دانلود کتاب Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning

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Introduction
The penguins and the polar bear
So what\'s new?
A new attitude to quantum theory: `features\'
A new form of mathematics: `diagrams\'
A new foundation for physics: `process theories\'
A new paradigm: `quantum picturalism\'
Historical notes and references
Processes as diagrams
From processes to diagrams
Processes as boxes and systems as wires
Process theories
Diagrams are mathematics
Process equations
Diagram substitution
Circuit diagrams
Parallel composition
Sequential composition
Two equivalent definitions of circuits
Diagrams beat algebra
Functions and relations as processes
Sets
Functions
Relations
Functions vs. relations
Special processes
States, effects, and numbers
Saying the impossible: zero diagrams
Processes that are equal `up to a number\'
Dirac notation
Summary: what to remember
Advanced material*
Abstract tensor systems*
Symmetric monoidal categories*
General diagrams vs. circuits*
Historical notes and references
String diagrams
Cups, caps and string diagrams
Separability
Process-state duality
The yanking equations
String diagrams
Transposition and trace
The transpose
Transposition of composite systems
The trace and partial trace
Reflecting diagrams
Adjoints
Conjugates
The inner product
Unitarity
Positivity
-positivity
Projectors
Quantum features from string diagrams
A no-go theorem for universal separability
Two no-go theorems for cloning
...as if time flows backwards
Teleportation
Summary: what to remember
Advanced material*
String diagrams in abstract tensor systems*
Dual types and self-duality*
Dagger compact closed categories*
Historical notes and references
Hilbert space from diagrams
Bases and matrices
Basis for a type
Matrix of a process
Sums of processes
Processes from matrices
Matrices of isometries and unitaries
Matrices of self-adjoint and positive processes
Traces of matrices
Matrix calculus
Sequential composition of matrices
Parallel composition of matrices
Matrix form of cups and caps
String diagrams of matrices
Matrices as process theories
Hilbert spaces
Linear maps and Hilbert spaces from diagrams
Positivity from conjugation
Why mathematicians love complex numbers
The spectral theorem
The dimension theorem
Classical logic gates as linear maps
The X-basis and the Hadamard linear map
Bell basis and Bell maps
Hilbert spaces versus diagrams
String diagrams are complete for linear maps
The set-theoretic definition of Hilbert spaces
Summary: what to remember
Advanced material*
Beyond finite dimensions*
Categories with sums and bases*
Sums in knot theory*
Equivalence of symmetric monoidal categories*
Historical notes and references
Quantum processes
Pure quantum maps from doubling
Doubling generates probabilities
Doubling eliminates global phases
The process theory of pure quantum maps
Things preserved by doubling
Things not preserved by doubling
The doubled numbers are `probabilities\'
Sums in the doubled theory represent `mixing\'
Doubled ONB effects are `quantum measurements\'
Quantum maps from discarding
Discarding
Discarding is not a pure quantum map
There is only one linear map fit for purpose
Discarding does not preserve pure quantum states
Impurity
Weight and causality for quantum states
The process theory of quantum maps
Causality for quantum maps
Isometry and unitarity from causality
Kraus decomposition and mixing
The no-broadcasting theorem
Relativity in process theories
Causal structure
Causality implies non-signalling
Causality and covariance
Quantum processes
Non-deterministic quantum processes
Non-deterministic realisation of all quantum maps
Purification of quantum processes
Teleportation needs classical communication
Controlled processes
Quantum teleportation in detail
Summary: what to remember
Advanced material*
Doubling general process theories*
Axiomatizing doubling*
And now for something completely different*
Historical notes and references
Quantum measurement
ONB measurements
A dodo\'s intro to measurement devices
Demolition ONB measurements
Non-demolition ONB measurements
Superposition and interference
...the next-best-thing to observation
Measurement dynamics and quantum protocols
Measurement-induced dynamics I: backaction
Example: gate teleportation
Measurement-induced dynamics II: collapse
Example: entanglement swapping
More general species of measurement
von Neumann measurements
von Neumann\'s quantum formalism
POVM measurements
Naimark and Ozawa dilation
Tomography
State tomography
Informationally complete measurements
Local tomography = process tomography
Summary: what to remember
Advanced material*
Do quantum measurements even exist?*
Projectors and quantum logic*
Failure of local tomography*
Historical notes and references
Picturing classical-quantum processes
Classical systems as wires
Double versus single wires
Example: dense coding
Measurement and encoding
Classical-quantum maps
Deleting and causality
Classical maps from spiders
Classical maps
Copying and deleting
Deleting
Copying
Copying and deleting
Matching
Spiders
If it behaves like a spider it is one
All linear maps as spiders + isometries
Spider diagrams and completeness
Quantum maps from spiders
Measuring and encoding as spiders
Decoherence
Classical, quantum, and bastard spiders
Mixing with spiders
Entanglement for impure states
Measurements and protocols with spiders
ONB measurements
Controlled unitaries
Teleportation
Dense coding
Entanglement swapping
von Neumann measurements
POVMs and Naimark dilation
Summary: what to remember
Advanced material*
Spiders are Frobenius algebras*
Non-commutative spiders*
Hairy spiders*
Spiders as words*
Historical notes and references
Picturing phases and complementarity
Decorated spiders
Unbiasedness and phase states
Phase spiders
Phase spider fusion
The phase group
Phase gates
Multicoloured spiders
Complementary spiders
Complementarity and unbiasedness
The CNOT-gate from complementarity
`Colours\' of classical data
Complementary measurements
Quantum key distribution
Teleportation with complementary measurements
Strong complementarity
The missing rules
Monogamy of strong complementarity
Faces of strong complementarity
The classical subgroup
Parity maps from spiders
Classifying strong complementarity
ZX-calculus
ZX-diagrams are universal
ZX-calculus for Clifford diagrams
ZX for dodos: just diagrams, nothing else
ZX for pros: build your own calculus
ZX for the god(esse)s: completeness
Where we stand with full ZX-calculus
Summary: what to remember
Advanced material*
Strongly complementary spiders are Hopf algebras*
Strong complementarity and normal forms*
Historical notes and references
Quantum theory: the full picture
The diagrams
Circuit diagrams
String diagrams
Doubled diagrams
Spider diagrams
ZX-diagrams
The processes
Causality
Process decomposition and no-broadcasting
Examples
Classical maps
Quantum maps
Classical-quantum interactions
The laws
Complementarity
Strong complementarity
ZX-calculus
Historical notes and references
Quantum foundations
Quantum non-locality
Refinements of quantum theory
GHZ-Mermin scenarios
Drawing a contradiction
Quantum-like process theories
Complementarity in relations
Spekkens\' toy quantum theory
Phases in spek
ZX-calculus for spek
Non-locality in spek?
Summary: what to remember
Historical notes and references
Quantum computation
The circuit model
Quantum computing as ZX-diagrams
Building quantum gates as ZX-diagrams
Circuit universality
Constructing Toffoli
Constructing controlled unitaries
Putting the pieces together...
Quantum Algorithms
A quantum oracle\'s (false?) magic
The Deutsch-Jozsa algorithm
Given.
Problem.
Quantum algorithm.
Quantum search
Given.
Problem.
Quantum algorithm.
The hidden subgroup problem
Given.
Problem.
Quantum algorithm.
Measurement-based quantum computation
Graph states and cluster states
Measuring graph states
Feed-forward
...with classical wires
Universality
Summary: what to remember
Historical notes and references
to 1.25Appendix ASome notations
References
Index