Contextuality of Quantum Error-Correcting Codes

• URL: http://arxiv.org/abs/2502.02553v1
• Date: Tue, 04 Feb 2025 18:23:24 GMT
• Title: Contextuality of Quantum Error-Correcting Codes
• Authors: Derek Khu, Andrew Tanggara, Kishor Bharti,
• Abstract summary: We establish the first direct link between contextuality and quantum error-correcting codes. We prove the equivalence of contextuality definitions from Abramsky--Brandenburger's sheaf-theoretic framework. We show that subsystem stabilizer codes with two or more gauge qubits are strongly contextual, while others are noncontextual.
• Score: 0.0
• License:
• Abstract: Quantum error correction is vital for fault-tolerant quantum computation, with deep connections to entanglement, magic, and uncertainty relations. Entanglement, for instance, has driven key advances like surface codes and has deepened our understanding of quantum gravity through holographic quantum codes. While these connections are well-explored, the role of contextuality, a fundamental non-classical feature of quantum theory, remains unexplored. Notably, Bell nonlocality is a special case of contextuality, and prior works have established contextuality as a key resource for quantum computational advantage. In this work, we establish the first direct link between contextuality and quantum error-correcting codes. Using a sheaf-theoretic framework, we define contextuality for such codes and prove key results on its manifestation. Specifically, we prove the equivalence of contextuality definitions from Abramsky--Brandenburger's sheaf-theoretic framework and Kirby--Love's tree-based approach for the partial closure of Pauli measurement sets. We present several findings, including the proof of a conjecture by Kim and Abramsky [1]. We further show that subsystem stabilizer codes with two or more gauge qubits are strongly contextual, while others are noncontextual. Our findings reveal a direct connection between contextuality and quantum error correction, offering new insights into the non-classical resources enabling fault-tolerant quantum computation.

Related papers

• Quantum Information Processing, Sensing and Communications: Their Myths, Realities and Futures [61.25494706587422]
  The state-of-the-art, knowledge gaps and future evolution of quantum machine learning are discussed. We conclude with a set of promising future research ideas in the field of ultimately secure quantum communications.
  arXiv  Detail & Related papers  (2024-12-01T22:28:02Z)
• Characterizing Contextuality via Rank Separation with Applications to Cloning [0.0]
  Quantum contextuality is a key nonclassical feature essential for understanding advantages in quantum computation and communication. We introduce a new framework to study contextuality based solely on information processing statistics. We show that quantum contextuality provides the resource in optimal phase-covariant and universal cloning schemes.
  arXiv  Detail & Related papers  (2024-06-27T17:56:04Z)
• A computational test of quantum contextuality, and even simpler proofs of quantumness [43.25018099464869]
  We show that an arbitrary contextuality game can be compiled into an operational "test of contextuality" involving a single quantum device. Our work can be seen as using cryptography to enforce spatial separation within subsystems of a single quantum device.
  arXiv  Detail & Related papers  (2024-05-10T19:30:23Z)
• Classical Verification of Quantum Learning [42.362388367152256]
  We develop a framework for classical verification of quantum learning. We propose a new quantum data access model that we call "mixture-of-superpositions" quantum examples. Our results demonstrate that the potential power of quantum data for learning tasks, while not unlimited, can be utilized by classical agents.
  arXiv  Detail & Related papers  (2023-06-08T00:31:27Z)
• Experimental investigation of quantum uncertainty relations with classical shadows [7.675613458661457]
  We experimentally investigate quantum uncertainty relations construed with relative entropy of coherence. We prepare a family of quantum states whose purity can be fully controlled. Our results indicate the tightness of quantum coherence lower bounds dependents on the reference bases as well as the purity of quantum state.
  arXiv  Detail & Related papers  (2022-02-14T00:26:31Z)
• Interactive Protocols for Classically-Verifiable Quantum Advantage [46.093185827838035]
  "Interactions" between a prover and a verifier can bridge the gap between verifiability and implementation. We demonstrate the first implementation of an interactive quantum advantage protocol, using an ion trap quantum computer.
  arXiv  Detail & Related papers  (2021-12-09T19:00:00Z)
• Experimental violations of Leggett-Garg's inequalities on a quantum computer [77.34726150561087]
  We experimentally observe the violations of Leggett-Garg-Bell's inequalities on single and multi-qubit systems. Our analysis highlights the limits of nowadays quantum platforms, showing that the above-mentioned correlation functions deviate from theoretical prediction as the number of qubits and the depth of the circuit grow.
  arXiv  Detail & Related papers  (2021-09-06T14:35:15Z)
• Quantum Causal Inference in the Presence of Hidden Common Causes: an Entropic Approach [34.77250498401055]
  We put forth a new theoretical framework for merging quantum information science and causal inference by exploiting entropic principles. We apply our proposed framework to an experimentally relevant scenario of identifying message senders on quantum noisy links. This approach can lay the foundations of identifying originators of malicious activity on future multi-node quantum networks.
  arXiv  Detail & Related papers  (2021-04-24T22:45:50Z)
• Quantum Entropic Causal Inference [30.939150842529052]
  We put forth a new theoretical framework for merging quantum information science and causal inference by exploiting entropic principles. We apply our proposed framework to an experimentally relevant scenario of identifying message senders on quantum noisy links.
  arXiv  Detail & Related papers  (2021-02-23T15:51:34Z)
• Formalization of Bohr's contextuality within theory of open quantum systems [0.0]
  Bohr was the first who pointed to contextuality of quantum measurements. The original Bohr's contextuality, as contextuality of each quantum measurement, was practically forgotten. This note is applied to formalization of Bohr's contextuality within the the scheme of indirect measurements.
  arXiv  Detail & Related papers  (2021-02-18T06:59:56Z)
• Secure Two-Party Quantum Computation Over Classical Channels [63.97763079214294]
  We consider the setting where the two parties (a classical Alice and a quantum Bob) can communicate only via a classical channel. We show that it is in general impossible to realize a two-party quantum functionality with black-box simulation in the case of malicious quantum adversaries. We provide a compiler that takes as input a classical proof of quantum knowledge (PoQK) protocol for a QMA relation R and outputs a zero-knowledge PoQK for R that can be verified by classical parties.
  arXiv  Detail & Related papers  (2020-10-15T17:55:31Z)

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.