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pith:ZM25MLRU

pith:2025:ZM25MLRU7MMPLM3XLDMCWRUO3N

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Robust self-testing and certified randomness based on chained Bell inequality

Alok Kumar Pan, Rajdeep Paul, Sneha Munshi

Violations of the chained Bell inequality enable device-independent self-testing of quantum states and measurements even with noise.

arxiv:2505.19917 v2 · 2025-05-26 · quant-ph

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Claims

C1strongest claim

We demonstrate the DI self-testing based on the arbitrary-input chained Bell inequality. We devise a systematic and elegant sum-of-squares (SOS) technique enabling dimension-independent optimization of the quantum violation. Our approach enables the derivation of the state along with the relationship between the local observables directly from the optimization condition.

C2weakest assumption

The assumption that the sum-of-squares relaxation exactly captures the optimal quantum violation of the chained Bell inequality for arbitrary input numbers and that the resulting algebraic relations directly yield the physical state and observables without additional dimension-dependent constraints.

C3one line summary

Derives robust device-independent self-testing and two-bit certified randomness from the optimal quantum violation of the arbitrary-input chained Bell inequality via a dimension-independent sum-of-squares technique.

References

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[1] 11d +aA i 2 ⊗ 11d +bB j 2 ρAB # (47) wherea,b∈ ±1. We know, for a maximally entangled state, ⟨Ai⟩ρAB =0,⟨B j⟩ρAB =0,∀i,j∈[n]. Hence, we get P a,b|A i,B j = 1 4 2021

[2] (1) of the main text, we get the chained Bell inequality C3 =(A 1 +A 2)B1 +(A 2 +A 3)B2 +(A 3 −A 1)B3 ≤4 (B1) Following the SOS approach as outlined in Sec

[3] This, in turn, provides (C3)opt Q =3 √ 3=6 cos π 3 (B6) Clearly, Alice’s observables follow the relation ⟨{Ai,A i+x}⟩=2 cos πx 3 ,∀i∈[2],x∈[3−i] (B7) Following Eq. (18) (more details are given in Appe

[4] Detailed derivation forn=5 Substitutingn=5 in Eq. (1) of the main text, we get the chained Bell inequality C5 =(A 1 +A 2)B1 +(A 2 +A 3)B2 +(A 3 +A 4)B3 +(A 4 +A 5)B4 +(A 5 −A 1)B5 ≤8 (B12) Following t

[5] (1) of the main text forn=7, we get C7 = 7X i=1 (Ai +A i+1)Bi ≤12 (B27) whereA 8 =−A 1

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Receipt and verification

First computed	2026-05-28T01:05:10.516560Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb35d62e34fb18f5b37758d82b468edb422a47b11d276b2f121e2c0393136d23

Aliases

arxiv: 2505.19917 · arxiv_version: 2505.19917v2 · doi: 10.48550/arxiv.2505.19917 · pith_short_12: ZM25MLRU7MMP · pith_short_16: ZM25MLRU7MMPLM3X · pith_short_8: ZM25MLRU

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/ZM25MLRU7MMPLM3XLDMCWRUO3N \
  | jq -c '.canonical_record' \
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# expect: cb35d62e34fb18f5b37758d82b468edb422a47b11d276b2f121e2c0393136d23

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a9a09ecfe290adabe36cc2f873f69c99545113d679bd2b12ba8f408daa88d60d",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2025-05-26T12:40:57Z",
    "title_canon_sha256": "d85185e3ea8f126cec28af30c98d5459d50fa8b7840fabf9dde2cf6737aa4402"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.19917",
    "kind": "arxiv",
    "version": 2
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}