Research Interaction Team on Quantum Information

Fall 2017 Spring 2018 Fall 2018 Fall 2020

 

(See also: The IQC-QuICS Math and Computer Science Seminar.)

Organizers

Email

Office

Office hours

Brad Lackey

bclackey@umd.edu

3100G Atlantic Building

Mon 3:00-4:00 pm

Carl Miller

camiller@umd.edu

3102 Atlantic Building

By appointment

Overview

This research-interaction seminar focuses on mathematical aspects of quantum information, with a view towards quantum foundations, quantum cryptography, quantum computing, and other topics in theoretical physics. The current semester will focus on nonlocal games and Bell inequalities as a central topic, but may include other topics suggested by participants. No previous experience in quantum theory is required, however linear algebra and (discrete) probability is a must.

(Research Interaction Team participation does not require enrollment in MATH489/689, however it is required to obtain credits.)

Next Meeting(s)

We had our final meeting of the fall semester on December 11th, and we will pick up again in the spring.

Reading Rack

Books and Lecture Notes

Scientific Articles

Past Meetings

Coordinates: Monday, 28 August 2017, 4:15pm, Atlantic Building 3100A.
Title: Organizational Meeting.
Speakers: Brad Lackey, Carl Miller.

Coordinates: Monday, 18 September 2017, 4:15pm, Atlantic Building 3100A.
Title: Foundations of Quantum Theory I.
Speakers: Brad Lackey.
Abstract: I will provide a rapid introduction to the foundations of quantum theory, with an emphasis on the differences between classical and quantum probability.

Coordinates: Monday, 25 September 2017, 4:15pm, Atlantic Building 3100A.
Title: Foundations of Quantum Theory II.
Speakers: Brad Lackey.
Abstract: I will continue with a rapid introduction to the foundations of quantum theory, focussing on bipartite systems and measurement.

Coordinates: Monday, 2 October 2017, 4:15pm, Atlantic Building 3100A.
Title: Picture-Languages for Quantum Information I.
Speakers: Carl Miller.
Abstract: The conventional way to express proofs in quantum information is via vector spaces and linear operators. I will discuss a newer, intuitive approach which is based on local manipulations of box-and-wire diagrams. The first talk will introduce picture elements for some basic concepts (registers, states, processes). The primary references for this material are arXiv:1510.05468, arXiv:1605.08617, and the book Picturing Quantum Processes (see Reading Rack).

Coordinates: Monday, 9 October 2017, 4:15pm, Atlantic Building 3100A.
Title: Picture-Languages for Quantum Information II.
Speaker: Carl Miller.
Abstract: I will continue with an introduction to proofs-by-picture in quantum information, and discuss some directions for further development.

Coordinates: Monday, 16 October 2017, 4:15pm, Atlantic Building 3100A.
Title: Quantum Strategy Formalism I.
Speaker: Yuan Su.
Abstract: This talk will focus on the quantum strategy formalism proposed by Gus Gutoski and John Watrous. In this new formalism, the strategy of each participant in any multi-party interaction is associated with a positive semidefinite operator, and the interaction output probability is given by the inner product of two such operators. The first part of the talk discusses basic notions of quantum strategy formalism, with occasional detour to quantum information preliminaries.
References: (see Reading Rack)
[1] J. Watrous, The Theory of Quantum Information.
[2] G. Gutoski and J. Watrous, Toward a general theory of quantum games.
[3] G. Chiribella, G. M. D'Ariano, and P. Perinotti, Theoretical framework for quantum networks.

Coordinates: Monday, 23 October 2017, 4:15pm, Atlantic Building 3100A.
Title: Quantum Strategy Formalism II.
Speaker: Yuan Su.
Abstract: We continue from October 16. The second part of the talk presents a characterization of strategies in terms of linear constraints on positive semidefinite operators, with occasional detour to quantum information preliminaries.

Coordinates: Monday, 30 October 2017, 4:15pm, Atlantic Building 3100A.
Title: A Quantum-Secure Non-Interactive Zero-Knowledge Proof System.
Speaker: Shaopeng Zhu.
Abstract: We introduce a method to convert sigma protocols, a 3-round proof system where the prover interacts with the verifier via three messages ("commitment", "challenge" and "response") and tries to convince the verifier of the validity of its proof, into non-interactive zero-knowledge proofs (NIZK), where the verifier can efficiently verify the proof without learning any additional "knowledge" or having extra interaction(s). According to Unruh's paper [1], this is the first known such conversion that is secure against quantum adversaries.
References:
[1]: Unruh, Dominique. "Non-Interactive Zero-Knowledge Proofs in the Quantum Random Oracle Model." EUROCRYPT (2). 2015.

