# Institut Transdisciplinaire d'Information Quantique (INTRIQ)

### Meeting de l'INTRIQ (Juin 2010)

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**Meeting de l'INTRIQ (7 - 8 juin 2010)**

**Location**

**Program**

**Monday, June 7th**

9h00-10h00 Registration - Continental break

10h00-11h00 Alain Tapp:* A computer scientist's perspective on non locality*

11h00-12h00 Gilles Brassard: *Quantum Foundations in the Light of Quantum Information*

12h00-14h00 Lunch

14h00-15h00 Stefano Pironio: *Device independent information processing: **QKD and random number generation*

15h00-15h30 Stéphane Virally *Experiment in generation of entangled photons*

15h30-16h00 Coffee break

16h00-17h00 Serge Massar: *1)* *Device independent information processing: **coin tossing** and bit commitment 2) Frequency Bin Entanglement.*17h00-19h00 Free time

**Tuesday, 8th**

8h30-9h30 Business meeting, members only (breakfast served)

9h30-10h30 Anne Broadbent: *QMIP=MIP** 10h30-11h00 Gabrielle Denhez: *Error Correction With Superconducting Qubit*11h00-12h00 Marc Kaplan:

*Non-local box complexity and secure function evaluation*

*Protocols for Non-locality Distillation*

*Théorème adiabatique et optimisation*

*Trade-off Capacities for Quantum Channels I: Dephasing, Cloning, and Unruh Channels*

*Trade-off Capacities for Quantum Channels II: Completing the Analogy between*

*the Classical and Quantum Worlds*

*Speakers**Gilles Brassard*LITQ

Université de Montréal

**Quantum Foundations in the Light of Quantum Information**Consider the two great physical theories of the twentieth century: relativity and quantum mechanics. Einstein derived relativity from very simple principles such as: “The speed of light in empty space is independent of the speed of its source” and “Physics should appear the same in all inertial reference frames”. By contrast, the foundation of quantum mechanics is built on a set of rather strange, disjointed and ad hoc axioms. Why is that? Must quantum mechanics be inherently less elegant than relativity? Or is it rather that the current axioms of quantum mechanics reflect at best the history that led to its discovery by too many people (compared to one person for relativity), over too long a period of time? The purpose of this talk is to argue that a better foundation for quantum mechanics lies within the teachings of quantum information science. We postulate that the truly fundamental laws of Nature concern information, not waves or particles. For example, it has been proven, from the current axioms of quantum mechanics, that “Nature allows for the unconditionally secure transmission of confidential information”, but “Nature does not allow for unconditionally secure bit commitment” (these are standard classical cryptographic primitives). For another example, nature is nonlocal but not as nonlocal as is imposed by causality. We propose to turn the table round, start from these theorems and possibly others, upgrade them as axioms, and ask how much of quantum mechanics they can derive. This provocative talk is meant as an eye-opener: we shall ask far more questions than we shall resolve.

*Anne Broadbent*Institute for Quantum Computing &

Department of Combinatorics and Optimization

University of Waterloo

**QMIP=MIP***The way quantum information influences the power of multi-prover interactive proof systems is a long-standing open question. We make progress towards answering this question by showing that the entire power of quantum information in multi-prover interactive proof systems is captured by the shared entanglement and not by the quantum communication. More precisely, we show that that the class of languages recognized by quantum multi-prover interactive proof systems, QMIP, is equal to MIP*, the class of languages recognized by classical multi-prover interactive proof systems where the provers share entanglement. After the recent result by Jain, Ji, Upadhyay and Watrous showing that QIP=IP, our work completes the picture from the verifier's perspective by showing that also in the setting of multiple provers with shared entanglement, a quantum verifier is no more powerful than a classical one: QMIP=MIP*.

*Gabrielle Denhez*Université de Sherbrooke

**Error Correction With Superconducting Qubit**Most error correcting codes do not take into account the physical particularities of the system used as a qubit. I will discuss the possibility to adapt some error correcting codes to the physics of superconducting qubits. I will focus on the three qubit code using transmon, a particular kind of superconducting qubit. I will also talk about the four qubit code proposed in PhysRevA.56.2567 by Leug, Nielsen, Chuang and Yamamoto.

*Peter Høyer*Department of Computer Science

University of Calgary

**Protocols for Non-locality Distillation **Popescu and Rohrlich proposed in 1994 a hypothetical nonlocal box (NLB) that attains the maximum value for the CHSH inequality without allowing for communication between two spatially separated parties, Alice and Bob. Their seminal work has have long-lasting impact on how we study quantum correlations and significantly increased our understanding of why certain correlations are not allowed by quantum physics.

A hypothesized world in which nonlocal boxes are available have profound implications. Van Dam showed that perfect nonlocal boxes imply trivial communication complexity for boolean functions, i.e. any boolean function may be computed by a single bit of communication between Alice and Bob. This was extended by Brassard, Buhrman, Linden, Méthot, Tapp, and Unger to include nonlocal boxes that work correctly with probability greater than 0.908. Pawlowski, Paterek, Kaszlikowski, Scarani, Winter, and Zukowski showed that all strategies that violate Tsirelson’s bound also violate the principle of information causality which states that the transmission of

*n* classical bits can cause an information gain of at most *n*bits. It is unclear if such results hold for all non-quantum correlations. Is the nonlocal box introduced by Popescu and Rohrlich a representative for all non-quantum correlations, or are there foundational differences between non-quantum correlations? In this talk, I will address these questions through the study of distillation of nonlocal boxes. A distillation process for nonlocal boxes takes a non-perfect nonlocal box and makes it more perfect. I will formalize this notion, prove the optimality of a distillation process for oblivious distillation processes, introduce a new distillation process that distill a class of non-perfect nonlocal boxes better than any previously known protocol, and present results on the possible non-existence of a single optimal distillation process for all non-perfect boxes.

