bibkey: arai2023diversity
authors: Hayato Arai
year: 2023
title: "The Diversity of Entanglement Structures with Self-Duality and Non-Orthogonal State Discrimination in General Probabilistic Theories"
doi: null
url: https://arxiv.org/abs/2302.12361v1
claim: "The thesis classifies the two-outcome dual-operator-valued measures (DOVMs) of bipartite entanglement structures by the eigenvalues of their effects, defines quantum n-simulability of a DOVM on its domain of non-negative probabilities, proves that beyond-quantum (BQ) DOVMs are not simulable, and leaves open whether advantage-quantum (AQ) DOVMs are."
strata_touched:
  - D5/S3/Quantum/Measurement/AdvantageQuantumNonSimulability
license: citation-only
triage: anchor

The Diversity of Entanglement Structures with Self-Duality and Non-Orthogonal State Discrimination in General Probabilistic Theories

H. Arai, Ph.D. thesis, Nagoya University; arXiv:2302.12361v1 (2023-02-23). Quotations are from the v1 TeX source.

DOVMs:

In this thesis, we call a measurement in ${\text{cM}}_2(\mathrm{SEP}(A;B),I)$ a \textit{Dual-Operator-Valued Measure} (DOVM),

The AQ class:

We say that a measurement $\text{cM}=\{M_i{\}}_{i=1}^2\in \mathrm{DOVM}(\mathrm{A};\mathrm{B})$ is Advantage Quantum (AQ) if one of the effects $M_i$ satisfies the inequalities ${\lambda }_1(M_i)<0$ and $1+{\lambda }_1(M_i)<{\lambda }_d(M_i)<1$.

The domain:

\cD(X):={\rho\in\cL_{\mathrm{H}}^+(\cH_A\otimes\cH_B)\mid\Tr \rho X\ge0}.

Quantum $n$-simulability:

We say that $\text{cM}$ is quantum $n$-simulable if there exists a natural number $n$ and a POVM $\text{cN}=\{N_i{\}}_{i\in I}$ on $({\text{cH}}_A\otimes {\text{cH}}_B{)}^{\otimes n}$ such that \Tr \rho^{\otimes n} N_i=\Tr \rho M_i \quad ^\forall\rho\in\cD(\cM)

The open problem:

Similarly, it is considered that AQ measurement might be non-simulable because AQ measurement also has an extraordinary performance. This is an open problem.

Verified locator

Source: https://arxiv.org/abs/2302.12361v1

• URL: https://arxiv.org/abs/2302.12361v1 (source Thesis_6.tex, md5 fd8792d156d227d9682e46b1fb7416f8):
  • SEP, l. 1650–1651;
  • measurements, l. 1294–1302;
  • DOVMs, l. 1994–1998;
  • the AQ class, l. 2018–2021;
  • the domain, l. 2165–2177;
  • quantum $n$-simulability, l. 2179–2186;
  • the open problem, l. 3930–3938.