[pour la version française, cliquer ici]

I presented this work in three slightly different lectures : 

• first, at the "séminaire de logique catégorique" (Paris 7, June 18, 2014),

• second, at the Workshop on diffeology, etc. (Aix-en-Provence, June 25, 2014),

• third at the "séminaire d'été du laboratoire LISMMA-Quartz" (Supméca Paris, July 2, 2014).

The following videos were recorded after those lectures, but with approximately the same content.

S. Dugowson

Supméca

Warning

The videos and the pictures of this page are intended to give a brief introduction (in English) to the text (in French) entitled 

"Structures connectives de l'intrication quantique" (46 pages). 

Thank the user to excuse the imperfections of these videos, slightly wobbly and fuzzy, and to excuse my poor English too. In doubt, thank you to refer to the text.

The prezi document can be found there :

Connectivity Structure of Quantum Entanglement (July 19, 2014)

Table of content

• 1 Introduction

• 2 Connectivity Spaces

• 3 Two general quantum formalisms for entanglement

• 4 Connectivity Structures of Entangled Quantum States

• 5 Connectivity structures of multi-local devices

• 6 Connectivity Structures of Families of Random Variables

• 7 Recapitulative table

• 8 Conclusion

• 9 Reference

• 10 Detailed table of content

More detailed table of content

• 1 Introduction

  • 1.1 Plan of the lecture

• 2 Connectivity Spaces

  • 2.1 Definition

  • 2.2 Examples

  • 2.3 Brunn's theorem

  • 2.4 Generation

  • 2.5 Connectivity order

• 3 Two general quantum formalisms for entanglement

  • 3.1 Common aspects of the two formalisms

  • 3.2 State vector formalism

  • 3.3 Density operator formalism

• 4 Connectivity Structures of Entangled Quantum States

  • 4.1 Disentanglement connectivity structures

  • 4.2 Density connectivity structures

  • 4.3 Questions

• 5 Connectivity structures of multi-local devices

  • 5.1 Multi-local devices

  • 5.2 Tensorial structures

  • 5.3 Ludic structures

  • 5.4 Domanial structures

  • 5.5 Questions

• 6 Connectivity Structures of Families of Random Variables

• 7 Recapitulative table

• 8 Conclusion

• 9 Reference

  • 9.1 Text and "prezientation" associate with this lecture

  • 9.2 Other references

• 10 Detailed table of content

Introduction

Plan of the lecture

Connectivity Spaces

Definition

Examples

Brunn's theorem

Generation

Connectivity order

Two general quantum formalisms for entanglement

Common aspects of the two formalisms

Quantum systems

Measurement

Composite systems

State vector formalism

States

Projective measurement

Composite systems and entanglement

Density operator formalism

States

Projective measurement

Composite systems and entanglement

Connectivity Structures of Entangled Quantum States

Disentanglement connectivity structures

Aravind's idea

J-states and their partial separability

Entanglement types on J of a global state

Disentanglement connectivity structure on I

Example 1 : EPR

Example 2 : GHZ

Density connectivity structures

Correlation and entanglement of a density state on J

Correlation connectivity structure

Entanglement connectivity structure

Questions

Connectivity structures of multi-local devices

Multi-local devices

Definition

Sub-devices. Tensor product.

Quantum experiments as multilocal devices

Tensorial structures

Separability and locality

Definition of tensorial connectivity structures 

Examples

The non-partially separable (NPS) connectivity structure,

the non-quasi separable (NQS) connectivity structure 

and the non-separable (NS) connectivity structure of 

three multi-local devices : EPR1, EPR2, GHZ and K.

For of the EPR1 multi-local device, 

the non-partially separable (NPS) connectivity structure 

and the non-quasi separable (NQS) connectivity structure 

are discrete... This fact can be understood as the source of 

the Bertlmann's socks argument

Ludic structures

Domanial structures

Questions

Connectivity Structures of Families of Random Variables

Recapitulative table

Exercise : complete this table (click to enlarge)

Some connectivity structures of the GHZ state are the borromean one.

A state of connectivity order 2

Conclusion

Reference

Text and "prezientation" associate with this lecture

HAL : S. Dugowson, "Structures connectives de l'intrication quantique" (July 19, 2014) : pdf

Prezi : Connectivity Structure of Quantum Entanglement (July 19, 2014)

Other references

• Padmanabhan K. Aravind, "Borromean entanglement of the GHZ state" (1997)

http://users.wpi.edu/~paravind/Publications/borrom.pdf

• Ayumu Sugita, "Borromean Entanglement Revisited" (2007)

http://arxiv.org/abs/0704.1712

• Other references are given in S. Dugowson, "Structures connectives de l'intrication quantique" (July 19, 2014) : pdf

Detailed table of content

• 1 Introduction

  • 1.1 Plan of the lecture

• 2 Connectivity Spaces

  • 2.1 Definition

  • 2.2 Examples

  • 2.3 Brunn's theorem

  • 2.4 Generation

  • 2.5 Connectivity order

• 3 Two general quantum formalisms for entanglement

  • 3.1 Common aspects of the two formalisms

    • 3.1.1 Quantum systems

    • 3.1.2 Measurement

    • 3.1.3 Composite systems

  • 3.2 State vector formalism

    • 3.2.1 States

    • 3.2.2 Projective measurement

    • 3.2.3 Composite systems and entanglement

  • 3.3 Density operator formalism

    • 3.3.1 States

    • 3.3.2 Projective measurement

    • 3.3.3 Composite systems and entanglement

• 4 Connectivity Structures of Entangled Quantum States

  • 4.1 Disentanglement connectivity structures

    • 4.1.1 Aravind's idea

    • 4.1.2 J-states and their partial separability

    • 4.1.3 Entanglement types on J of a global state

    • 4.1.4 Disentanglement connectivity structure on I

    • 4.1.5 Example 1 : EPR

    • 4.1.6 Example 2 : GHZ

  • 4.2 Density connectivity structures

    • 4.2.1 Correlation and entanglement of a density state on J

    • 4.2.2 Correlation connectivity structure

    • 4.2.3 Entanglement connectivity structure

  • 4.3 Questions

• 5 Connectivity structures of multi-local devices

  • 5.1 Multi-local devices

    • 5.1.1 Definition

    • 5.1.2 Quantum experiments as multilocal devices

  • 5.2 Tensorial structures

    • 5.2.1 Separability and locality

    • 5.2.2 Definition of tensorial connectivity structures 

    • 5.2.3 Examples

  • 5.3 Ludic structures

  • 5.4 Domanial structures

  • 5.5 Questions

• 6 Connectivity Structures of Families of Random Variables

• 7 Recapitulative table

• 8 Conclusion

• 9 Reference

  • 9.1 Text and "prezientation" associate with this lecture

    • 9.1.1 HAL : S. Dugowson, "Structures connectives de l'intrication quantique" (July 19, 2014) : pdf

    • 9.1.2 Prezi : Connectivity Structure of Quantum Entanglement (July 19, 2014)

  • 9.2 Other references

    • 9.2.1 Padmanabhan K. Aravind, "Borromean entanglement of the GHZ state" (1997)

    • 9.2.2 Ayumu Sugita, "Borromean Entanglement Revisited" (2007)

    • 9.2.3 Other references are given in S. Dugowson, "Structures connectives de l'intrication quantique" (July 19, 2014) : pdf

• 10 Detailed table of content