Pith Number

pith:SIKKWVFN

pith:2026:SIKKWVFNATNIPAS265PJB666KG

not attested not anchored not stored refs pending

Quantum Bayesian Networks: Compositionality and Typing via Linear Logic

Claudia Faggian, R\'emi Di Guardia, Thomas Ehrhard

Quantum Bayesian networks receive a compositional semantics and linear-logic typing that reduces to standard Bayesian networks for classical data and to tensor networks for quantum data.

arxiv:2604.26059 v2 · 2026-04-28 · cs.LO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SIKKWVFNATNIPAS265PJB666KG}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

A key feature of our compositional semantics is that when all causes are classical, it coincides with the standard factor-based semantics of Bayesian networks, while in the purely quantum case it reduces to tensor networks. We then propose a typed formalism based on linear logic proof-nets, where types ensure well-behaved composition of systems.

C2weakest assumption

That the proposed linear-logic typing and compositional semantics correctly capture all causal relations and measurement probabilities in mixed classical-quantum systems without requiring extra constraints or losing expressiveness.

C3one line summary

Quantum Bayesian networks receive a compositional semantics and linear-logic typing that reduces to standard Bayesian networks for classical data and to tensor networks for quantum data.

Receipt and verification

First computed	2026-05-27T01:05:55.127839Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9214ab54ad04da87825af75e90fbde518e3efa02b8cb87fc39702b2986ef9b07

Aliases

arxiv: 2604.26059 · arxiv_version: 2604.26059v2 · doi: 10.48550/arxiv.2604.26059 · pith_short_12: SIKKWVFNATNI · pith_short_16: SIKKWVFNATNIPAS2 · pith_short_8: SIKKWVFN

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/SIKKWVFNATNIPAS265PJB666KG \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 9214ab54ad04da87825af75e90fbde518e3efa02b8cb87fc39702b2986ef9b07

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2c025ae9db2b2d9a7952c1b346a1e1151c984808b4d3219999a3446aedd5a022",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LO",
    "submitted_at": "2026-04-28T18:55:47Z",
    "title_canon_sha256": "83c5ff879a76ab9a4788594e174323796967178dcfcb5edca6a9960c1bc002d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.26059",
    "kind": "arxiv",
    "version": 2
  }
}