Publications (56)
Expanding bipartite Bell inequalities for maximum multi-partite randomness
Lewis Wooltorton, Peter Brown, Roger Colbeck
Nonlocal tests on multi-partite quantum correlations form the basis of protocols that certify randomness in a device-independent (DI) way. Such correlations admit a rich structure,…
Correlation Self-Testing of Quantum Theory against Generalised Probabilistic Theories with Restricted Relabelling Symmetry
Kuntal Sengupta, Mirjam Weilenmann, Roger Colbeck
Correlation self-testing of quantum theory involves identifying a task or set of tasks whose optimal performance can be achieved only by theories that can realise the same set of c…
Theories with no superluminal signaling have greater information-processing power than theories with no superluminal causation
V. Vilasini, Roger Colbeck
A central goal in the foundations of physics is to understand the structure of physical theories, such as quantum theory, from physical principles. This is often explored by consid…
Non-Shannon inequalities in the entropy vector approach to causal structures
Mirjam Weilenmann, Roger Colbeck
A causal structure is a relationship between observed variables that in general restricts the possible correlations between them. This relationship can be mediated by unobserved sy…
The standard no-signalling constraints in Bell scenarios are neither sufficient nor necessary for preventing superluminal signalling with general interventions
V. Vilasini, Roger Colbeck
Non-classical correlations resulting from entangled quantum systems have sparked debates about the compatibility of quantum theory and relativity, and about the right way to think…
Quantum And Relativistic Protocols For Secure Multi-Party Computation
Roger Colbeck
After a general introduction, the thesis is divided into four parts. In the first, we discuss the task of coin tossing, principally in order to highlight the effect different physi…
Unconditionally secure device-independent quantum key distribution with only two devices
Jonathan Barrett, Roger Colbeck, Adrian Kent
Device-independent quantum key distribution is the task of using uncharacterized quantum devices to establish a shared key between two users. If a protocol is secure regardless of…
A system's wave function is uniquely determined by its underlying physical state
Roger Colbeck, Renato Renner
We address the question of whether the quantum-mechanical wave function of a system is uniquely determined by any complete description of the system's physical state. We…
Introduction to UniversalQCompiler
Raban Iten, Oliver Reardon-Smith, Emanuel Malvetti +5
We introduce an open source software package UniversalQCompiler written in Mathematica that allows the decomposition of arbitrary quantum operations into a sequence of single-qubit…
Free randomness can be amplified
Roger Colbeck, Renato Renner
Are there fundamentally random processes in nature? Theoretical predictions, confirmed experimentally, such as the violation of Bell inequalities, point to an affirmative answer. H…
Self-testing of physical theories, or, is quantum theory optimal with respect to some information-processing task?
Mirjam Weilenmann, Roger Colbeck
Self-testing usually refers to the task of taking a given set of observed correlations that are assumed to arise via a process that is accurately described by quantum theory, and t…
Variable Bias Coin Tossing
Roger Colbeck, Adrian Kent
Alice is a charismatic quantum cryptographer who believes her parties are unmissable; Bob is a (relatively) glamorous string theorist who believes he is an indispensable guest. To…
Towards correlation self-testing of quantum theory in the adaptive Clauser-Horne-Shimony-Holt game
Mirjam Weilenmann, Roger Colbeck
Correlation self-testing of a theory addresses the question of whether we can identify the set of correlations realisable in a theory from its performance in a particular informati…
A framework for quantum-secure device-independent randomness expansion
Peter J. Brown, Sammy Ragy, Roger Colbeck
A device-independent randomness expansion protocol aims to take an initial random seed and generate a longer one without relying on details of how the devices operate for security.…
Quantum Circuits for Isometries
Raban Iten, Roger Colbeck, Ivan Kukuljan +2
We consider the decomposition of arbitrary isometries into a sequence of single-qubit and Controlled-NOT (C-NOT) gates. In many experimental architectures, the C-NOT gate is relati…
Simple Channel Coding Bounds
Ligong Wang, Roger Colbeck, Renato Renner
New channel coding converse and achievability bounds are derived for a single use of an arbitrary channel. Both bounds are expressed using a quantity called the "smooth 0-divergenc…
Bell Inequalities From No-Signalling Distributions
Thomas Cope, Roger Colbeck
A Bell inequality is a constraint on a set of correlations whose violation can be used to certify non-locality. They are instrumental for device-independent tasks such as key distr…
Is a system's wave function in one-to-one correspondence with its elements of reality?
