pith:MGWAO3HY
Mixed-State Long-Range Entanglement from Dimensional Constraints
Maximally mixed states on translation-invariant subspaces of a 1D ring are long-range entangled due to subspace dimension mismatch.
arxiv:2605.15201 v1 · 2026-05-14 · quant-ph · cond-mat.stat-mech · cond-mat.str-el
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Claims
This state is LRE because translationally symmetric short-range entangled states span a subspace whose dimension grows only polynomially with system size, whereas the full translation-invariant subspace grows exponentially.
That the dimension of the translationally symmetric short-range entangled subspace grows only polynomially with system size while the full translation-invariant subspace grows exponentially, and that this dimensional mismatch directly implies long-range entanglement in the maximally mixed state.
The maximally mixed state in the translation-invariant subspace of a 1D ring is long-range entangled because the dimension of translationally symmetric short-range entangled states grows polynomially while the full subspace grows exponentially.
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| First computed | 2026-05-17T21:40:24.930488Z |
|---|---|
| Last reissued | 2026-05-18T12:28:38.357277Z |
| Builder | pith-number-builder-2026-05-17-v1 |
| Signature | Pith Ed25519
(pith-v1-2026-05) · public key |
| Schema | pith-number/v1.0 |
Canonical hash
61ac076cf8e8d99b1dcc68338cc22260df2550aef08c8069b0f61fdb7aa2371d
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curl -sH 'Accept: application/ld+json' https://pith.science/pith/MGWAO3HY5DMZWHOMNAZYZQRCMD \
| 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: 61ac076cf8e8d99b1dcc68338cc22260df2550aef08c8069b0f61fdb7aa2371d
Canonical record JSON
{
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"license": "http://creativecommons.org/licenses/by-sa/4.0/",
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"submitted_at": "2026-05-14T17:59:59Z",
"title_canon_sha256": "bb8a51666dc4b47de73d8a109554800164809cdbf8e326515438dc13823087b7"
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