Catalytic and asymptotic equivalence for quantum entanglement

• URL: http://arxiv.org/abs/2305.03488v1
• Date: Fri, 5 May 2023 12:57:59 GMT
• Title: Catalytic and asymptotic equivalence for quantum entanglement
• Authors: Ray Ganardi, Tulja Varun Kondra, Alexander Streltsov
• Abstract summary: Many-copy entanglement manipulation procedures allow for highly entangled pure states from noisy states. We show that using an entangled catalyst cannot enhance the singlet distillation rate of a distillable quantum state. Our findings provide a comprehensive understanding of the capabilities and limitations of both catalytic and state transformations of entangled states.
• Score: 68.8204255655161
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Entanglement is a fundamental resource in quantum information processing, yet understanding its manipulation and transformation remains a challenge. Many tasks rely on highly entangled pure states, but obtaining such states is often challenging due to the presence of noise. Typically, entanglement manipulation procedures involving asymptotically many copies of a state are considered to overcome this problem. These procedures allow for distilling highly entangled pure states from noisy states, which enables a wide range of applications, such as quantum teleportation and quantum cryptography. When it comes to manipulating entangled quantum systems on a single copy level, using entangled states as catalysts can significantly broaden the range of achievable transformations. Similar to the concept of catalysis in chemistry, the entangled catalyst is returned unchanged at the end of the state manipulation procedure. Our results demonstrate that despite the apparent conceptual differences between the asymptotic and catalytic settings, they are actually strongly connected and fully equivalent for all distillable states. Our methods rely on the analysis of many-copy entanglement manipulation procedures which may establish correlations between different copies. As an important consequence, we demonstrate that using an entangled catalyst cannot enhance the asymptotic singlet distillation rate of a distillable quantum state. Our findings provide a comprehensive understanding of the capabilities and limitations of both catalytic and asymptotic state transformations of entangled states, and highlight the importance of correlations in these processes.

Related papers

• Second Law of Entanglement Manipulation with Entanglement Battery [41.94295877935867]
  A central question since the beginning of quantum information science is how two distant parties can convert one entangled state into another. It has been conjectured that entangled state transformations could be executed reversibly in an regime, mirroring the nature of Carnot cycles in classical thermodynamics. We investigate the concept of an entanglement battery, an auxiliary quantum system that facilitates quantum state transformations without a net loss of entanglement.
  arXiv  Detail & Related papers  (2024-05-17T07:55:04Z)
• Arbitrary Amplification of Quantum Coherence in Asymptotic and Catalytic Transformation [0.0]
  We show how well one can prepare good coherent states from low coherent states and whether a given coherent state is convertible to another one. For a variant of coherence where one aims to prepare desired states in local subsystems, the rate of transformation becomes unbounded regardless of how weak the initial coherence is. Applying this to the standard setting, we find that a catalyst can increase the coherence rate significantly -- from zero to infinite rate.
  arXiv  Detail & Related papers  (2023-08-23T18:00:02Z)
• No-go theorem for entanglement distillation using catalysis [49.24817625059456]
  We show that catalytic transformations can never allow for the distillation of entanglement from a bound entangled state. This precludes the possibility that entanglement theoryally reversible based operations under even permissive choices.
  arXiv  Detail & Related papers  (2023-05-05T12:57:59Z)
• The power of noisy quantum states and the advantage of resource dilution [62.997667081978825]
  Entanglement distillation allows to convert noisy quantum states into singlets. We show that entanglement dilution can increase the resilience of shared quantum states to local noise.
  arXiv  Detail & Related papers  (2022-10-25T17:39:29Z)
• Catalysis of entanglement and other quantum resources [39.58317527488534]
  Instead of chemical reactions, quantum enhances our ability to convert quantum states into each other under physical constraints. This article reviews the most recent developments in quantum preservation and gives a historical overview of this research direction.
  arXiv  Detail & Related papers  (2022-07-12T17:15:18Z)
• Unconventional mechanism of virtual-state population through dissipation [125.99533416395765]
  We report a phenomenon occurring in open quantum systems by which virtual states can acquire a sizable population in the long time limit. This means that the situation where the virtual state remains unpopulated can be metastable. We show how these results can be relevant for practical questions such as the generation of stable and metastable entangled states in dissipative systems of interacting qubits.
  arXiv  Detail & Related papers  (2022-02-24T17:09:43Z)
• Entanglement catalysis for quantum states and noisy channels [41.94295877935867]
  We investigate properties of entanglement and its role for quantum communication. For transformations between bipartite pure states, we prove the existence of a universal catalyst. We further develop methods to estimate the number of singlets which can be established via a noisy quantum channel.
  arXiv  Detail & Related papers  (2022-02-10T18:36:25Z)
• Catalytic Transformations of Pure Entangled States [62.997667081978825]
  Entanglement entropy is the von Neumann entropy of quantum entanglement of pure states. The relation between entanglement entropy and entanglement distillation has been known only for the setting, and the meaning of entanglement entropy in the single-copy regime has so far remained open. Our results imply that entanglement entropy quantifies the amount of entanglement available in a bipartite pure state to be used for quantum information processing, giving results an operational meaning also in entangled single-copy setup.
  arXiv  Detail & Related papers  (2021-02-22T16:05:01Z)
• Einselection from incompatible decoherence channels [62.997667081978825]
  We analyze an open quantum dynamics inspired by CQED experiments with two non-commuting Lindblad operators. We show that Fock states remain the most robust states to decoherence up to a critical coupling.
  arXiv  Detail & Related papers  (2020-01-29T14:15:19Z)

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.