Special features of the Weyl-Heisenberg Bell basis imply unusual entanglement structure of Bell-diagonal states

• URL: http://arxiv.org/abs/2307.10727v2
• Date: Wed, 17 Jan 2024 12:32:15 GMT
• Title: Special features of the Weyl-Heisenberg Bell basis imply unusual entanglement structure of Bell-diagonal states
• Authors: Christopher Popp and Beatrix C. Hiesmayr
• Abstract summary: We show that a standard construction of a complete orthonormal Bell-basis by Weyl-Heisenberg operators has strong implication on error correction schemes. In particular, it implies a equivalence between a Pauli channel and a twirl channel. Other complete orthonormal Bell-bases do break the equivalence and lead to a completely different entanglement structure.
• Score: 0.021756081703276
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Maximally entangled Bell states are of crucial importance for entanglement based methods in quantum information science. Typically, a standard construction of a complete orthonormal Bell-basis by Weyl-Heisenberg operators is considered. We show that the group structure of these operators has strong implication on error correction schemes and on the entanglement structure within Bell-diagonal states. In particular, it implies a equivalence between a Pauli channel and a twirl channel. Interestingly, other complete orthonormal Bell-bases do break the equivalence and lead to a completely different entanglement structure, for instance in the share of PPT-entangled states. In detail, we find that the standard Bell basis has the highest observed share on PPT-states and PPT-entangled states compared to other Bell bases. In summary, our findings show that the standard Bell basis construction exploits a very special structure with strong implications to quantum information theoretic protocols if a deviation is considered.

Related papers

• Bell Nonlocality from Wigner Negativity in Qudit Systems [1.2499537119440245]
  We show that Wigner negativity is necessary for nonlocality in qudit systems. We propose a family of Bell inequalities that inquire correlations related to Wigner negativity of stabilizer states.
  arXiv  Detail & Related papers  (2024-05-23T09:44:36Z)
• Quantum resource theory of Bell nonlocality in Hilbert space [0.0]
  We introduce a Hilbert space based resource theory of Bell nonlocality with the aim of providing bona fide measures of quantum nonlocality. We construct our theory by defining the set of local (or free) states, i.e., the states that do not violate the Clauser-Horne-Shimony-Holt inequality. We illustrate the general resource theory so developed by applying it to specific classes of quantum states, including two-qubit Werner states, Bell-diagonal states, and Bell-diagonal states at fixed convexity.
  arXiv  Detail & Related papers  (2023-11-03T14:26:58Z)
• The distinctive symmetry of Bell states [65.268245109828]
  The Bell's basis is composed of four maximally entangled states of two qubits. The aim of this paper is to find out the symmetries that determine a Bell state.
  arXiv  Detail & Related papers  (2023-08-14T17:02:41Z)
• Derivation of Standard Quantum Theory via State Discrimination [53.64687146666141]
  General Probabilistic Theories (GPTs) is a new information theoretical approach to single out standard quantum theory. We focus on the bound of the performance for an information task called state discrimination in general models. We characterize standard quantum theory out of general models in GPTs by the bound of the performance for state discrimination.
  arXiv  Detail & Related papers  (2023-07-21T00:02:11Z)
• Genuine Bell locality and nonlocality in the networks [0.0]
  Local hidden variables are strictly distributed in the specific observers rather than the whole ones. Moreors are involved in the proposed linear and non-linear Bell-type inequalities. How entanglement swapping replaces the joint measurements in the Bell tests is demonstrated.
  arXiv  Detail & Related papers  (2022-09-23T04:23:16Z)
• Pseudo standard entanglement structure cannot be distinguished from standard entanglement structure [61.12008553173672]
  An experimental verification of the maximally entangled state does not guarantee that the state is exactly the same as the maximally entangled state. In our setting, any maximally entangled state can be arbitrarily approximated by an entangled state that belongs to our obtained pseudo standard entanglement structure.
  arXiv  Detail & Related papers  (2022-03-15T14:56:43Z)
• 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)
• Bell nonlocality in networks [62.997667081978825]
  Bell's theorem proves that quantum theory is inconsistent with local physical models. In the last decade, the investigation of nonlocality has moved beyond Bell's theorem to consider more sophisticated experiments. This review discusses the main concepts, methods, results and future challenges in the emerging topic of Bell nonlocality in networks.
  arXiv  Detail & Related papers  (2021-04-21T18:00:48Z)
• Bilocal Bell inequalities violated by the quantum Elegant Joint Measurement [0.0]
  We investigate the simplest network, known as the bilocality scenario. We report noise-tolerant quantum correlations that elude bilocal variable models. We pave the way for an experimental realisation by presenting a simple two-qubit quantum circuit.
  arXiv  Detail & Related papers  (2020-06-30T11:32:26Z)
• One-Way LOCC Indistinguishable Lattice States via Operator Structures [0.0]
  We develop a technique for the construction of relatively small sets of lattice states not distinguishable by one-way LOCC schemes. We show examples, show the construction extends to generalized Pauli states, and compare the construction to other recent work.
  arXiv  Detail & Related papers  (2020-04-24T14:37:56Z)
• Quantum Mechanical description of Bell's experiment assumes Locality [91.3755431537592]
  Bell's experiment description assumes the (Quantum Mechanics-language equivalent of the classical) condition of Locality. This result is complementary to a recently published one demonstrating that non-Locality is necessary to describe said experiment. It is concluded that, within the framework of Quantum Mechanics, there is absolutely no reason to believe in the existence of non-Local effects.
  arXiv  Detail & Related papers  (2020-02-27T15:04:08Z)

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.