arXiv subjects

Lidia del Rio

Publications and source records attributed to Lidia del Rio.

11 recordsLinked to original sources

arXiv2021

Impossibility of composable Oblivious Transfer in relativistic quantum cryptography

We study the cryptographic primitive Oblivious Transfer; a composable construction of this resource would allow arbitrary multi-party computation to be carried out in a secure way, i.e. to compute functions in a distributed way while keeping inputs from different parties private. First we review a framework that allows us to analyze composability of classical and quantum cryptographic protocols in special relativity: Abstract Cryptography implemented with Causal Boxes. We then (1) explore and formalize different versions of oblivious transfer found in the literature, (2) prove that their equivalence holds also in relativistic quantum settings, (3) show that it is impossible to composably construct any of these versions of oblivious transfer from only classical or quantum communication among distrusting agents in relativistic settings, (4) prove that the impossibility also extends to multi-party computation, and (5) provide a mutual construction between oblivious transfer and bit commitment.

quant-ph↗

arXiv2020

The first law of general quantum resource theories

We extend the tools of quantum resource theories to scenarios in which multiple quantities (or resources) are present, and their interplay governs the evolution of physical systems. We derive conditions for the interconversion of these resources, which generalise the first law of thermodynamics. We study reversibility conditions for multi-resource theories, and find that the relative entropy distances from the invariant sets of the theory play a fundamental role in the quantification of the resources. The first law for general multi-resource theories is a single relation which links the change in the properties of the system during a state transformation and the weighted sum of the resources exchanged. In fact, this law can be seen as relating the change in the relative entropy from different sets of states. In contrast to typical single-resource theories, the notion of free states and invariant sets of states become distinct in light of multiple constraints. Additionally, generalisations of the Helmholtz free energy, and of adiabatic and isothermal transformations, emerge. We thus have a set of laws for general quantum resource theories, which generalise the laws of thermodynamics. We first test this approach on thermodynamics with multiple conservation laws, and then apply it to the theory of local operations under energetic restrictions.

quant-ph↗

arXiv2020

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 modelling 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. We apply this method to toy examples and show that the network finds the physically relevant parameters, exploits conservation laws to make predictions, and can help to gain conceptual insights, e.g. Copernicus' conclusion that the solar system is heliocentric.

quant-ph↗

arXiv2019

Thermodynamic Computing

The hardware and software foundations laid in the first half of the 20th Century enabled the computing technologies that have transformed the world, but these foundations are now under siege. The current computing paradigm, which is the foundation of much of the current standards of living that we now enjoy, faces fundamental limitations that are evident from several perspectives. In terms of hardware, devices have become so small that we are struggling to eliminate the effects of thermodynamic fluctuations, which are unavoidable at the nanometer scale. In terms of software, our ability to imagine and program effective computational abstractions and implementations are clearly challenged in complex domains. In terms of systems, currently five percent of the power generated in the US is used to run computing systems - this astonishing figure is neither ecologically sustainable nor economically scalable. Economically, the cost of building next-generation semiconductor fabrication plants has soared past $10 billion. All of these difficulties - device scaling, software complexity, adaptability, energy consumption, and fabrication economics - indicate that the current computing paradigm has matured and that continued improvements along this path will be limited. If technological progress is to continue and corresponding social and economic benefits are to continue to accrue, computing must become much more capable, energy efficient, and affordable. We propose that progress in computing can continue under a united, physically grounded, computational paradigm centered on thermodynamics. Herein we propose a research agenda to extend these thermodynamic foundations into complex, non-equilibrium, self-organizing systems and apply them holistically to future computing systems that will harness nature's innate computational capacity. We call this type of computing "Thermodynamic Computing" or TC.

cs.CY↗

arXiv2019

Multi-agent paradoxes beyond quantum theory

Which theories lead to a contradiction between simple reasoning principles and modelling observers' memories as physical systems? Frauchiger and Renner have shown that this is the case for quantum theory, with a thought experiment that leads to a multi-agent paradox. Here we generalize the conditions of the Frauchiger-Renner result so that they can be applied to arbitrary physical theories, and in particular to those expressed as generalized probabilistic theories (GPTs). We then apply them to a particular GPT, box world, and find a deterministic contradiction in the case where agents may share a PR box, which is stronger than the quantum paradox, in that it does not rely on post-selection. Obtaining an inconsistency for the framework of GPTs broadens the landscape of theories which are affected by the application of classical rules of reasoning to physical agents. In addition, we model how observers' memories may evolve in box world, in a way consistent with Barrett's criteria for allowed operations.

