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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.20208 |
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| _version_ | 1866908719214755840 |
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| author | Simonov, Kyrylo Wagner, Rafael Galvão, Ernesto |
| author_facet | Simonov, Kyrylo Wagner, Rafael Galvão, Ernesto |
| contents | Bargmann invariants of order $n$, defined as multivariate traces of quantum states $\text{Tr}[ρ_1ρ_2 \ldots ρ_n]$, are useful in applications ranging from quantum metrology to certification of nonclassicality. A standard quantum circuit used to estimate Bargmann invariants is the cycle test. In this work, we propose generalizations of the cycle test applicable to a situation where $n$ systems are given and unknown, and classical information on $m$ systems ($m\leq n)$ is available, allowing estimation of invariants of order $n+m$. Our main result is a generalization of results on 4th order invariants appearing in double weak values from Chiribella et al. [Phys. Rev. Research 6, 043043 (2024)]. The use of classical information on some of the states enables circuits on fewer qubits and with fewer gates, decreasing the experimental requirements for their estimation, and enabling multiple applications we briefly review. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_20208 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Estimation of multivariate traces of states given partial classical information Simonov, Kyrylo Wagner, Rafael Galvão, Ernesto Quantum Physics Bargmann invariants of order $n$, defined as multivariate traces of quantum states $\text{Tr}[ρ_1ρ_2 \ldots ρ_n]$, are useful in applications ranging from quantum metrology to certification of nonclassicality. A standard quantum circuit used to estimate Bargmann invariants is the cycle test. In this work, we propose generalizations of the cycle test applicable to a situation where $n$ systems are given and unknown, and classical information on $m$ systems ($m\leq n)$ is available, allowing estimation of invariants of order $n+m$. Our main result is a generalization of results on 4th order invariants appearing in double weak values from Chiribella et al. [Phys. Rev. Research 6, 043043 (2024)]. The use of classical information on some of the states enables circuits on fewer qubits and with fewer gates, decreasing the experimental requirements for their estimation, and enabling multiple applications we briefly review. |
| title | Estimation of multivariate traces of states given partial classical information |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2505.20208 |