*Marc Kaplan*Laboratoire d'Informatique Théorique et Quantique

Université de Montréal

**Non-local box complexity and secure function evaluation **A non-local box is an abstract device into which Alice and Bob input bits x and y respectively and receive outputs a and b respectively, wherea, b are uniformly distributed and the parity of a+b equals the product of x and y. Such boxes have been central to the study of quantum and generalized non-locality, as well as the simulation of non-signaling distributions. In this talk, we are interested in the number of non-local boxes that Alice and Bob need in order to compute a Boolean function f. We will show tight upper and lower bounds in terms of the communication complexity of the function both in the deterministic and randomized case. We will then show the applications of non-local box complexity to classical cryptography, in particular to secure function evaluation. We study the question posed by Beimel and Malkin of how many Oblivious Transfer calls Alice and Bob need in order to securely compute a function f. We will show how this question is related to the non-local box complexity of the function and conclude by greatly improving their bounds. Finally, another consequence of our results is that traceless two-outcome measurements on maximally entangled states can be simulated with 3 non-local boxes, while no finite bound was previously known.

*Serger Massar*Laboratoire d'Informatique Quantique

Université libre de Bruxelles

**1) ****Device independent information processing: coin tossing and bit Commitment. **

**2)**

**Frequency Bin Entanglement.**

*Stefano Pironio*Laboratoire d'Informatique Quantique

Université Libre de Bruxelles

**Device independent information processing: QKD and random number generation**

*Louis Renaud-Desjardins*Université de Montréal

**Théorème adiabatique et optimisation**L’approximation adiabatique en mécanique quantique stipule que si on commence dans un état propre d’un système quantique déterminé par un Hamiltonien H(t) et que l’évolution est «assez» lente, alors on restera dans l’état propre instantané relié à H(t). Qu’est-ce qu’une évolution «assez» lente? Le critère de lenteur introduit par Born et Fock en 1928 a changé récemment parce que qu’il n’était pas valide pour toutes les situations, notamment un spin dans un champ magnétique constant tournant à vitesse constante. Le nouveau critère sera expliqué pendant la conférence.

Par après, une méthode pour maximiser le résultat de l’approximation adiabatique sera présentée. Avec un Hamiltonien initial connu, un Hamiltonien final connu et un temps d’expérience fixé, cette idée permet d’avoir un test pour déterminer quelle évolution de l’Hamiltonien sera optimale. On utilise un développement variationnel qui s’inspire du calcul variationnel en mécanique classique pour obtenir ce résultat.

*Al**ain Tapp*Laboratoire d'Informatique Théorique et Quantique

Université de Montréal

**A computer scientist's perspective on non locality **In this introduction talk I will present the most important aspects of non locality, pseudo- telepathy and quantum communication complexity. This will be done with a computer scientist’s perspective and I will not assume any knowledge of the field. I will also introduce the non local boxes.

*Dave Touchette*McGill University

**Trade-off Capacities for Quantum Channels I: Dephasing, Cloning, and Unruh Channels **An important goal in quantum information theory is to determine the maximum rates at which a sender can transmit information reliably over a noisy quantum channel. In this first talk, we begin by introducing the notion of classical capacity, quantum capacity, entanglement-assisted capacity, and trade-off capacity. The computation of information transmission rates requires an optimization over arbitrarily many parallel uses of a channel and is generally intractable. We show that the computation of a trade-off capacity is tractable for a certain class of channels known as the Hadamard channels. Three natural subclasses of these channels are generalized dephasing channels, cloning channels, and Unruh channels. We can parametrize the trade-off capacity region for these channels, and we find that a carefully chosen coding strategy beats the naive time-sharing strategy. We finally introduce a measure to quantify this improvement.

Joint Work with Kamil Bradler, Patrick Hayden and Mark M. Wilde

*Stéphane Virally*École Polytechnique de Montréal

**Experiment in generation of entangled photons**

*Mark M. Wilde*McGill University

**Trade-off Capacities for Quantum Channels II: Completing the Analogy between the Classical and Quantum Worlds **A quantum channel has many different capacities for communication, depending upon the type of information that a sender wishes to transmit to a receiver and whether the parties possess assisting resources. For example, a given information processing task could generate or consume the following noiseless resources in addition to many uses of the noisy channel: public classical communication, private classical communication, secret key, quantum communication, and entanglement. An interesting optimization question then arises for future "quantum telephone companies": How can we optimally trade these resources with each other for a given quantum channel? In this second talk, we do not answer the full question for all five resources, but instead discuss two different but related trade-off questions. We discuss trade-off formulas and capacity regions for classical communication, quantum communication, and entanglement, and then discuss different but related formulas and capacity regions for public classical communication, private classical communication, and secret key. The result is a step toward a unifying picture of dynamic quantum Shannon theory. Finally, it is not too often that we can obtain a calculable formula for even a single type of capacity, but here we can compute and plot the full capacity regions for the aforementioned class of Hadamard channels and also for the erasure channels.