Pith Number

pith:R77H3U5Y

pith:2026:R77H3U5YMSRMPJEEAOBHKMQM4N

not attested not anchored not stored refs resolved

No-cloning with unitary scaling

Dafa Li

It is impossible to produce a U-copy of an arbitrary unknown quantum pure state using unitary evolution.

arxiv:2604.22960 v2 · 2026-04-24 · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{R77H3U5YMSRMPJEEAOBHKMQM4N}

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

we call U |ψ>, where U is any unitary operator, a U-copy of the state |ψ> and show it is impossible to make a U-copy of an arbitrary unknown quantum pure state by using unitary evolution.

C2weakest assumption

The definition of a U-copy as simply U|ψ> for a fixed unitary U independent of the unknown state |ψ>, combined with the restriction to unitary evolution on the composite system, as introduced in the abstract.

C3one line summary

It is impossible to produce a U-copy of an arbitrary unknown quantum pure state using unitary evolution.

References

8 extracted · 8 resolved · 1 Pith anchors

[1] W. K. Wootters and W. H. Zurek. A Single quantum cannot be cloned. Nature 299, 802-803 (1982) 1982

[2] Nielsen, Chuang, I.L.:Quantum Computation and Quantum Informa- tion(Cambridge Univ 2000

[3] Two non-orthogonal states can be cloned by a unitary-reduction process 1998 · arXiv:quant-ph/9704020

[4] Bennett et al., Phys.Rev.A 1996

[5] : A. R. Calderbank, Peter W. Shor, Phys. Rev. A, Vol. 54, No. 2, pp. 1098- 1106, 1996 1996

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-20T00:01:42.058503Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8ffe7dd3b864a2c7a484038275320ce35d96f37c0074659ceb43ec3189077345

Aliases

arxiv: 2604.22960 · arxiv_version: 2604.22960v2 · doi: 10.48550/arxiv.2604.22960 · pith_short_12: R77H3U5YMSRM · pith_short_16: R77H3U5YMSRMPJEE · pith_short_8: R77H3U5Y

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/R77H3U5YMSRMPJEEAOBHKMQM4N \
  | 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: 8ffe7dd3b864a2c7a484038275320ce35d96f37c0074659ceb43ec3189077345

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e4c489caa1d85abafd9696c07b00f33595d30635f1e5d56c9adfa7c2830e3cf5",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-04-24T19:03:39Z",
    "title_canon_sha256": "aa563e5fd23b2fde9c86664a4927a1b1d3d64bc6c0b3ed61de9fab14167f0060"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.22960",
    "kind": "arxiv",
    "version": 2
  }
}