No-go theorems for deterministic purification and probabilistic enhancement of coherence

• URL: http://arxiv.org/abs/2203.15238v1
• Date: Tue, 29 Mar 2022 05:02:31 GMT
• Title: No-go theorems for deterministic purification and probabilistic enhancement of coherence
• Authors: Qiming Ding and Quancheng Liu
• Abstract summary: We prove that a quantum state cannot be deterministically purified if it can be expressed as a convex combination of an incoherent state and a coherent state. Our findings have repercussions on the understanding of quantum coherence in real quantum systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The manipulation of quantum coherence is one of the principal issues in the resource theory of coherence, with two critical topics being the purification and enhancement of coherence. Here, we present two no-go theorems for the deterministic purification of coherence and the probabilistic enhancement of coherence, respectively. Specifically, we prove that a quantum state cannot be deterministically purified if it can be expressed as a convex combination of an incoherent state and a coherent state. Besides, we give an easy-to-verified sufficient and necessary condition to determine whether a state can be probabilistically enhanced via a stochastic strictly incoherent operation (sSIO). Our findings provide two feasibility criteria for the deterministic purification and the probabilistic enhancement of coherence, respectively. These results have repercussions on the understanding of quantum coherence in real quantum systems.

Related papers

• 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. In 2008, a promising formulation was proposed, linking resource convertibility to the optimal performance of a variant of the quantum version of hypothesis testing. 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)
• Unveiling quantum steering by quantum-classical uncertainty complementarity [0.0]
  We introduce a novel complementarity relation between system's quantum and classical uncertainties. We demonstrate a superior steering detection efficiency compared to an entropic uncertainty relation.
  arXiv  Detail & Related papers  (2023-12-02T07:49:20Z)
• Quantifying quantum coherence via nonreal Kirkwood-Dirac quasiprobability [0.0]
  Kirkwood-Dirac (KD) quasiprobability is a quantum analog of phase space probability of classical statistical mechanics. Recent works have revealed the important roles played by the KD quasiprobability in the broad fields of quantum science and quantum technology.
  arXiv  Detail & Related papers  (2023-09-17T04:34:57Z)
• Quantification of Entanglement and Coherence with Purity Detection [16.01598003770752]
  Entanglement and coherence are fundamental properties of quantum systems, promising to power near future quantum technologies. Here, we demonstrate quantitative bounds to operationally useful entanglement and coherence. Our research offers an efficient means of verifying large-scale quantum information processing.
  arXiv  Detail & Related papers  (2023-08-14T11:03:40Z)
• A Measure-Theoretic Axiomatisation of Causality [55.6970314129444]
  We argue in favour of taking Kolmogorov's measure-theoretic axiomatisation of probability as the starting point towards an axiomatisation of causality. Our proposed framework is rigorously grounded in measure theory, but it also sheds light on long-standing limitations of existing frameworks.
  arXiv  Detail & Related papers  (2023-05-19T13:15:48Z)
• Biorthogonal resource theory of genuine quantum superposition [0.0]
  We introduce a pseudo-Hermitian representation of the density operator, wherein its diagonal elements correspond to biorthogonal extensions of Kirkwood-Dirac quasi-probabilities. This representation provides a unified framework for the inter-basis quantum superposition and basis state indistinguishability, giving rise to what we term as textitgenuine quantum superposition.
  arXiv  Detail & Related papers  (2022-10-05T17:17:37Z)
• Improved Quantum Algorithms for Fidelity Estimation [77.34726150561087]
  We develop new and efficient quantum algorithms for fidelity estimation with provable performance guarantees. Our algorithms use advanced quantum linear algebra techniques, such as the quantum singular value transformation. We prove that fidelity estimation to any non-trivial constant additive accuracy is hard in general.
  arXiv  Detail & Related papers  (2022-03-30T02:02:16Z)
• Non-standard entanglement structure of local unitary self-dual models as a saturated situation of repeatability in general probabilistic theories [61.12008553173672]
  We show the existence of infinite structures of quantum composite system such that it is self-dual with local unitary symmetry. We also show the existence of a structure of quantum composite system such that non-orthogonal states in the structure are perfectly distinguishable.
  arXiv  Detail & Related papers  (2021-11-29T23:37:58Z)
• Creating and destroying coherence with quantum channels [62.997667081978825]
  We study optimal ways to create a large amount of quantum coherence via quantum channels. correlations in multipartite systems do not enhance the ability of a quantum channel to create coherence. We show that a channel can destroy more coherence when acting on a subsystem of a bipartite state.
  arXiv  Detail & Related papers  (2021-05-25T16:44:13Z)
• Quantum indistinguishability through exchangeable desirable gambles [69.62715388742298]
  Two particles are identical if all their intrinsic properties, such as spin and charge, are the same. Quantum mechanics is seen as a normative and algorithmic theory guiding an agent to assess her subjective beliefs represented as (coherent) sets of gambles. We show how sets of exchangeable observables (gambles) may be updated after a measurement and discuss the issue of defining entanglement for indistinguishable particle systems.
  arXiv  Detail & Related papers  (2021-05-10T13:11:59Z)
• Resource theory of quantum coherence with probabilistically non-distinguishable pointers and corresponding wave-particle duality [0.6882042556551611]
  We study the resource theory of quantum coherence with respect to an arbitrary set of quantum state vectors. We identify a class of measures of the quantum coherence, and in particular establish a monotonicity property of the measures. We report a relation between quantum coherence and path complementary distinguishability in a double-slit set-up.
  arXiv  Detail & Related papers  (2020-05-17T16:56:31Z)

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.