Coordinates: Monday, 6 November 2017, 4:15pm, Atlantic Building 3100A.
Title: Parallel Repetition of Nonlocal Games.
Speaker: Carl Miller.
Abstract: Parallel repetition occurs when N copies of a nonlocal game are played simultaneously. In some cases, an optimal strategy for this setting is for the players to play each copy of the game independently. In other cases, they can actually win more often by coordinating their answers to different copies of the game. Determining when there is a benefit to this kind of coordination is a subtle problem that involves interesting mathematics. I will present an approach to the quantum parallel repetition problem that uses semidefinite programming duality.
Reference: R. Cleve, W. Slofstra, F. Unger, S. Upadhyay. Perfect Parallel Repetition Theorem for Quantum XOR Proof Systems. Computational Complexity 17, pp. 282-299 (2008).

Coordinates: Monday, 13 November 2017, 4:15pm, Atlantic Building 3100A.
Title: Characterization of Rigid Magic Binary Constraint Games on Graphs.
Speaker: Aaron Ostrander.
Abstract: Two player binary constraint games are games where Alice and Bob are asked to assign 0 and 1 to variables subject to some constraints. The magic pentagram game and magic square game are two such games with unique quantum strategies that win with probability 1 (while classical strategies succeed with probability less than 1). For a class of games that generalizes the magic square and pentagram, we show that any game with a unique strategy is basically equivalent to either the magic square or magic pentagram. We provide a graph theoretic characterization of these games.

Coordinates: Monday, 20 November 2017, 4:15pm, Atlantic Building 3100A.
Title: Syntax & Semantics in Quantum Information.
Speaker: Spencer Breiner.
Abstract: In this talk I will discuss some additional aspects of Coecke & Kissinger's diagrammatic language for quantum processes. I will begin with a brief review of string diagrams and quantum ("doubled") processes. I will introduce Frobenius algebras together with their diagrammatic analogues, called spiders. These can be used to encode orthonormal bases, providing a means for describing measurement and encoding. This allows us to incorporate both quantum and classical data, as well as their interaction, into the diagrammatic formalism.

Coordinates: Monday, 27 November 2017, 4:15pm, Atlantic Building 3100A.
Title: Nonlocal games with synchronous correlations.
Speaker: Brad Lackey.
Abstract: We examine analogues of Bell’s inequalities for synchronous correlations. Unlike general correlations and the CHSH inequality, there can be no quantum Bell violation among synchronous correlations with two measurement settings. However we exhibit explicit analogues of Bell’s inequalities for synchronous correlation with three measurement settings and two outputs and provide an analogue of Tsirl’son’s bound in this setting, and give explicit quantum correlations that saturate this bound.

Coordinates: Monday, 4 December 2017, 4:15pm, Atlantic Building 3100A.
Title:Nonlocal games with synchronous correlations (cont'd).
Speaker: Brad Lackey.
Abstract: We finish our discussion from last week of synchronous quantum correlations. We continue our example of three measurement settings and two outputs and provide an analogue of Tsirl’son’s bound in this setting, and give explicit quantum correlations that saturate this bound. If time allows, we will discuss categories whose morphisms are the classical, quantum, or nonsignaling nonlocal games with synchronous correlations, and characterize sections, retractions, monomorphisms, and epimorphisms in each of these categories.

Coordinates: Monday, 11 December 2017, 4:15pm, Atlantic Building 3100A.
Title:Unique Games are easy with Entangled Provers.
Speaker: Aarthi Sundaram.
Abstract: Unique games are non-local games where the constraints enforced by the verifier are ‘unique’ constraints (i.e., permutations). The Unique Games Conjecture (UGC) by Khot in 2002 states that approximating the value of these games using classical strategies is NP-hard. I will present an approach to approximate the value of a unique game when the provers share entanglement thereby falsifying a variant of the UGC for entangled provers. Essentially, the proof uses semi-definite programming (SDP) and a "quantum rounding technique" which takes a solution to an SDP and transforms it into a strategy for entangled provers. Additionally, by taking advantage of the structure of the SDP used, a parallel repetition thoerem for unique entangled games can also be shown.
Reference: Unique Games with Entangled Provers Are Easy. Julia Kempe, Oded Regev, and Ben Toner. SIAM Journal on Computing 2010 39:7, 3207-3229. arXiv:0710.0655