Quantum Physics

Classical probability theory makes the (mostly, tacit) assumption that any two random experiments can be performed jointly.  This assumption seems to fail in quantum theory.  A rapidly growing literature seeks to understand QM by placing it in a much broader mathematical landscape of ``generalized probabilistic theories", or GPTs,  in which incompatible experiments are permitted.   Among other things, this effort has led to  (i) a better appreciation that many "characteristically quantum" phenomena (e.g., entanglement)  are in fact generic to non-classical probabilistic theories, (ii) a suite of reconstructions of (mostly, finite-dimensional) QM from small packages of assumptions of a probabilistic or operational nature, and (iii) a clearer view of the options available for generalizing QM.  This course will offer a survey of this literature,  starting from scratch and concluding with a discussion of recent developments. 

Mathematical prerequisites: finite-dimensional linear algebra, ideally including tensor products and duality, plus some exposure to category theory (though I will briefly review this material as needed).  

Scheduling note: There will be 5 lectures from March 12-26, then a gap of two weeks before the final 2 lectures held April 16 & 18.

Format: In-person only; lectures will be recorded for PIRSA but not live on Zoom.

Quantum position verification (QPV) schemes use the properties of quantum information and the relativistic signalling bound to verify the location of an object (sometimes called a “tag”) to distant observers in an environment that may contain would-be spoofers. The guarantee is based on the assumptions of the underlying security model; various theoretically and practically interesting security models have been proposed. The area is attracting increasing interest, with new theoretical developments in security analyses, emerging experimental studies of QPV systems, and recently discovered surprising and intriguing connections to topics in quantum gravity. A workshop on QPV will be held at the Perimeter Institute for Theoretical Physics.

The workshop will cover topics related to all aspects of QPV, including, but not limited to:

• Theoretical developments related to the security of QPV schemes, including development or refinement of security models, proofs of security within given models, tradeoffs between security and efficiency, and Experimental studies of QPV and theoretical work aimed at developing practical QPV schemes.
• QPV’s relationship to other cryptographic tasks and primitives.
• QPV’s relationship to holography and quantum gravity.

 

Sponsored in part by:  

Territorial Land Acknowledgement

Perimeter Institute acknowledges that it is situated on the traditional territory of the Anishinaabe, Haudenosaunee, and Neutral peoples.

Perimeter Institute is located on the Haldimand Tract. After the American Revolution, the tract was granted by the British to the Six Nations of the Grand River and the Mississaugas of the Credit First Nation as compensation for their role in the war and for the loss of their traditional lands in upstate New York. Of the 950,000 acres granted to the Haudenosaunee, less than 5 percent remains Six Nations land. Only 6,100 acres remain Mississaugas of the Credit land. 

We thank the Anishinaabe, Haudenosaunee, and Neutral peoples for hosting us on their land.

Recently we have seen exciting results at the intersection of quantum foundations and the statistical analysis of causal hypotheses by virtue of the centrality of latent variable models to both fields.

In this workshop we will explore how academics from both sides can move the shared frontiers forward. Towards that end, we are including extensive breakout collaboration opportunities in addition to formal presentations. In order to make concrete progress on problems pertinent to both communities, we have selected the topic of causal models with restricted cardinality of the latent variables as a special focus for this workshop. 

Sponsorship for this workshop has been provided by:

https://pirsa.org/C23017

Territorial Land Acknowledgement

Perimeter Institute acknowledges that it is situated on the traditional territory of the Anishinaabe, Haudenosaunee, and Neutral peoples.

Perimeter Institute is located on the Haldimand Tract. After the American Revolution, the tract was granted by the British to the Six Nations of the Grand River and the Mississaugas of the Credit First Nation as compensation for their role in the war and for the loss of their traditional lands in upstate New York. Of the 950,000 acres granted to the Haudenosaunee, less than 5 percent remains Six Nations land. Only 6,100 acres remain Mississaugas of the Credit land. 

We thank the Anishinaabe, Haudenosaunee, and Neutral peoples for hosting us on their land.

