Belief Propagation with Quantum Messages for Symmetric Q-ary Pure-State Channels

• URL: http://arxiv.org/abs/2601.21330v1
• Date: Thu, 29 Jan 2026 06:47:18 GMT
• Title: Belief Propagation with Quantum Messages for Symmetric Q-ary Pure-State Channels
• Abstract summary: Belief propagation with quantum messages (BPQM) provides a low-complexity alternative to collective measurements for communication over classical--quantum channels.<n>Here, we generalize BPQM to symmetric q-ary pure-state channels whose output Gram matrix is circulant.<n>This provides a DE framework for symmetric q-ary PSCs that allows one to estimate BPQM decoding thresholds for LDPC codes.
• Score: 5.8151438956682115
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Belief propagation with quantum messages (BPQM) provides a low-complexity alternative to collective measurements for communication over classical--quantum channels. Prior BPQM constructions and density-evolution (DE) analyses have focused on binary alphabets. Here, we generalize BPQM to symmetric q-ary pure-state channels (PSCs) whose output Gram matrix is circulant. For this class, we show that bit-node and check-node combining can be tracked efficiently via closed-form recursions on the Gram-matrix eigenvalues, independent of the particular physical realization of the output states. These recursions yield explicit BPQM unitaries and analytic bounds on the fidelities of the combined channels in terms of the input-channel fidelities. This provides a DE framework for symmetric q-ary PSCs that allows one to estimate BPQM decoding thresholds for LDPC codes and to construct polar codes on these channels.

Related papers

• Quantum Message Passing Convergence and Vanishing Block-Error Probability for Random LDPC Codes [9.855041870231533]
  Belief propagation with quantum messages (BPQM) is a quantum algorithm that decodes classical codes transmitted over classical--quantum channels.<n>We construct a two-stage BPQM decoder for random $q$-ary LDPC codes over symmetric $q$-ary pure-state channels.<n>We prove that its ensemble-average block-error probability vanishes as the blocklength $N$ tends to infinity.
  arXiv  Detail & Related papers  (2026-09-05T03:36:03Z)
• Quantum Key Distribution Without Shared Reference Frame Under Unital Noise [42.7789646649633]
  We consider a general and practical scenario of quantum key distribution (QKD) over an unknown, stationary, unital qubit channel.<n>We propose two methods to overcome the physical qubit noise and the lack of shared reference frame.
  arXiv  Detail & Related papers  (2026-06-22T12:24:11Z)
• Entanglement Fidelity in Standard Quantum Channels [7.792020418343022]
  Entanglement fidelity quantifies how well a quantum channel preserves the correlations between a transmitted system and an inaccessible reference system.<n>We derive closed-form expressions for the entanglement fidelity associated with several standard quantum noise models.
  arXiv  Detail & Related papers  (2026-03-08T18:50:15Z)
• Design and Optimization of Adaptive Diversity Schemes in Quantum MIMO Channels [45.812053169933705]
  We study an adaptive diversity strategy for discrete-variable QuMIMO systems based on universal asymmetric cloning at the transmitter and probabilistic purification at the receiver.<n>Results show that the proposed scheme yields significant fidelity gains in crosstalk-dominated settings and automatically adapts to channel symmetry and channel conditions.<n>This work provides design guidelines for future QuMIMO systems and establishes a robust baseline for more advanced transmission and decoding strategies.
  arXiv  Detail & Related papers  (2025-11-19T15:58:10Z)
• Quantum Hypothesis Testing Lemma for Deterministic Identification over Quantum Channels [49.126395046088014]
  This work shows that the existence of a DI code in the quantum setting follows from a suitable packing in a modified space of output quantum states.<n>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)
• Quantum code division multiple access based continuous-variable quantum key distribution [2.3020018305241337]
  We propose a quantum code division multiple access (q-CDMA) based continuous-variable quantum key distribution (CV-QKD) system.<n>In the proposed system, the quantum states of two senders ($textAlice_1,2$) are chaotically encoded through chaotic phase shifters and then transmitted over a quantum channel.<n>We characterize the input-output relation of the quadrature between the two senders and receivers and then analyze the secret key rate (SKR) of the q-CDMA-based CV-QKD system.
  arXiv  Detail & Related papers  (2025-02-13T07:14:57Z)
• Quantum Communication and Mixed-State Order in Decohered Symmetry-Protected Topological States [2.5070297884580874]
  We investigate the ability to transmit quantum information using decohered SPT states. This perspective leads to the identification of a class of quantum channels. We quantify the ability to transmit quantum information in decohered SPT states through the coherent quantum information.
  arXiv  Detail & Related papers  (2024-05-09T17:59:05Z)
• Quantum reservoir computing in finite dimensions [4.903263899016404]
  This paper shows that alternative representations can provide better insights when dealing with design and assessment questions.<n>It is shown that these vector representations yield state-affine systems previously introduced in the classical reservoir computing literature.
  arXiv  Detail & Related papers  (2022-12-01T09:58:03Z)
• Symmetric Pruning in Quantum Neural Networks [111.438286016951]
  Quantum neural networks (QNNs) exert the power of modern quantum machines. QNNs with handcraft symmetric ansatzes generally experience better trainability than those with asymmetric ansatzes. We propose the effective quantum neural tangent kernel (EQNTK) to quantify the convergence of QNNs towards the global optima.
  arXiv  Detail & Related papers  (2022-08-30T08:17:55Z)
• Belief Propagation with Quantum Messages for Symmetric Classical-Quantum Channels [6.831109886531548]
  In 2016, Renes introduced a belief propagation with quantum messages (BPQM) We propose an extension of BPQM to general binary-input symmetric classical-quantum (BSCQ) channels based on the implementation of a symmetric "paired measurement"
  arXiv  Detail & Related papers  (2022-07-11T16:14:49Z)
• Three-fold way of entanglement dynamics in monitored quantum circuits [68.8204255655161]
  We investigate the measurement-induced entanglement transition in quantum circuits built upon Dyson's three circular ensembles. We obtain insights into the interplay between the local entanglement generation by the gates and the entanglement reduction by the measurements.
  arXiv  Detail & Related papers  (2022-01-28T17:21:15Z)
• Coherent control and distinguishability of quantum channels via PBS-diagrams [59.94347858883343]
  We introduce a graphical language for coherent control of general quantum channels inspired by practical quantum optical setups involving polarising beam splitters (PBS) We characterise the observational equivalence of purified channels in various coherent-control contexts, paving the way towards a faithful representation of quantum channels under coherent control.
  arXiv  Detail & Related papers  (2021-03-02T22:56:25Z)
• Sampling Overhead Analysis of Quantum Error Mitigation: Uncoded vs. Coded Systems [69.33243249411113]
  We show that Pauli errors incur the lowest sampling overhead among a large class of realistic quantum channels. We conceive a scheme amalgamating QEM with quantum channel coding, and analyse its sampling overhead reduction compared to pure QEM.
  arXiv  Detail & Related papers  (2020-12-15T15:51:27Z)
• Quasi-probability distributions in Loop Quantum Cosmology [0.0]
  We introduce a complete family of parametrized quasi-probability distributions in phase space and their corresponding Weyl quantization maps. We expect our results may serve to analyze several fundamental aspects within the Loop Quantum Cosmology program.
  arXiv  Detail & Related papers  (2020-07-02T18:05:32Z)
• 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.