Beyondiid 2014 - Scientific Program

### Program

 18 May, Sun 19:30 Welcome Reception
 20 May, Tues Session Chairs: Stephanie Wehner (Morning), Valerio Scarani (Afternoon) 09:00 Andreas Winter (Universitat Autònoma de Barcelona) Strong converses for quantum channel capacities Abstract Channel capacities are the maximum rate of information (quantum, classical, private, ...) at which many independent uses of a channel can perform asymptotically reliably. By contrapositive, at larger rates, the error parameter cannot go to zero. But what is the real tradeoff between error and amount of information transmitted by $n \gg 1$ channel uses? For many situations in the classical information theory, it turns out that a "strong converse" holds, which means that for rates above the capacity, the error goes to its maximum (usually unity). This is a non-trivial statement, and not necessarily true, for instance in models with memory. Even without memory, it is not an easy result; in the talk i will discuss the challenges in establishing strong converses for quantum channel capacities, and the techniques that have been used to obtain them, or partial results. A strong converse can be viewed as a first step towards a more detailed finite blocklength understanding of the channel performance: Once we know it, we learn that for any error $0 < \epsilon < 1$, the amount of information that can be sent is $nC + f(\epsilon)o(n)$, with some function $f(\epsilon)$ and a sub-linear function $o(n)$ of the number $n$ of channel uses. This is the starting point of the so-called second-order analysis: i.e., the characterization of the functions $f(\epsilon)$ and $o(n)$. | PDF Presentation 10:00 Coffee/Tea Break 10:30 Ciara Morgan (Leibniz Universität Hanover) Efficient achievability for quantum protocols using decoupling theorems Abstract Proving achievability of protocols in quantum Shannon theory usually does not consider the efficiency at which the goal of the protocol can be achieved. Nevertheless it is known that protocols such as coherent state merging are efficiently achievable at optimal rate. We aim to investigate this fact further in a general one-shot setting, by considering certain classes of decoupling theorems and give exact rates for these classes. Moreover we compare results of general decoupling theorems using Haar distributed unitaries with those using smaller sets of operators, in particular $\epsilon$-approximate 2-designs. We also observe the behavior of our rates in special cases such as $\epsilon$ approaching zero and the asymptotic limit. This is joint work with Christoph Hirche. | PDF Presentation 11:10 Masahito Hayashi (Nagoya University/CQT NUS) Asymptotic conversion of probability distribution and entangled state Abstract The classical and quantum security can be treated as conversion of probability distribution with classical and quantum side information. Further, conversion of entangled state by LOCC is also reduced to conversion of probability distribution. Firstly, I present our results for generation of uniform distribution with classical and quantum side information the one-shot form. Then, I apply it to quantum independent and identical case and classical Markovian case with asymptotic analysis. Further, I extended this analysis to conversion between arbitrary independent and identical distributions without side information. I also consider the reversible conversion. This talk contains joint works with Marco Tomamichel, Shun Watanabe, Toyohiro Tsurumaru, Wataru Kumagai, and Kosuke Ito. | PDF Presentation 11:50 Shun Watanabe (University of Tokushima) A Converse Bound on Secret Key Agreement and Its Applications Abstract We consider secret key agreement by multiple parties observing correlated data and communication interactively over an insecure communication channel. By relating secret key agreement and binary hypothesis testing, we derive a single-shot converse bound on the length of secret key. Furthermore, we apply the bound for secure computation problems, and derive converse bounds on those problems. The talk is based on joint work with Himanshu Tyagi (https://eprint.iacr.org/2014/088). | PDF Presentation 12:25 Lunch-break 13:45 Yaoyun Shi (University of Michigan, Ann Arbor) Reining in quantum adversaries: the case of randomness expansion Abstract How can we generate near-perfect randomness securely, in large quantities, and efficiently? This is an important question for modern day information processing, especially for cryptography. Randomness expansion protocols provide a remarkable quantum solution based on Bell inequality violations. Such a protocol transforms a uniform seed to a much longer random output, by interacting classically with communication-restricted quantum devices whose inner-workings may be imperfect or even malicious. In this talk, I will analyze a variant of known protocols, showing that this class of exponentially expanding protocols not only are quantum-secure, but also enjoy several highly desirable new features such as cryptographic level of security, tolerance of a constant level of device imperfection, etc. Those features widen the application scope of the protocols and facilitate their practical implementations using current technologies. My talk will emphasize our proof