Inverse Problem of Alchemical Resource Theory: Replication and Programming Single Out Imaginarity and Parity Asymmetry

• URL: http://arxiv.org/abs/2609.12988v1
• Date: Fri, 11 Sep 2026 15:52:01 GMT
• Title: Inverse Problem of Alchemical Resource Theory: Replication and Programming Single Out Imaginarity and Parity Asymmetry
• Abstract summary: We study the inverse problem of alchemical resource theories, which we define as resource theories admitting a resource that can both replicate itself exactly and universally program quantum instruments.<n>We show that for qubit single systems only two nontrivial universality theories survive, up to a common local unitary change of basis: parity asymmetry and imaginarity.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum resource theories usually begin with a prescribed free structure and ask what tasks become possible when a resource is supplied. We study the inverse problem of alchemical resource theories, which we define as resource theories admitting a resource that can both replicate itself exactly and universally program quantum instruments. Under natural consistency assumptions and branchwise complete freeness, we show that for qubit single systems only two nontrivial theories survive, up to a common local unitary change of basis: parity asymmetry and imaginarity. We further show that exact universality exhibits an all-or-nothing trade-off: any nonmaximal resource state can exactly program only free unitaries. These results demonstrate that prescribed operational capabilities can strongly constrain the underlying resource structure and reveal a fundamental trade-off between computational capability and the precision required for physical implementation.

Related papers

• Polytopic Quantum Resource Theories: Geometry and Structures [0.09851812512860353]
  Quantum resource theories provide a unifying framework to quantify, compare, manipulate quantum resources under well-defined operational constraints.<n>Here, we consider any resource theory where the set of free states can be expressed as a combination of a set of quantum states.<n>We formulate a novel representation of PQRTs that reveals the underlying geometry of these theories.
  arXiv  Detail & Related papers  (2026-05-29T23:41:04Z)
• Manipulating heterogeneous quantum resources over a network [0.0]
  Quantum information processing relies on a variety of resources, including entanglement, coherence, non-Gaussianity, and magic.<n>In realistic settings, protocols run on networks of parties with heterogeneous local resource constraints, so different resources coexist and interact.<n>We develop a unified framework for composite quantum resource theories that describes distributed networks of locally constrained parties.
  arXiv  Detail & Related papers  (2026-02-19T20:11:32Z)
• From Atomic to Composite: Reinforcement Learning Enables Generalization in Complementary Reasoning [83.94543243783285]
  We study Complementary Reasoning, a complex task that requires integrating internal parametric knowledge with external contextual information.<n>We find that RL acts as a reasoning synthesizer rather than a probability amplifier.
  arXiv  Detail & Related papers  (2025-12-01T18:27:25Z)
• Universal tradeoff relations between resource cost and irreversibility of channels: General-resource Wigner-Araki-Yanase theorems and beyond [0.0]
  We show a universal relation between the energetic cost and the irreversibility for arbitrary channels.<n>We extend the energy-error tradeoff to free energy and work costs.<n>These findings reveal a universal relationship between quantumness and irreversibility.
  arXiv  Detail & Related papers  (2025-07-31T17:48:14Z)
• Generalized Quantum Stein's Lemma and Second Law of Quantum Resource Theories [47.02222405817297]
  A fundamental question in quantum information theory is whether an analogous second law can be formulated to characterize the convertibility of resources for quantum information processing by a single function.<n>In 2008, a promising formulation was proposed, linking resource convertibility to the optimal performance of a variant of the quantum version of hypothesis testing.<n>In 2023, a logical gap was found in the original proof of this lemma, casting doubt on the possibility of such a formulation of the second law.
  arXiv  Detail & Related papers  (2024-08-05T18:00:00Z)
• Is there a finite complete set of monotones in any quantum resource theory? [39.58317527488534]
  We show that there does not exist a finite set of resource monotones which completely determines all state transformations. We show that totally ordered theories allow for free transformations between all pure states.
  arXiv  Detail & Related papers  (2022-12-05T18:28:36Z)
• 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)
• Investigating the Global Properties of a Resource Theory of Contextuality [0.0]
  We will investigate some properties of a resource theory for quantum contextuality. This characteristic ensures the impossibility of interpreting the results of quantum measurements as revealing properties that are independent of the set of measurements being made. We will use the so called cost and yield monotones, extending the results of reference Quantum 4, 280 ( 2020) to general contextuality scenarios.
  arXiv  Detail & Related papers  (2022-10-07T00:33:49Z)
• Stochastic approximate state conversion for entanglement and general quantum resource theories [41.94295877935867]
  An important problem in any quantum resource theory is to determine how quantum states can be converted into each other. Very few results have been presented on the intermediate regime between probabilistic and approximate transformations. We show that these bounds imply an upper bound on the rates for various classes of states under probabilistic transformations. We also show that the deterministic version of the single copy bounds can be applied for drawing limitations on the manipulation of quantum channels.
  arXiv  Detail & Related papers  (2021-11-24T17:29:43Z)
• 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)
• Resource theory of imaginarity: Quantification and state conversion [48.7576911714538]
  Resource theory of imaginarity has been introduced, allowing for a systematic study of complex numbers in quantum mechanics and quantum information theory. We investigate imaginarity quantification, focusing on the geometric imaginarity and the robustness of imaginarity, and apply these tools to the state conversion problem in imaginarity theory. Our study reveals the significance of complex numbers in quantum physics, and proves that imaginarity is a resource in optical experiments.
  arXiv  Detail & Related papers  (2021-03-02T15:30:27Z)
• Operational Resource Theory of Imaginarity [48.7576911714538]
  We show that quantum states are easier to create and manipulate if they only have real elements. As an application, we show that imaginarity plays a crucial role for state discrimination.
  arXiv  Detail & Related papers  (2020-07-29T14:03:38Z)
• General Quantum Resource Theories: Distillation, Formation and Consistent Resource Measures [3.8073142980733]
  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 intractable mathematical structure to analyze, such as non-uniqueness of maximally resourceful states, lack of convexity, and infinite dimension. We investigate state conversion and resource measures in general QRTs under minimal assumptions to figure out universal properties of physically motivated quantum resources.
  arXiv  Detail & Related papers  (2020-02-06T19:00:01Z)

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.