bibkey: zjawinschmidhobansainz2023channel
authors: Beata Zjawin; David Schmid; Matty J. Hoban; Ana Belén Sainz
year: 2023
title: "The resource theory of nonclassicality of channel assemblages"
doi: 10.22331/q-2023-10-10-1134
url: https://arxiv.org/abs/2209.10177v3
claim: "The paper develops an LOSR resource theory for channel assemblages, gives semidefinite programs that test freeness and LOSR convertibility, and, from SDP observations on the family R of assemblages produced by a Bell-state-controlled y rotation, conjectures that R^θ1 converts to R^θ2 under LOSR if and only if θ1 ≥ θ2."
strata_touched:
  - D5/S3/Quantum/QuantumChannels/ChannelAssemblageLOSRRefutation
license: citation-only
triage: anchor

The resource theory of nonclassicality of channel assemblages

B. Zjawin, D. Schmid, M. J. Hoban and A. B. Sainz, arXiv:2209.10177v3 [quant-ph]; Quantum 7, 1134 (2023). Quotations are from the v3 TeX source.

The family $\mathcal{R}$ (the macro \FA):

First, we focus on an infinite family of quantum-realizable channel assemblages.

The conjecture:

Let the two resources ${\text{In}}_{\text{A}|\text{X}}^{{\theta }_1}$ and ${\text{In}}_{\text{A}|\text{X}}^{{\theta }_2}$ belong to the infinite family of assemblages $\text{FA}$. Then, the conversion ${\text{In}}_{\text{A}|\text{X}}^{{\theta }_1}\stackrel{\text{LOSR}}{⟶}{\text{In}}_{\text{A}|\text{X}}^{{\theta }_2}$ is possible if and only if ${\theta }_1\ge {\theta }_2$.

Verified locator

Source: https://arxiv.org/abs/2209.10177v3

• URL: https://arxiv.org/abs/2209.10177v3 (source channel-quantum.tex, md5 1478712c3cb6058c040039d9ae9978e6):
  • free channel assemblages, Eq. eq:free-channel, l. 214–226;
  • LOSR transformations, Eq. eq:LOSRtrans-channel, l. 246–270;
  • the family $\mathcal{R}$, Eqs. eq:CR and eq:CRfam, l. 316–333;
  • the SDP observation and Conjecture 3, l. 351–355;
  • Conjecture 4, l. 359–361.
• DOI: 10.22331/q-2023-10-10-1134 (https://doi.org/10.22331/q-2023-10-10-1134; Crossref lists Quantum, volume 7, article 1134, published 10 October 2023).