techniques for managing two sources of security challenges: the repeatedly used devices that may cheat adaptively, and the adversary who may exploit her quantum correlation with the devices to reduce the output randomness. A notion of quantum Renyi entropy recently shown by several authors to be useful for quantum information theory also plays an instrumental role in our proof. Joint work with Carl A. Miller (arXiv:1402.0489). | PDF Presentation 14:45 Coffee/Tea Break 15:15 Yanbao Zhang (IQC, University of Waterloo) Analysis of tests of local realism Abstract Reliable rejection of local realism is highly desirable not only for understanding the foundation of quantum mechanics but also for facilitating quantum information tasks, such as quantum key distribution and randomness generation. The confidence for rejecting local realism is usually estimated by comparing Bell-inequality violation with experimental standard deviation. However, as we show, this method can overestimate the rejection confidence and so is not valid. We propose a prediction-based ratio (PBR) protocol to lower bound the rejection confidence without using a predetermined Bell inequality. The PBR protocol works even if the prepared quantum state, measurement settings, and local realistic models vary arbitrarily during an experiment. If the prepared state and measurement settings do not vary, the rejection-confidence bound is asymptotically tight. For comparison, confidence bounds derived from Bell-inequality violations using martingale theory [R. Gill, arXiv:quant-ph/0110137] are studied. It is found that bounds from martingale theory are not tight. We also simplify the implementation of the PBR protocol by using a set of predetermined Bell inequalities. The simplified PBR protocol can be applied to any test with linear witnesses, such as tests for verifying entanglement, contextuality, or system dimensionality. | PDF Presentation 15:55 Graeme Smith (IBM, New York) Bound entangled states with secret key and their classical counterpart Abstract Entanglement is a fundamental resource for quantum information processing. In its pure form, it allows quantum teleportation and sharing classical secrets. Realistic quantum states are noisy and their usefulness is only partially understood. Bound-entangled states are central to this question---they have no distillable entanglement, yet sometimes still have a private classical key. We present a construction of bound-entangled states with private key based on classical probability distributions. From this emerge states possessing a new classical analogue of bound entanglement, distinct from the long-sought bound information. We also find states of smaller dimensions and higher key rates than previously known. Our construction has implications for classical cryptography: we show that existing protocols are insufficient for extracting private key from our distributions due to their "bound-entangled" nature. We propose a simple extension of existing protocols that can extract key from them. 16:30 Break 16:45 Nilanjana Datta (University of Cambridge) Second-order asymptotics for source coding, dense coding and pure-state entanglement conversions Abstract We introduce two variants of the information spectrum relative entropy defined by Tomamichel and Hayashi which have the particular advantage of satisfying the data- processing inequality. This property allows us to obtain one-shot bounds for various information-processing tasks in terms of these quantities. In contrast to one-shot bounds given in terms of smooth min-/max- entropies, these bounds can be numerically computed to arbitrary precision. Moreover, these relative entropies have a second order asymptotic expansion, which in turn yields tight second order asymptotics for optimal rates of these tasks in the i.i.d. setting. The tasks considered are fixed-length quantum source coding, noisy dense coding, entanglement concentration and pure-state entanglement dilution. We also prove how the discrepancy between the optimal rates of entanglement concentration and dilution in the second order implies the irreversibility of entanglement concentration established by Kumagai and Hayashi. In addition, the spectral divergence rates of the Information Spectrum Approach (ISA) can be retrieved from our relative entropies in the asymptotic limit. This enables us to directly obtain the more general results of the ISA from our one-shot bounds. This is joint work with Felix Leditzky. | PDF Presentation 17:25 Yuval Kochman (Hebrew University of Jerusalem) Rate-distortion theory: did we get it all wrong? Abstract In this talk we revisit some basic definitions in rate-distortion theory, and argue that they fail to capture the full operational trade-offs of compression. Specifically, we argue that the concept of expected distortion, which strikes a balance between the reconstruction quality given different source values is not suitable in many scenarios. We also consider the excess-distortion probability, and find that it unnecessarily couples the quantizer dimension with user experience. For both issues, we offer some remedy in the form of new information-theoretic quantities. Based on joint work with Uri Erez and Gregory W. Wornell. | PDF Presentation 19:30 Conference Dinner