Related papers: Quantum Resource Theories beyond Convexity
Connections between the resource theories of coherence and purity (or non-uniformity) are well known for discrete-variable, finite-dimensional, quantum systems. We establish analogous results for continuous-variable systems, in particular…
A key ingredient in quantum resource theories is a notion of measure. Such as a measure should have a number of fundamental properties, and desirably also a clear operational meaning. Here we show that a natural measure known as the convex…
Recently, various non-classical properties of quantum states and channels have been characterized through an advantage they provide in specific quantum information tasks over their classical counterparts. Such advantage can be typically…
Higher-order quantum theory deals with causal quantum processes, described by quantum combs, and test procedures, described by quantum testers, "measuring" these processes. In this work, we show that "jointly non-implementable" or…
I give a self-contained introduction to the resource theory approach to quantum thermodynamics. I will introduce in an elementary manner the technical machinery necessary to unpack and prove the core statements of the theory. The topics…
Resource theories play a crucial role in characterizing states and properties essential for quantum information processing. A significant challenge is protecting resources from errors. We explore strategies for correcting quantum resources.…
Quantum information theory is built upon the realisation that quantum resources like coherence and entanglement can be exploited for novel or enhanced ways of transmitting and manipulating information, such as quantum cryptography,…
Quantum theory departs from classical probabilistic theories in foundational ways. These departures--termed quantumness here--power quantum information and computation. This thesis charts the role of discrete structures in assessing…
Resource theories provide a general framework for the characterization of properties of physical systems in quantum mechanics and beyond. Here, we introduce methods for the quantification of resources in general probabilistic theories…
In developing quantum science and technologies, it is essential to demonstrate the so-called quantum advantages, which are performances that can be achieved only with the assistance of quantum resources. Most of the time, different quantum…
Quantum resource theories (QRTs) provide a unified theoretical framework for understanding inherent quantum-mechanical properties that serve as resources in quantum information processing, but resources motivated by physics may possess…
Tensor networks provide succinct representations of quantum many-body states and are an important computational tool for strongly correlated quantum systems. Their expressive and computational power is characterized by an underlying…
We review the basic idea behind resource theories, where we quantify quantum resources by specifying a restricted class of operations. This divides the state space into various sets, including states which are free (because they can be…
Quantum resources exist in a hierarchy of multiple levels. At order zero, quantum states are transformed by linear maps (channels, or gates) in order to perform computations or simulate other states. At order one, gates and channels are…
Quantum coherence is a critical resource for many operational tasks. Understanding how to quantify and manipulate it also promises to have applications for a diverse set of problems in theoretical physics. For certain applications, however,…
Standard formulations of quantum theory are based on complex numbers: Quantum states can be in superpositions, with weights given by complex probability amplitudes. Motivated by quantum theory promising a range of practical advantages over…
The developments of special relativity and quantum mechanics marked the beginning of the modern physics age. The former has taught us that while space and time are frame dependent notions, there is a quantity -- the space-time interval --…
We propose an approach to the study of quantum resource manipulation based on the basic observation that quantum channels which preserve certain sets of states are contractive with respect to the base norms induced by those sets. We forgo…
Quantum complexity is emerging as a key property of many-body systems, including black holes, topological materials, and early quantum computers. A state's complexity quantifies the number of computational gates required to prepare the…
Quantum resource theory under different classes of quantum operations advances multiperspective understandings of inherent quantum-mechanical properties, such as quantum coherence and quantum entanglement. We establish hierarchies of…