This workshop will bring together a group of young trendsetters working at the frontier of machine learning and quantum information. The workshop will feature two days of talks, and ample time for participants to interact and form new collaborations in the inspiring environment of the Perimeter Institute. Topics will include machine learning, quantum field theory, quantum information, and unifying theoretical concepts.

https://pirsa.org/C22034

Territorial Land Acknowledgement

Perimeter Institute acknowledges that it is situated on the traditional territory of the Anishinaabe, Haudenosaunee, and Neutral peoples.

Perimeter Institute is located on the Haldimand Tract. After the American Revolution, the tract was granted by the British to the Six Nations of the Grand River and the Mississaugas of the Credit First Nation as compensation for their role in the war and for the loss of their traditional lands in upstate New York. Of the 950,000 acres granted to the Haudenosaunee, less than 5 percent remains Six Nations land. Only 6,100 acres remain Mississaugas of the Credit land. 

We thank the Anishinaabe, Haudenosaunee, and Neutral peoples for hosting us on their land.

In the first edition of the meeting, CATMIN (Cold ATom Molecule INteractions) was a new satellite meeting of ICPEAC devoted to the study of atomic and molecular systems, where long-range interactions and the extreme properties of highly excited electrons produce new physics and lead to new technologies. CATMIN's objective is to strengthen the links between cold atom physics, molecular physics, chemistry and condensed matter physics, so that new concepts and breakthroughs can emerge. Ions, atoms and molecules are naturally made quantum systems that can be controlled with light and low frequency electromagnetic fields, thus lending themselves to precision investigations and use in quantum technologies. The second CATMIN conference will be held a few days before the ICAP, which is a major conference in AMO physics, with the idea that scientists can attend both meetings. The CATMIN meeting will be a two-day conference held at the Perimeter Institute in Waterloo, ON, centered on Rydberg-atom physics, cold ion physics and the interplay between these experimental platforms. Rydberg atom physics is experiencing a renaissance due to the application of the exaggerated properties of highly excited atoms for quantum information and quantum simulation. Rydberg states can even be observed in solids which is a subject of increasing interest. Cold ions, similarly, are exciting for quantum simulation and computing, becoming one of the central platforms in the race to build a quantum computer. Many exciting developments are also in progress in the area of cold-molecules. Long-range interactions open up fields of research such as the photo-association of cold atoms to form ultra-cold molecules, and the excitation of Rydberg molecules demonstrating novel kinds of molecular bonding. Strong long-range interactions in all the systems permit the investigation of the few-body and many-body regimes, including the few- to many-body transition. The conference aims to share the latest developments and results in these exciting fields among the various ICAP communities as well as the broader physics and chemistry communities. Overall, the conference can forward quantum science and the application of quantum science, which furthers these fields of research by concentrating interest to attract people and resources to the field.

Sponsorship for this event has been provided by:

https://pirsa.org/C22028

Perimeter Institute will make every effort to host the conference as an in-person event.  However, we reserve the right to change to an online program to align with changes in regulations due to the COVID-19 pandemic.

 

Territorial Land Acknowledgement

Perimeter Institute acknowledges that it is situated on the traditional territory of the Anishinaabe, Haudenosaunee, and Neutral peoples.

Perimeter Institute is located on the Haldimand Tract. After the American Revolution, the tract was granted by the British to the Six Nations of the Grand River and the Mississaugas of the Credit First Nation as compensation for their role in the war and for the loss of their traditional lands in upstate New York. Of the 950,000 acres granted to the Haudenosaunee, less than 5 percent remains Six Nations land. Only 6,100 acres remain Mississaugas of the Credit land. 

We thank the Anishinaabe, Haudenosaunee, and Neutral peoples for hosting us on their land.

We will review the notion of entanglement in quantum mechanics form the point of view of information theory, and how to quantify it and distinguish it from classical correlations. We will derive Bell inequalities and discuss their importance, and how quantum information protocols can use entanglement as a resource. Then we will analyze measurement theory in quantum mechanics, the notion of generalized measurements and quantum channels and their importance in the processing and transmission of information. We will introduce the notions of quantum circuits and see some of the most famous algorithms in quantum information processing, as well as in quantum cryptography. We will also talk about the notion of distances and fidelity between states from the point of view of information theory and we will end with a little introduction to the notions of relativistic quantum information.