quant-ph↗

arXiv2018

Composable security in relativistic quantum cryptography

Relativistic protocols have been proposed to overcome some impossibility results in classical and quantum cryptography. In such a setting, one takes the location of honest players into account, and uses the fact that information cannot travel faster than the speed of light to limit the abilities of dishonest agents. For example, various relativistic bit commitment protocols have been proposed. Although it has been shown that bit commitment is sufficient to construct oblivious transfer and thus multiparty computation, composing specific relativistic protocols in this way is known to be insecure. A composable framework is required to perform such a modular security analysis of construction schemes, but no known frameworks can handle models of computation in Minkowski space. By instantiating the systems model from the Abstract Cryptography framework with Causal Boxes, we obtain such a composable framework, in which messages are assigned a location in Minkowski space (or superpositions thereof). This allows us to analyse relativistic protocols and to derive novel possibility and impossibility results. We show that (1) coin flipping can be constructed from the primitive channel with delay, (2) biased coin flipping, bit commitment and channel with delay are all impossible without further assumptions, and (3) it is impossible to improve a channel with delay. Note that the impossibility results also hold in the computational and bounded storage settings. This implies in particular non-composability of all proposed relativistic bit commitment protocols, of bit commitment in the bounded storage model, and of biased coin flipping.

quant-ph↗

arXiv2017

Operational locality in global theories

Within a global physical theory, a notion of locality allows us to find and justify information-processing primitives, like non-signalling between distant agents. Here we propose exploring the opposite direction: to take agents as the basic building blocks through which we test a physical theory, and recover operational notions of locality from signalling conditions. First we introduce an operational model for the effective state spaces of individual agents, as well as the range of their actions. We then formulate natural secrecy conditions between agents and identify the aspects of locality relevant for signalling. We discuss the possibility of taking commutation of transformations as a primitive of physical theories, as well as applications to quantum theory and generalized probability frameworks. This "it from bit" approach establishes an operational connection between local action and local observations, and gives a global interpretation to concepts like discarding a subsystem or composing local functions.

quant-ph↗

arXiv2016

Currencies in resource theories

How may we quantify the value of physical resources, such as entangled quantum states, heat baths or lasers? Existing resource theories give us partial answers; however, these rely on idealizations, like perfectly independent copies of states or exact knowledge of a quantum state. Here we introduce the general tool of currencies to quantify realistic descriptions of resources, applicable in experimental settings when we do not have perfect control over a physical system, when only the neighbourhood of a state or some of its properties are known, or when there is no obvious way to decompose a global space into subsystems. Currencies are a special set of resources chosen to quantify all others - like Bell pairs in LOCC or a lifted weight in thermodynamics. We show that from very weak assumptions on the theory we can already find useful currencies that give us necessary and sufficient conditions for resource conversion, and we build up more results as we impose further structure. This work is an application of Resource theories of knowledge [arXiv:1511.08818], generalizing axiomatic approaches to thermodynamic entropy, work and currencies made of local copies.

quant-ph↗

arXiv2015

Resource theories of knowledge

How far can we take the resource theoretic approach to explore physics? Resource theories like LOCC, reference frames and quantum thermodynamics have proven a powerful tool to study how agents who are subject to certain constraints can act on physical systems. This approach has advanced our understanding of fundamental physical principles, such as the second law of thermodynamics, and provided operational measures to quantify resources such as entanglement or information content. In this work, we significantly extend the approach and range of applicability of resource theories. Firstly we generalize the notion of resource theories to include any description or knowledge that agents may have of a physical state, beyond the density operator formalism. We show how to relate theories that differ in the language used to describe resources, like micro and macroscopic thermodynamics. Finally, we take a top-down approach to locality, in which a subsystem structure is derived from a global theory rather than assumed. The extended framework introduced here enables us to formalize new tasks in the language of resource theories, ranging from tomography, cryptography, thermodynamics and foundational questions, both within and beyond quantum theory.

quant-ph↗

arXiv2014

Relative Thermalization

When studying thermalization of quantum systems, it is typical to ask whether a system interacting with an environment will evolve towards a local thermal state. Here, we show that a more general and relevant question is "when does a system thermalize relative to a particular reference?" By relative thermalization we mean that, as well as being in a local thermal state, the system is uncorrelated with the reference. We argue that this is necessary in order to apply standard statistical mechanics to the study of the interaction between a thermalized system and a reference. We then derive a condition for relative thermalization of quantum systems interacting with an arbitrary environment. This condition has two components: the first is state-independent, reflecting the structure of invariant subspaces, like energy shells, and the relative sizes of system and environment; the second depends on the initial correlations between reference, system and environment, measured in terms of conditional entropies. Intuitively, a small system interacting with a large environment is likely to thermalize relative to a reference, but only if, initially, the reference was not highly correlated with the system and environment. Our statement makes this intuition precise, and we show that in many natural settings this thermalization condition is approximately tight. Established results on thermalization, which usually ignore the reference, follow as special cases of our statements.

quant-ph↗

arXiv2009

Critical hybridization for the Kondo resonance in gapless systems

We study the Kondo resonance in a spin-1/2 single impurity Anderson model with a gapless conduction band using the equation of motion approach in order to obtain the impurity spectral function. We study two different scenarios for gapless systems: a purely power-law energy dependence of the density of states or a constant density of states with a gapless behavior near the Fermi level. We demonstrate that strong electron-electron correlations lead to a sharp peak in the impurity spectral function in the case of a large exchange coupling ($J>J_{c}$) or equivalently, a strong hybridization ($V>V_{c}$). This Kondo-like peak emerges much below the Fermi level in the case of a strongly depleted density of states. These results are compared with the ones from renormalization group approaches.

cond-mat.str-el↗