Roger Colbeck, Renato Renner
Although quantum mechanics is one of our most successful physical theories, there has been a long-standing debate about the interpretation of the wave function---the central object…
Smooth manifold structure for extreme channels
Raban Iten, Roger Colbeck
A quantum channel from a system of dimension to a system of dimension is a completely positive trace-preserving map from complex to $d_B\times d…
Tight analytic bound on the trade-off between device-independent randomness and nonlocality
Lewis Wooltorton, Peter Brown, Roger Colbeck
Two parties sharing entangled quantum systems can generate correlations that cannot be produced using only shared classical resources. These nonlocal correlations are a fundamental…
A short note on the concept of free choice
Roger Colbeck, Renato Renner
We argue that the concepts of "freedom of choice" and of "causal order" are intrinsically linked: a choice is considered "free" if it is correlated only to variables in its causal…
An Entanglement-Based Protocol For Strong Coin Tossing With Bias 1/4
Roger Colbeck
In the literature, strong coin tossing protocols based on bit commitment have been proposed. Here we examine a protocol that instead tries to achieve the task by sharing entangleme…
No extension of quantum theory can have improved predictive power
Roger Colbeck, Renato Renner
According to quantum theory, measurements generate random outcomes, in stark contrast with classical mechanics. This raises the question of whether there could exist an extension o…
Quantum Self-Correcting Stabilizer Codes
Alastair Kay, Roger Colbeck
In this paper, we explicitly construct (Abelian) anyonic excitations of arbitrary stabilizer Hamiltonians which are local on a 2D lattice of qubits. This leads directly to the conc…
Arbitrarily many independent observers can share the nonlocality of a single maximally entangled qubit pair
Peter J. Brown, Roger Colbeck
Alice and Bob each have half of a pair of entangled qubits. Bob measures his half and then passes his qubit to a second Bob who measures again and so on. The goal is to maximize th…
Hidden variable models for quantum theory cannot have any local part
Roger Colbeck, Renato Renner
It was shown by Bell that no local hidden variable model is compatible with quantum mechanics. If, instead, one permits the hidden variables to be entirely non-local, then any quan…
Analysing causal structures using Tsallis entropies
V. Vilasini, Roger Colbeck
Understanding cause-effect relationships is a crucial part of the scientific process. As Bell's theorem shows, within a given causal structure, classical and quantum physics impose…
The completeness of quantum theory for predicting measurement outcomes
Roger Colbeck, Renato Renner
The predictions that quantum theory makes about the outcomes of measurements are generally probabilistic. This has raised the question whether quantum theory can be considered comp…
An experimental test of all theories with predictive power beyond quantum theory
Terence E. Stuart, Joshua A. Slater, Roger Colbeck +2
According to quantum theory, the outcomes of future measurements cannot (in general) be predicted with certainty. In some cases, even with a complete physical description of the sy…
A Fully Quantum Asymptotic Equipartition Property
Marco Tomamichel, Roger Colbeck, Renato Renner
The classical asymptotic equipartition property is the statement that, in the limit of a large number of identical repetitions of a random experiment, the output sequence is virtua…
Higher rates for semi-device-independent randomness expansion by recycling input randomness
Rutvij Bhavsar, Hamid Tebyanian, Roger Colbeck
Although quantum random number generators rely on the inherent indeterminism of quantum mechanics, ensuring that the numbers produced are secure remains a significant challenge. We…
Duality Between Smooth Min- and Max-Entropies
Marco Tomamichel, Roger Colbeck, Renato Renner
In classical and quantum information theory, operational quantities such as the amount of randomness that can be extracted from a given source or the amount of space needed to stor…
Private Randomness Expansion With Untrusted Devices
Roger Colbeck, Adrian Kent
Randomness is an important resource for many applications, from gambling to secure communication. However, guaranteeing that the output from a candidate random source could not hav…
All reversible dynamics in maximally non-local theories are trivial
David Gross, Markus Mueller, Roger Colbeck +1
A remarkable feature of quantum theory is non-locality (i.e. the presence of correlations which violate Bell inequalities). However, quantum correlations are not maximally non-loca…
Device-independent quantum key distribution with arbitrarily small nonlocality
Lewis Wooltorton, Peter Brown, Roger Colbeck
Device-independent quantum key distribution (DIQKD) allows two users to set up shared cryptographic key without the need to trust the quantum devices used. Doing so requires nonloc…
Advantages of multi-copy nonlocality distillation and its application to minimizing communication complexity
Giorgos Eftaxias, Mirjam Weilenmann, Roger Colbeck
Nonlocal correlations are a central feature of quantum theory, and understanding why quantum theory has a limited amount of nonlocality is a fundamental problem. Since nonlocality…
Multi-system measurements in generalized probabilistic theories and their role in information processing
Giorgos Eftaxias, Mirjam Weilenmann, Roger Colbeck
Generalized probabilistic theories (GPTs) provide a framework in which a range of possible theories can be examined, including classical theory, quantum theory and those beyond. In…
