Pith Number

pith:EO6FEDBC

pith:2026:EO6FEDBCBGS2Z3VR2HUOXO5U5E

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Additivity Results for the R\'enyi-2 Entanglement of Purification

Shokoufe Faraji, Zahra Baghali Khanian

A simple algebraic condition on quantum maps makes the Rényi-2 entanglement of purification additive.

arxiv:2605.15439 v1 · 2026-05-14 · quant-ph · cs.IT · math.IT

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Claims

C1strongest claim

Whenever a completely positive map N:L(B')→L(A) satisfies N† ∘ N = a id_A + b Tr[·] I_d for constants a,b ≥ 0, the quantity υ₂(N) is multiplicative under tensor powers; this implies additivity for the associated Rényi-2 entanglement of purification.

C2weakest assumption

The reformulation of the Rényi entanglement of purification as the constrained maximal output Schatten p-norm problem (for p=2) is equivalent to the original definition and preserves the relevant multiplicativity properties.

C3one line summary

Proves that υ₂(Ω) is multiplicative for CP maps satisfying N† ∘ N = a id + b Tr[·]I, including depolarizing and transpose-depolarizing channels, implying additivity of Rényi-2 entanglement of purification.

References

32 extracted · 32 resolved · 4 Pith anchors

[1] In order to obtain sharp bounds (and later to identify candidate optimizers), it is essential to know the spectrum ofτAA′ explicitly

[2] → L (A)is CP,Λ : L(B1 ⊗B 2) → L (E)is CPTP, andΦ B′ 1B1 d andΦ B′ 2B2 d are normalized maximally entangled states of dimensiond. Finally, we obtain the following explicit form of(Γc t)† in Lemma 40: (

[3] → L(A)is the adjoint of the complementary channel ofΓt. This is a CP map obtained as (Γc t)†(Y) = Tr B′ 2(St Y S t), where St = (a+ +a −)IB′ 1B′ 2 + (a+ −a −)ΠB′ 1B′ 2 .(C16) HereΠ B′ 1B′ 2 is the fli

[4] Terhal, Michał Horodecki, Debbie W 2002

[5] R. F. Werner and A. S. Holevo. Counterexample to an additivity conjecture for output purity of quantum channels.Journal of Mathematical Physics, 43(9):4353–4357, 2002 2002

Receipt and verification

First computed	2026-05-20T00:00:58.626788Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

23bc520c2209a5aceeb1d1e8ebbbb4e90d91405a8e6690b6ca3813d109cce031

Aliases

arxiv: 2605.15439 · arxiv_version: 2605.15439v1 · doi: 10.48550/arxiv.2605.15439 · pith_short_12: EO6FEDBCBGS2 · pith_short_16: EO6FEDBCBGS2Z3VR · pith_short_8: EO6FEDBC

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/EO6FEDBCBGS2Z3VR2HUOXO5U5E \
  | 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: 23bc520c2209a5aceeb1d1e8ebbbb4e90d91405a8e6690b6ca3813d109cce031

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7dc1be3dab84149465bdd8d114034adbb019f633da3f7c9bc3fad755b23b635c",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-05-14T21:41:31Z",
    "title_canon_sha256": "171ed99c43984e256b1a138673220b7c5d61ea7c3e100d77b7667b2da7b48bc3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15439",
    "kind": "arxiv",
    "version": 1
  }
}