One-Shot Manipulation of Dynamical Quantum Resources

• URL: http://arxiv.org/abs/2012.02215v3
• Date: Thu, 5 Aug 2021 17:30:34 GMT
• Title: One-Shot Manipulation of Dynamical Quantum Resources
• Authors: Bartosz Regula and Ryuji Takagi
• Abstract summary: We develop a unified framework to characterize one-shot transformations of dynamical quantum resources in terms of resource quantifiers. Our framework encompasses all dynamical resources represented as quantum channels. We show that our conditions become necessary and sufficient for broad classes of important theories.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We develop a unified framework to characterize one-shot transformations of dynamical quantum resources in terms of resource quantifiers, establishing universal conditions for exact and approximate transformations in general resource theories. Our framework encompasses all dynamical resources represented as quantum channels, including those with a specific structure --- such as boxes, assemblages, and measurements --- thus immediately applying in a vast range of physical settings. For the particularly important manipulation tasks of distillation and dilution, we show that our conditions become necessary and sufficient for broad classes of important theories, enabling an exact characterization of these tasks and establishing a precise connection between operational problems and resource monotones based on entropic divergences. We exemplify our results by considering explicit applications to: quantum communication, where we obtain exact expressions for one-shot quantum capacity and simulation cost assisted by no-signalling, separability-preserving, and positive partial transpose-preserving codes; as well as to nonlocality, contextuality, and measurement incompatibility, where we present operational applications of a number of relevant resource measures.

Related papers

• End-to-end resource analysis for quantum interior point methods and portfolio optimization [63.4863637315163]
  We provide a complete quantum circuit-level description of the algorithm from problem input to problem output. We report the number of logical qubits and the quantity/depth of non-Clifford T-gates needed to run the algorithm.
  arXiv  Detail & Related papers  (2022-11-22T18:54:48Z)
• Unifying different notions of quantum incompatibility into a strict hierarchy of resource theories of communication [60.18814584837969]
  We introduce the notion of q-compatibility, which unifies different notions of POVMs, channels, and instruments incompatibility. We are able to pinpoint exactly what each notion of incompatibility consists of, in terms of information-theoretic resources.
  arXiv  Detail & Related papers  (2022-11-16T21:33:31Z)
• Real quantum operations and state transformations [44.99833362998488]
  Resource theory of imaginarity provides a useful framework to understand the role of complex numbers. In the first part of this article, we study the properties of real'' (quantum) operations in single-party and bipartite settings. In the second part of this article, we focus on the problem of single copy state transformation via real quantum operations.
  arXiv  Detail & Related papers  (2022-10-28T01:08:16Z)
• Quantum Dynamical Resource Theory under Resource Non-increasing Framework [0.0]
  We show that maximally incoherent operations (MIO) and incoherent operations (IO) in the static coherence resource theory are free in the sense of dynamical coherence. We also present convenient measures and give the analytic calculation for the amplitude damping channel.
  arXiv  Detail & Related papers  (2022-03-13T04:19:01Z)
• Entropic and operational characterizations of dynamic quantum resources [3.2074558838636262]
  We provide new methods for characterizing general closed and convex quantum resource theories. We propose a resource-theoretic generalization of the quantum conditional min-entropy. We show that every well-defined robustness-based measure of a channel can be interpreted as an operational advantage of the channel over free channels in a communication task.
  arXiv  Detail & Related papers  (2021-12-13T18:58:36Z)
• One-Shot Yield-Cost Relations in General Quantum Resource Theories [5.37133760455631]
  We establish a relation between the one-shot distillable resource yield and dilution cost. We show that our techniques provide strong converse bounds relating the distillable resource and resource dilution cost in the regime.
  arXiv  Detail & Related papers  (2021-10-05T17:59:30Z)
• Quantifying Qubit Magic Resource with Gottesman-Kitaev-Preskill Encoding [58.720142291102135]
  We define a resource measure for magic, the sought-after property in most fault-tolerant quantum computers. Our formulation is based on bosonic codes, well-studied tools in continuous-variable quantum computation.
  arXiv  Detail & Related papers  (2021-09-27T12:56:01Z)
• Error mitigation and quantum-assisted simulation in the error corrected regime [77.34726150561087]
  A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations. We show how the addition of noisy magic resources allows one to boost classical quasiprobability simulations of a quantum circuit.
  arXiv  Detail & Related papers  (2021-03-12T20:58:41Z)
• One-shot dynamical resource theory [16.046979670252814]
  We consider tasks of one-shot resource distillation and dilution with a single copy of the resource. For any target of unitary channel or pure state preparation channel, we establish a universal strategy to determine upper and lower bounds on rates that convert between any given resource and the target. Our results are applicable to general dynamical resource theories with potential applications in quantum communication, fault-tolerant quantum computing, and quantum thermodynamics.
  arXiv  Detail & Related papers  (2020-12-04T18:57:42Z)
• Operational quantification of continuous-variable quantum resources [6.308539010172309]
  We introduce a general method of quantifying resources for continuous-variable quantum systems based on the measure. We show that the robustness constitutes a well-behaved, bona fide resource quantifier in any convex resource theory.
  arXiv  Detail & Related papers  (2020-09-23T18:00:03Z)
• Genuine quantum networks: superposed tasks and addressing [68.8204255655161]
  We show how to make quantum networks, both standard and entanglement-based, genuine quantum. We provide them with the possibility of handling superposed tasks and superposed addressing.
  arXiv  Detail & Related papers  (2020-04-30T18:00:06Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.