Inability of the entropy vector method to certify nonclassicality in linelike causal structures
Mirjam Weilenmann, Roger Colbeck
Bell's theorem shows that our intuitive understanding of causation must be overturned in light of quantum correlations. Nevertheless, quantum mechanics does not permit signalling a…
Device-independent randomness expansion against quantum side information
Wen-Zhao Liu, Ming-Han Li, Sammy Ragy +9
The ability to produce random numbers that are unknown to any outside party is crucial for many applications. Device-independent randomness generation does not require trusted devi…
The Uncertainty Principle in the Presence of Quantum Memory
Mario Berta, Matthias Christandl, Roger Colbeck +2
The uncertainty principle, originally formulated by Heisenberg, dramatically illustrates the difference between classical and quantum mechanics. The principle bounds the uncertaint…
Impossibility of superluminal signalling in Minkowski space-time does not rule out causal loops
V. Vilasini, Roger Colbeck
Causality is fundamental to science, but it appears in several different forms. One is relativistic causality, which is tied to a space-time structure and forbids signalling outsid…
Keyring models: an approach to steerability
Carl A. Miller, Roger Colbeck, Yaoyun Shi
If a measurement is made on one half of a bipartite system, then, conditioned on the outcome, the other half has a new reduced state. If these reduced states defy classical explana…
Quantum Circuits for Quantum Channels
Raban Iten, Roger Colbeck, Matthias Christandl
We study the implementation of quantum channels with quantum computers while minimizing the experimental cost, measured in terms of the number of Controlled-NOT (C-NOT) gates requi…
Memory Attacks on Device-Independent Quantum Cryptography
Jonathan Barrett, Roger Colbeck, Adrian Kent
Device-independent quantum cryptographic schemes aim to guarantee security to users based only on the output statistics of any components used, and without the need to verify their…
Defining the local part of a hidden variable model: a comment
Roger Colbeck, Renato Renner
In [Physical Review Letters 101, 050403 (2008)], we showed that quantum theory cannot be explained by a hidden variable model with a non-trivial local part. The purpose of this com…
Analysing causal structures in generalised probabilistic theories
Mirjam Weilenmann, Roger Colbeck
Causal structures give us a way to understand the origin of observed correlations. These were developed for classical scenarios, but quantum mechanical experiments necessitate thei…
Experimental investigation of the uncertainty principle in the presence of quantum memory
Robert Prevedel, Deny R. Hamel, Roger Colbeck +2
Heisenberg's uncertainty principle provides a fundamental limitation on an observer's ability to simultaneously predict the outcome when one of two measurements is performed on a q…
Analysing causal structures with entropy
Mirjam Weilenmann, Roger Colbeck
A central question for causal inference is to decide whether a set of correlations fit a given causal structure. In general, this decision problem is computationally infeasible and…
Genuine multipartite entanglement is not necessary for standard device-independent conference key agreement
Lewis Wooltorton, Peter Brown, Roger Colbeck
Conference key agreement aims to establish shared, private randomness among many separated parties in a network. Device-independent conference key agreement (DICKA) is a variant in…
On the insufficiency of entropic inequalities for detecting non-classicality in the Bell causal structure
V. Vilasini, Roger Colbeck
Classical and quantum physics impose different constraints on the joint probability distributions of observed variables in a causal structure. These differences mean that certain c…
The Impossibility Of Secure Two-Party Classical Computation
Roger Colbeck
We present attacks that show that unconditionally secure two-party classical computation is impossible for many classes of function. Our analysis applies to both quantum and relati…
Improved device-independent randomness expansion rates using two sided randomness
Rutvij Bhavsar, Sammy Ragy, Roger Colbeck
A device-independent randomness expansion protocol aims to take an initial random string and generate a longer one, where the security of the protocol does not rely on knowing the…
A general framework for cyclic and fine-tuned causal models and their compatibility with space-time
V. Vilasini, Roger Colbeck
Causal modelling is a tool for generating causal explanations of observed correlations and has led to a deeper understanding of correlations in quantum networks. Existing framework…
Quantum Circuits for Sparse Isometries
Emanuel Malvetti, Raban Iten, Roger Colbeck
We consider the task of breaking down a quantum computation given as an isometry into C-NOTs and single-qubit gates, while keeping the number of C-NOT gates small. Although several…
Uncertainty relations from simple entropic properties
Patrick J. Coles, Roger Colbeck, Li Yu +1
Uncertainty relations provide constraints on how well the outcomes of incompatible measurements can be predicted, and, as well as being fundamental to our understanding of quantum…
Closing the problem of which causal structures of up to six total nodes have a classical-quantum gap
Shashaank Khanna, Matthew Pusey, Roger Colbeck
The discovery of Bell that there exist quantum correlations that cannot be reproduced classically is one of the most important in the foundations of quantum mechanics, as well as h…