Marcin Pawlowski

Information causality as a physical principle

Quantum physics has remarkable distinguishing characteristics. For example, it gives only probabilistic predictions (non-determinism) and does not allow copying of unknown states (no-cloning). Quantum correlations may be stronger than any classical ones, but information cannot be transmitted faster than light (no-signalling). However, these features do not uniquely define quantum physics. A broad class of theories exist that share such traits and allow even stronger (than quantum) correlations. Here we introduce the principle of ‘information causality’ and show that it is respected by classical and quantum physics but violated by all no-signalling theories with stronger than (the strongest) quantum correlations. The principle relates to the amount of information that an observer (Bob) can gain about a data set belonging to another observer (Alice), the contents of which are completely unknown to him. Using all his local resources (which may be correlated with her resources) and allowing classical communication from her, the amount of information that Bob can recover is bounded by the information volume (m) of the communication. Namely, if Alice communicates m bits to Bob, the total information obtainable by Bob cannot be greater than m. For m = 0, information causality reduces to the standard no-signalling principle. However, no-signalling theories with maximally strong correlations would allow Bob access to all the data in any m-bit subset of the whole data set held by Alice. If only one bit is sent by Alice (m = 1), this is tantamount to Bob’s being able to access the value of any single bit of Alice’s data (but not all of them). Information causality may therefore help to distinguish physical theories from non-physical ones. We suggest that information causality—a generalization of the no-signalling condition—might be one of the foundational properties of nature.

Recovering part of the boundary between quantum and nonquantum correlations from information causality

Department of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom 2 H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom Institute of Theoretical Physics and Astrophysics, University of Gdansk, 80-952 Gdansk, Poland Centre for Quantum Technologies and Department of Physics, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore (Dated: October 15, 2009)

Weak randomness in device-independent quantum key distribution and the advantage of using high-dimensional entanglement

We show that in device-independent quantum key distribution protocols the privacy of randomness is of crucial importance. For sublinear test sample sizes even the slightest guessing probability by an eavesdropper will completely compromise security. We show that a combined attack exploiting test sample and measurement choices compromises the security even with a linear-size test sample and otherwise device-independent security considerations. We explicitly derive the sample size needed to retrieve security as a function of the randomness quality. We demonstrate that exploiting features of genuinely higher-dimensional systems, one can reduce this weakness and provide device-independent security more robust against weak randomness sources.

Monogamy of Bell's Inequality Violations in Nonsignaling Theories

We derive monogamy relations (tradeoffs) between strengths of violations of Bells inequalities from the nonsignaling condition. Our result applies to general Bell inequalities with an arbitrary large number of partners, outcomes, and measurement settings. The method is simple, efficient, and does not require linear programing. The results are used to derive optimal fidelity for asymmetric cloning in nonsignaling theories.

Non-local setting and outcome information for violation of Bell's inequality

Bells theorem is a no-go theorem stating that quantum mechanics cannot be reproduced by a physical theory based on realism, freedom to choose experimental settings and two locality conditions: setting (SI) and outcome (OI) independence. We provide a novel analysis of what it takes to violate Bells inequality within the framework in which both realism and freedom of choice are assumed, by showing that it is impossible to model a violation without having information in one laboratory about both the setting and the outcome at the distant one. While it is possible that outcome information can be revealed from shared hidden variables, the assumed experimenters freedom to choose the settings ensures that the setting information must be non-locally transferred even when the SI condition is obeyed. The amount of transmitted information about the setting that is sufficient to violate the CHSH inequality up to its quantum mechanical maximum is 0.736 bits.

Free randomness amplification using bipartite chain correlations

A direct analysis of the task of randomness amplification from Santha-Vazirani sources using the violation of the chained Bell inequality is performed in terms of the convex combination of no-signaling boxes required to simulate quantum violation of the inequality. This analysis is used to find the exact threshold value of the initial randomness parameter from which perfect randomness can be extracted in the asymptotic limit of a large number of measurement settings. As a byproduct, we provide a tool for the analysis of randomness amplification protocols, namely a general characterization of the probability distributions of bits generated by Santha-Vazirani sources, which are shown to be mixtures of specific permutations of Bernoulli distributions with a parameter defined by the source.

Hyperbits: the information quasiparticles

Information theory has its particles, bits and qubits, just as physics has electrons and photons. However, in physics we have a special category of objects with no clear counterparts in information theory: quasiparticles. They are introduced to simplify complex emergent phenomena making otherwise very difficult calculations possible and providing additional insight into the inner workings of the system. We show that we can adopt a similar approach in information theory. We introduce the hyperbits, the first information quasiparticles which we prove to be a resource equivalent to entanglement and classical communication, and give examples how they can be used to simplify calculations and get more insight into communication protocols.

On the connection between mutually unbiased bases and orthogonal Latin squares

We offer a piece of evidence that the problems of finding the number of mutually unbiased bases (MUB) and mutually orthogonal Latin squares (MOLS) might not be equivalent. We study a particular procedure that has been shown to relate the two problems and generates complete sets of MUB in power-of-prime dimensions and three MUB in dimension six. For these cases, every square from an augmented set of MOLS has a corresponding MUB. We show that this no longer holds for certain composite dimensions.

The speed of quantum and classical learning for performing the kth root of NOT

We consider quantum learning machines—quantum computers that modify themselves in order to improve their performance in some way—that are trained to perform certain classical task, i.e. to execute a function that takes classical bits as input and returns classical bits as output. This allows a fair comparison between learning efficiency of quantum and classical learning machines in terms of the number of iterations required for completion of learning. We find an explicit example of the task for which numerical simulations show that quantum learning is faster than its classical counterpart. The task is extraction of the kth root of NOT (NOT = logical negation), with k = 2 m and m 2 N. The reason for this speed-up is that the classical machine requires memory of size logk = m to accomplish the learning, while the memory of a single qubit is sufficient for the quantum machine for any k.

Semi-device independent random number expansion protocol with n → 1 quantum random access codes

Department of Mathematics, University of Bristol, Bristol BS8 1TW,United Kingdom(Dated: Auguest 14, 2011)We study random number expansion protocols based on the n→1 quantum random access codes(QRACs). We consider them in the semi-device independent scenario where the inner workings ofthe devices are unknown to us but we can certify the dimensions of the systems being communicated.This approach does not require the use of the entanglement and makes the physical realization ofthese protocols much easier than in the standard device independent scenario. We calculate thedependence of the effectiveness of the randomness generation on n and find it optimal for n = 3.We provide the explanation for this fact.