Even though the theories of quantum information and operator algebras can both be traced back to the pioneering work of von Neumann in the 1930’s, which motivates our selection for the cover art, the usual finite dimensional approach to quantum information problems has somehow diluted such a common origin. The theories of operator spaces and operator systems provided the natural bridge reconnecting both worlds; and since they started to be used in quantum information theory around ten years ago, it became clear that the fields of operator algebras and quantum information can benefit each other in multiple ways.

This idea was fostered by a series of workshops and scientific programs bringing together open minded researchers from both areas; particularly those in Banff (2007, 2010, 2012) and Fields Institute (2009), as well as the program Quantum Information Theory at the Mittag Leffler Institute in Fall 2010.

In order to increase the visibility of how fruitful, broad, and rich this interconnection has been so far, we thought of the possibility of devoting a focus issue in a good journal to the topic and collecting a good number of excellent papers that cover most areas and problems in quantum information where operator algebra techniques (including operator spaces, operator systems, or free probability) are of crucial use. The Journal of Mathematical Physics (JMP) was for us the best candidate and Bruno Nachtergaele and all the team of JMP supported us from the very beginning with great enthusiasm.

This special issue consists of 20 papers. Most of them connect quantum information with operator algebras in a clear way. We decided to also include some papers belonging just to one of the two areas (quantum information or operator algebras) but in which the problems, ideas, or tools used could be of potential interest to the other community. Finally, there are three invited review papers that cover some of the areas in which the interconnection between operator algebras and quantum information has been especially fruitful.

We hope this special issue helps strengthen the bridge between operator algebras and quantum information. We also hope you enjoy it and find it helpful and inspiring.