Fundamental Limits for Realizing Quantum Processes in Spacetime.

Understanding the interface between quantum and relativistic theories is crucial for fundamental and practical advances, especially given that key physical concepts such as causality take different forms in these theories. Bell's no-go theorem reveals limits on classical processes, arising from relativistic causality principles. Considering whether similar fundamental limits exist on quantum processes, we derive no-go theorems for quantum experiments realizable in classical background spacetimes.

Security of quantum key distribution from generalised entropy accumulation.

The goal of quantum key distribution (QKD) is to establish a secure key between two parties connected by an insecure quantum channel. To use a QKD protocol in practice, one has to prove that a finite size key is secure against general attacks: no matter the adversary's attack, they cannot gain useful information about the key. A much simpler task is to prove security against collective attacks, where the adversary is assumed to behave identically and independently in each round.

The nonequilibrium cost of accurate information processing.

Accurate information processing is crucial both in technology and in nature. To achieve it, any information processing system needs an initial supply of resources away from thermal equilibrium. Here we establish a fundamental limit on the accuracy achievable with a given amount of nonequilibrium resources.

Optimal Universal Programming of Unitary Gates.

A universal quantum processor is a device that takes as input a (quantum) program, containing an encoding of an arbitrary unitary gate, and a (quantum) data register, on which the encoded gate is applied. While no perfect universal quantum processor can exist, approximate processors have been proposed in the past two decades. A fundamental open question is how the size of the smallest quantum program scales with the approximation error.

Chain Rule for the Quantum Relative Entropy.

The chain rule for the classical relative entropy ensures that the relative entropy between probability distributions on multipartite systems can be decomposed into a sum of relative entropies of suitably chosen conditional distributions on the individual systems. Here, we prove a chain rule inequality for the quantum relative entropy. The new chain rule allows us to solve an open problem in the context of asymptotic quantum channel discrimination: surprisingly, adaptive protocols cannot improve the error rate for asymmetric channel discrimination compared to nonadaptive strategies.

Advantage Distillation for Device-Independent Quantum Key Distribution.

Device-independent quantum key distribution (DIQKD) offers the prospect of distributing secret keys with only minimal security assumptions, by making use of a Bell violation. However, existing DIQKD security proofs have low noise tolerances, making a proof-of-principle demonstration currently infeasible. We investigate whether the noise tolerance can be improved by using advantage distillation, which refers to using two-way communication instead of the one-way error correction currently used in DIQKD security proofs.

Discovering Physical Concepts with Neural Networks.

Despite the success of neural networks at solving concrete physics problems, their use as a general-purpose tool for scientific discovery is still in its infancy. Here, we approach this problem by modeling a neural network architecture after the human physical reasoning process, which has similarities to representation learning. This allows us to make progress towards the long-term goal of machine-assisted scientific discovery from experimental data without making prior assumptions about the system.

Confidence Polytopes in Quantum State Tomography.

Quantum state tomography is the task of inferring the state of a quantum system from measurement data. A reliable tomography scheme should not only report an estimate for that state, but also well-justified error bars. These may be specified in terms of confidence regions, i.

Quantum theory cannot consistently describe the use of itself.

Quantum theory provides an extremely accurate description of fundamental processes in physics. It thus seems likely that the theory is applicable beyond the, mostly microscopic, domain in which it has been tested experimentally. Here, we propose a Gedankenexperiment to investigate the question whether quantum theory can, in principle, have universal validity.

Practical device-independent quantum cryptography via entropy accumulation.

Device-independent cryptography goes beyond conventional quantum cryptography by providing security that holds independently of the quality of the underlying physical devices. Device-independent protocols are based on the quantum phenomena of non-locality and the violation of Bell inequalities. This high level of security could so far only be established under conditions which are not achievable experimentally.

Catalytic Decoupling of Quantum Information.

The decoupling technique is a fundamental tool in quantum information theory with applications ranging from thermodynamics to many-body physics and black hole radiation whereby a quantum system is decoupled from another one by discarding an appropriately chosen part of it. Here, we introduce catalytic decoupling, i.e.

Axiomatic Relation between Thermodynamic and Information-Theoretic Entropies.

Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is a measure of uncertainty. In this Letter, we connect these two notions of entropy, using an axiomatic framework for thermodynamics [E.

