Choi-Defined Resource Theories
- URL: http://arxiv.org/abs/2402.12569v1
- Date: Mon, 19 Feb 2024 21:51:01 GMT
- Title: Choi-Defined Resource Theories
- Authors: Elia Zanoni, Carlo Maria Scandolo
- Abstract summary: resource theories of separable entanglement, non-positive partial entanglement, magic, and imaginarity share an interesting property.
An operation is free if and only if its renormalized Choi matrix is a free state.
We demonstrate how and under what conditions one can construct a Choi-defined resource theory.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The resource theories of separable entanglement, non-positive partial
transpose entanglement, magic, and imaginarity share an interesting property:
An operation is free if and only if its renormalized Choi matrix is a free
state. In this letter, we refer to resource theories exhibiting this property
as Choi-defined resource theories. We demonstrate how and under what conditions
one can construct a Choi-defined resource theory, and we prove that when such a
construction is possible, the free operations are all and only the completely
resource non-generating operations.
Related papers
- Conceptual and formal groundwork for the study of resource dependence relations [0.0]
A resource theory imposes a preorder over states, with one state being above another if the first can be converted to the second by a free operation.
It follows that there can be nontrivial dependence relations between different notions of resourcefulness.
arXiv Detail & Related papers (2024-06-28T18:04:31Z) - Axioms for AI Alignment from Human Feedback [44.51306968484829]
We develop novel rules for learning reward functions with strong axiomatic guarantees.
A key innovation from the standpoint of social choice is that our problem has a linear structure.
arXiv Detail & Related papers (2024-05-23T16:29:29Z) - Resource Theory of Imaginarity: New Distributed Scenarios [48.7576911714538]
imaginarity studies the operational value of imaginary parts in quantum states, operations, and measurements.
This arises naturally in bipartite systems where both parties work together to generate the maximum possible imaginarity on one of the subsystems.
We present a scenario that demonstrates the operational advantage of imaginarity: the discrimination of quantum channels without the aid of an ancillary system.
arXiv Detail & Related papers (2023-01-12T02:05:08Z) - 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) - The Axiom of Choice and the No-Signaling Principle [0.0]
We show that the axiom of choice, a basic yet controversial postulate of set theory, leads to revise the standard understanding of one of the pillars of our best physical theories.
We show-by invoking the axiom of choice-the opposite: Functional (deterministic) no-signaling resources can be stronger than probabilistic ones.
arXiv Detail & Related papers (2022-06-16T22:32:31Z) - 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) - Undecidability in resource theory: can you tell theories apart? [0.0]
We prove that in the context of quantum resource theories this class of problems is undecidable in general.
This is done by proving the undecidability of the membership problem for CPTP maps, which subsumes all the other results.
arXiv Detail & Related papers (2021-05-19T18:03:03Z) - Topological Quantum Gravity of the Ricci Flow [62.997667081978825]
We present a family of topological quantum gravity theories associated with the geometric theory of the Ricci flow.
First, we use BRST quantization to construct a "primitive" topological Lifshitz-type theory for only the spatial metric.
We extend the primitive theory by gauging foliation-preserving spacetime symmetries.
arXiv Detail & Related papers (2020-10-29T06:15:30Z) - Foundations of Reasoning with Uncertainty via Real-valued Logics [70.43924776071616]
We give a sound and strongly complete axiomatization that can be parametrized to cover essentially every real-valued logic.
Our class of sentences are very rich, and each describes a set of possible real values for a collection of formulas of the real-valued logic.
arXiv Detail & Related papers (2020-08-06T02:13:11Z) - Information-based approach towards a unified resource theory [0.0]
Resource theories identify resourceful states and channels that are potentially useful for the accomplishment of tasks that would be otherwise unreachable.
We develop a unifying approach that proves able to encompass several nonclassical aspects, including the newly developed concepts of quantum irreality and realism-based nonlocality.
arXiv Detail & Related papers (2020-01-21T12:53:24Z) - Monotones in General Resource Theories [0.0]
Various constructions of monotones appear in many different resource theories.
Monotones based on contractions arise naturally in the latter class.
We present our results within a novel framework for resource theories in which the notion of composition is independent of the types of the resources involved.
arXiv Detail & Related papers (2019-12-15T18:38:40Z)
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.