Continuous-Variable Quantum MacWilliams Identities

• URL: http://arxiv.org/abs/2502.09514v2
• Date: Thu, 27 Mar 2025 12:58:13 GMT
• Title: Continuous-Variable Quantum MacWilliams Identities
• Authors: Ansgar G. Burchards,
• Abstract summary: We derive bounds on general quantum error correcting codes against the displacement noise channel.<n>We argue that Gottesman--Kitaev--Preskill codes based on the $E_8$ and Leech lattices achieve optimal distances.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We derive bounds on general quantum error correcting codes against the displacement noise channel. The bounds limit the distances attainable by codes and also apply in an approximate setting. Our main result is a quantum analogue of the classical Cohn-Elkies bound on sphere packing densities attainable in Euclidean space. We further derive a quantum version of Levenshtein's sphere packing bound and argue that Gottesman--Kitaev--Preskill (GKP) codes based on the $E_8$ and Leech lattices achieve optimal distances. The main technical tool is a continuous-variable version of the quantum MacWilliams identities, which we introduce. The identities relate a pair of weight distributions which can be obtained for any two trace-class operators. General properties of these weight distributions are discussed, along with several examples.

Related papers

• Topological control of quantum speed limits [55.2480439325792]
  We show that even if the quantum state is completely dispersionless, QFI in this state remains momentum-resolved.<n>We find bounds on quantum speed limit which scales as $sqrt|C|$ in a (dispersionless) topological phase.
  arXiv  Detail & Related papers  (2025-07-21T18:00:07Z)
• Quantum Hypothesis Testing Lemma for Deterministic Identification over Quantum Channels [49.126395046088014]
  We show that the existence of a DI code in the quantum setting follows from a suitable packing in a modified space of output quantum states. This result enables us to tighten the capacity lower bound for DI over quantum channels beyond the simultaneous decoding approach.
  arXiv  Detail & Related papers  (2025-04-29T17:57:36Z)
• Exact path integrals on half-line in quantum cosmology with a fluid clock and aspects of operator ordering ambiguity [0.0]
  We perform $textitexact$ half-line path integral quantization of flat, homogeneous cosmological models containing a perfect fluid acting as an internal clock. We argue that a particular ordering prescription in the quantum theory can preserve two symmetries.
  arXiv  Detail & Related papers  (2025-01-20T19:00:02Z)
• The multimode conditional quantum Entropy Power Inequality and the squashed entanglement of the extreme multimode bosonic Gaussian channels [53.253900735220796]
  Inequality determines the minimum conditional von Neumann entropy of the output of the most general linear mixing of bosonic quantum modes. Bosonic quantum systems constitute the mathematical model for the electromagnetic radiation in the quantum regime.
  arXiv  Detail & Related papers  (2024-10-18T13:59:50Z)
• Normal quantum channels and Markovian correlated two-qubit quantum errors [77.34726150561087]
  We study general normally'' distributed random unitary transformations. On the one hand, a normal distribution induces a unital quantum channel. On the other hand, the diffusive random walk defines a unital quantum process.
  arXiv  Detail & Related papers  (2023-07-25T15:33:28Z)
• Quantum soft-covering lemma with applications to rate-distortion coding, resolvability and identification via quantum channels [7.874708385247353]
  We prove a one-shot quantum covering lemma in terms of smooth min-entropies. We provide new upper bounds on the unrestricted and simultaneous identification capacities of quantum channels.
  arXiv  Detail & Related papers  (2023-06-21T17:53:22Z)
• Entanglement measures for two-particle quantum histories [0.0]
  We prove that bipartite quantum histories are entangled if and only if the Schmidt rank of this matrix is larger than 1. We then illustrate the non-classical nature of entangled histories with the use of Hardy's overlapping interferometers.
  arXiv  Detail & Related papers  (2022-12-14T20:48:36Z)
• Quantum dynamics corresponding to chaotic BKL scenario [62.997667081978825]
  Quantization smears the gravitational singularity avoiding its localization in the configuration space. Results suggest that the generic singularity of general relativity can be avoided at quantum level.
  arXiv  Detail & Related papers  (2022-04-24T13:32:45Z)
• 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)
• Singleton Bounds for Entanglement-Assisted Classical and Quantum Error Correcting Codes [0.0]
  We show that entirely quantum Shannon theoretic methods can be used to derive Singleton bounds on the performance of EACQ error correcting codes. We show that a large part of this region is attainable by certain EACQ codes, whenever the local alphabet size is large enough.
  arXiv  Detail & Related papers  (2022-02-04T15:22:18Z)
• 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)
• 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)
• The Quantum Wasserstein Distance of Order 1 [16.029406401970167]
  We propose a generalization of the Wasserstein distance of order 1 to the quantum states of $n$ qudits. The proposed distance is invariant with respect to permutations of the qudits and unitary operations acting on one qudit. We also propose a generalization of the Lipschitz constant to quantum observables.
  arXiv  Detail & Related papers  (2020-09-09T18:00:01Z)
• Describing quantum metrology with erasure errors using weight distributions of classical codes [9.391375268580806]
  We consider using quantum probe states with a structure that corresponds to classical $[n,k,d]$ binary block codes of minimum distance. We obtain bounds on the ultimate precision that these probe states can give for estimating the unknown magnitude of a classical field.
  arXiv  Detail & Related papers  (2020-07-06T16:22:40Z)
• Using Quantum Metrological Bounds in Quantum Error Correction: A Simple Proof of the Approximate Eastin-Knill Theorem [77.34726150561087]
  We present a proof of the approximate Eastin-Knill theorem, which connects the quality of a quantum error-correcting code with its ability to achieve a universal set of logical gates. Our derivation employs powerful bounds on the quantum Fisher information in generic quantum metrological protocols.
  arXiv  Detail & Related papers  (2020-04-24T17:58:10Z)

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.