Relative thermalization.

Locally thermal quantum systems may contradict traditional thermodynamics: heat can flow from a cold body to a hotter one, if the two are highly entangled. We show that to recover thermodynamic laws, we must use a stronger notion of thermalization: a system S is thermal relative to a reference R if S is both locally thermal and uncorrelated with R. Considering a general quantum reference is particularly relevant for a thermodynamic treatment of nanoscale quantum systems.

Practical and Reliable Error Bars in Quantum Tomography.

Precise characterization of quantum devices is usually achieved with quantum tomography. However, most methods which are currently widely used in experiments, such as maximum likelihood estimation, lack a well-justified error analysis. Promising recent methods based on confidence regions are difficult to apply in practice or yield error bars which are unnecessarily large.

Universal recovery map for approximate Markov chains.

A central question in quantum information theory is to determine how well lost information can be reconstructed. Crucially, the corresponding recovery operation should perform well without knowing the information to be reconstructed. In this work, we show that the measures the performance of such recovery operations.

The minimal work cost of information processing.

Irreversible information processing cannot be carried out without some inevitable thermodynamical work cost. This fundamental restriction, known as Landauer's principle, is increasingly relevant today, as the energy dissipation of computing devices impedes the development of their performance. Here we determine the minimal work required to carry out any logical process, for instance a computation.

The ultimate physical limits of privacy.

Among those who make a living from the science of secrecy, worry and paranoia are just signs of professionalism. Can we protect our secrets against those who wield superior technological powers? Can we trust those who provide us with tools for protection? Can we even trust ourselves, our own freedom of choice? Recent developments in quantum cryptography show that some of these questions can be addressed and discussed in precise and operational terms, suggesting that privacy is indeed possible under surprisingly weak assumptions.

Security of continuous-variable quantum key distribution against general attacks.

We prove the security of Gaussian continuous-variable quantum key distribution with coherent states against arbitrary attacks in the finite-size regime. In contrast to previously known proofs of principle (based on the de Finetti theorem), our result is applicable in the practically relevant finite-size regime. This is achieved using a novel proof approach, which exploits phase-space symmetries of the protocols as well as the postselection technique introduced by Christandl, Koenig, and Renner [Phys.

Experimental bound on the maximum predictive power of physical theories.

The question of whether the probabilistic nature of quantum mechanical predictions can be alleviated by supplementing the wave function with additional information has received a lot of attention during the past century. A few specific models have been suggested and subsequently falsified. Here we give a more general answer to this question: We provide experimental data that, as well as falsifying these models, cannot be explained within any alternative theory that could predict the outcomes of measurements on maximally entangled particles with significantly higher probability than quantum theory.

Efficient polar coding of quantum information.

Polar coding, introduced 2008 by Arıkan, is the first (very) efficiently encodable and decodable coding scheme whose information transmission rate provably achieves the Shannon bound for classical discrete memoryless channels in the asymptotic limit of large block sizes. Here, we study the use of polar codes for the transmission of quantum information. Focusing on the case of qubit Pauli channels and qubit erasure channels, we use classical polar codes to construct a coding scheme that asymptotically achieves a net transmission rate equal to the coherent information using efficient encoding and decoding operations and code construction.

Reliable quantum state tomography.

Quantum state tomography is the task of inferring the state of a quantum system by appropriate measurements. Since the frequency distributions of the outcomes of any finite number of measurements will generally deviate from their asymptotic limits, the estimates computed by standard methods do not in general coincide with the true state and, therefore, have no operational significance unless their accuracy is defined in terms of error bounds. Here we show that quantum state tomography, together with an appropriate data analysis procedure, yields reliable and tight error bounds, specified in terms of confidence regions-a concept originating from classical statistics.

One-shot classical-quantum capacity and hypothesis testing.

The one-shot classical capacity of a quantum channel quantifies the amount of classical information that can be transmitted through a single use of the channel such that the error probability is below a certain threshold. In this work, we show that this capacity is well approximated by a relative-entropy-type measure defined via hypothesis testing. Combined with a quantum version of Stein's lemma, our results give a conceptually simple proof of the well-known Holevo-Schumacher-Westmoreland theorem for the capacity of memoryless channels.