Entanglement is a fact of life.
You have milk, sugar and the juice of dried tea leaves entangles in your tea.
We are rarely interested in separating these entangled contents.
Indeed the process that would reverse the making of tea will not be that simple at all.
Clearly the same thing at quantum level will be even more tricky.
Advent of black holes, or rather their quantum mechanical studies, have brought the issue to the fore in a very dramatic and critical way.
People in condensed matter have been living with entanglement in the form of the density matrix for a long time.
Sometimes you do with less amount of information than can be gathered from the physical systems. That is density matrix for you. For many applications that is all that you need.
But then the question arises can we get more information? And how?
That is when we start worrying about quantum mechanics itself rather than its application in condensed matter physics.
Of course it is then natural to think that the more sophisticated form of quantum mechanics, the quantum field theory, will tell us more about these issues than the plain non-relativistic quantum mechanics.
Those who are in the game of quantum mechanics and quantum field theory also know that prodding quantum field theory for such matters will be different ball game altogether.
To compound the issue we need an approach to quantum field theory that is well known, or rather notorious, for its complexity - the axiomatic or constructive quantum field theory.
These are the issues that Edward Witten takes up in his latest posting on the arXiv on Pi day - March 14, 2018. It is called Notes on Some entanglement Properties of Quantum Field Theory. You need not rush to it immediately - it is 70 pages long.
It is preparatory and non-rigorous document for the upcoming summer programme at the Institute of Advanced Studies at Princeton called Prospects in Theoretical Physics to be held in July 2018.
The original ideas are from different people like Borchers (163 pages), Haag ( a book the Local Quantum Physics, 392 pages), paper by Hollands and Sanders, called Entanglement Measures and Their Properties in Quantum Field Theory and finally another 161 pages long document by V.F.R. Jones called the van Neumann Algebras.
Witten's document has seven Sections and an Appendix. After the Introduction the next Section is on the Reech-Schlieder Theorem. Witten is an excellent communicator, when he has the time to indulge in pedagogy, so even in case of daunting topics one can relax.
Section 3 is about Modular Operator and the Relative Entropy in Quantum field Theory. Section 4 is about Finite Dimensional Systems and Some Lessons.
Section 5 discusses a Fundamental Example while Section 6 is about Algebras with a Universal Divergence in the Entanglement Entropy.
The last section is about Factorized States and the Appendix about More Holomorphy.
You have milk, sugar and the juice of dried tea leaves entangles in your tea.
We are rarely interested in separating these entangled contents.
Indeed the process that would reverse the making of tea will not be that simple at all.
Clearly the same thing at quantum level will be even more tricky.
Advent of black holes, or rather their quantum mechanical studies, have brought the issue to the fore in a very dramatic and critical way.
People in condensed matter have been living with entanglement in the form of the density matrix for a long time.
Sometimes you do with less amount of information than can be gathered from the physical systems. That is density matrix for you. For many applications that is all that you need.
But then the question arises can we get more information? And how?
That is when we start worrying about quantum mechanics itself rather than its application in condensed matter physics.
Of course it is then natural to think that the more sophisticated form of quantum mechanics, the quantum field theory, will tell us more about these issues than the plain non-relativistic quantum mechanics.
Those who are in the game of quantum mechanics and quantum field theory also know that prodding quantum field theory for such matters will be different ball game altogether.
To compound the issue we need an approach to quantum field theory that is well known, or rather notorious, for its complexity - the axiomatic or constructive quantum field theory.
These are the issues that Edward Witten takes up in his latest posting on the arXiv on Pi day - March 14, 2018. It is called Notes on Some entanglement Properties of Quantum Field Theory. You need not rush to it immediately - it is 70 pages long.
It is preparatory and non-rigorous document for the upcoming summer programme at the Institute of Advanced Studies at Princeton called Prospects in Theoretical Physics to be held in July 2018.
The original ideas are from different people like Borchers (163 pages), Haag ( a book the Local Quantum Physics, 392 pages), paper by Hollands and Sanders, called Entanglement Measures and Their Properties in Quantum Field Theory and finally another 161 pages long document by V.F.R. Jones called the van Neumann Algebras.
Witten's document has seven Sections and an Appendix. After the Introduction the next Section is on the Reech-Schlieder Theorem. Witten is an excellent communicator, when he has the time to indulge in pedagogy, so even in case of daunting topics one can relax.
Section 3 is about Modular Operator and the Relative Entropy in Quantum field Theory. Section 4 is about Finite Dimensional Systems and Some Lessons.
Section 5 discusses a Fundamental Example while Section 6 is about Algebras with a Universal Divergence in the Entanglement Entropy.
The last section is about Factorized States and the Appendix about More Holomorphy.