the wire: ∆ = = ⇒ ∆ = ρ Unbend the wire and try to broadcast to the right: ∆ = ρ = ⇒ ∆ = ρ

SLIDE 63

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Classical systems

Protocols, experiments, etc. are always about the interaction of quantum

and classical systems

SLIDE 64

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Classical systems

Protocols, experiments, etc. are always about the interaction of quantum

and classical systems

We extend graphical language:

quantum systems → double wires classical systems → single wires

SLIDE 65

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Classical systems

Protocols, experiments, etc. are always about the interaction of quantum

and classical systems

We extend graphical language:

quantum systems → double wires classical systems → single wires

States are probability distributions:

p =

j

pj j ↔      p1 p2 . . . pn     

SLIDE 66

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Classical systems

Protocols, experiments, etc. are always about the interaction of quantum

and classical systems

We extend graphical language:

quantum systems → double wires classical systems → single wires

States are probability distributions:

p =

j

pj j ↔      p1 p2 . . . pn     

Processes are stochastic maps:

f ↔        p1

1

p1

2

· · · p1

m

p2

1

p2

2

· · · p2

m

. . . . . . ... . . . pn

1

pn

2

· · · pn

m

      

SLIDE 67

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Classical operations

Deleting is marginalisation:

:=

i

SLIDE 68

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Classical operations

Deleting is marginalisation:

:=

i

Classical causality just means stochastic:

f =

SLIDE 69

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Classical operations

Deleting is marginalisation:

:=

i

Classical causality just means stochastic:

f =

We can broadcast classically:

= = where :=

i

i i i

SLIDE 70

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Generalising to spiders

These generalise to a whole family of maps, called spiders:

· · · · · · · · i i i i i i :=

n m

i

· · · · · · · ·

n m

SLIDE 71

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Generalising to spiders

These generalise to a whole family of maps, called spiders:

· · · · · · · · i i i i i i :=

n m

i

· · · · · · · ·

n m

where the only rule to remember is:

... ...

...

= ... ... ... ...

SLIDE 72

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Quantum spiders

A quantum spider is a classical spider, doubled:

... ... := double

...

...

=

... ...

SLIDE 73

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Quantum spiders

A quantum spider is a classical spider, doubled:

... ... := double

...

...

=

... ...

An example is the GHZ state:

GHZ := = double

i

i i i

SLIDE 74

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Quantum spiders

A quantum spider is a classical spider, doubled:

... ... := double

...

...

=

... ...

An example is the GHZ state:

GHZ := = double

i

i i i

They also fuse:

... ... ... ...

...

= ... ...

SLIDE 75

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Bastard spiders

The third type of spider treats some legs as classical, and some pairs of legs

as quantum: ... ... ... ... ... ... ... ... :=

SLIDE 76

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Bastard spiders

The third type of spider treats some legs as classical, and some pairs of legs

as quantum: ... ... ... ... ... ... ... ... :=

We call these (seemingly) weird things bastard spiders

SLIDE 77

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Bastard spiders

The third type of spider treats some legs as classical, and some pairs of legs

as quantum: ... ... ... ... ... ... ... ... :=

We call these (seemingly) weird things bastard spiders
Again they fuse together:

... ...

...

= ... ... ... ...

SLIDE 78

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Measurement’s a bastard

The most important example is ONB-measurement:

:: ρ →      P(1|ρ) P(2|ρ) . . . P(n|ρ)     

SLIDE 79

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Measurement’s a bastard

The most important example is ONB-measurement:

:: ρ →      P(1|ρ) P(2|ρ) . . . P(n|ρ)     

whose adjoint is ONB-encoding:

:: i → i

SLIDE 80

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Measurement’s a bastard

The most important example is ONB-measurement:

:: ρ →      P(1|ρ) P(2|ρ) . . . P(n|ρ)     

whose adjoint is ONB-encoding:

:: i → i

Combining these yields more general stuff, e.g. non-demo measurements:

=

SLIDE 81

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Multi-coloured spiders

Different bases → different coloured spiders

m

...

...

n

:=

i m

i

· · · · · i i · · · i

n

m

· · ·

· · · · ·

n

:=

i m

i

· · · · · i i · · · i

n

SLIDE 82

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Multi-coloured spiders

Different bases → different coloured spiders

m

...

...

n

:=

i m

i

· · · · · i i · · · i

n

m

· · ·

· · · · ·

n

:=

i m

i

· · · · · i i · · · i

n
Two spiders

and are complementary if: = (encode in ) + (measure in ) = (no data transfer)

SLIDE 83

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Complementarity – Stern-Gerlach

For example, we can model Stern-Gerlach:

N S

S N

X

Z Z

SLIDE 84

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Complementarity – Stern-Gerlach

For example, we can model Stern-Gerlach:

N S

S N

X

Z Z

which simplifies as:

= =

no data transfer

SLIDE 85

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Applications

Picturing Quantum Processes the rest...

SLIDE 86

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Applications

Picturing Quantum Processes the rest...

1. Quantum info: Complementarity and cousin strong complementary give

graphical presentations for many protocols, e.g. QKD, QSS

SLIDE 87

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Applications

Picturing Quantum Processes the rest...

1. Quantum info: Complementarity and cousin strong complementary give

graphical presentations for many protocols, e.g. QKD, QSS

2. Quantum computing: Complementary spiders give a handy toolkit for

building quantum circuits and MBQC

SLIDE 88

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Applications

Picturing Quantum Processes the rest...

1. Quantum info: Complementarity and cousin strong complementary give

graphical presentations for many protocols, e.g. QKD, QSS

2. Quantum computing: Complementary spiders give a handy toolkit for

building quantum circuits and MBQC

3. Quantum resources: Framework for resource theories, e.g. entanglement,

purity

SLIDE 89

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity

Applications

Picturing Quantum Processes the rest...

1. Quantum info: Complementarity and cousin strong complementary give

graphical presentations for many protocols, e.g. QKD, QSS

2. Quantum computing: Complementary spiders give a handy toolkit for

building quantum circuits and MBQC

3. Quantum resources: Framework for resource theories, e.g. entanglement,

purity

4. Quantum foundations: (spoiler alert!) GHZ/Mermin argument in

diagrams

SLIDE 90

Introduction

1. Linear maps
2. Quantum maps
3. Consequences
4. Classical
5. Complementarity