Sample efficient tomography via Pauli Measurements Article Swipe
Pauli Measurements are the most important measurements in both theoretical and experimental aspects of quantum information science. In this paper, we explore the power of Pauli measurements in the state tomography related problems. Firstly, we show that the \textit{quantum state tomography} problem of $n$-qubit system can be accomplished with ${\mathcal{O}}(\frac{10^n}{ε^2})$ copies of the unknown state using Pauli measurements. As a direct application, we studied the \textit{quantum overlapping tomography} problem introduced by Cotler and Wilczek in Ref. \cite{Cotler_2020}. We show that the sample complexity is $\mathcal{O}(\frac{10^k\cdot\log({{n}\choose{k}}/δ))}{ε^{2}})$ for quantum overlapping tomography of $k$-qubit reduced density matrices among $n$ is quantum system, where $1-δ$ is the confidential level, and $ε$ is the trace distance error. This can be achieved using Pauli measurements. Moreover, we prove that $Ω(\frac{\log(n/δ)}{ε^{2}})$ copies are needed. In other words, for constant $k$, joint, highly entangled, measurements are not asymptotically more efficient than Pauli measurements.
Related Topics
Concepts
Pauli exclusion principle
Quantum tomography
Trace distance
Qubit
Physics
Quantum state
Pauli matrices
Quantum
State (computer science)
SIC-POVM
Quantum mechanics
Mathematics
Combinatorics
Algorithm
Quantum operation
Open quantum system
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2009.04610
- https://arxiv.org/pdf/2009.04610
- OA Status
- green
- Cited By
- 6
- References
- 13
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W3083788897
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W3083788897Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.48550/arxiv.2009.04610Digital Object Identifier
- Title
-
Sample efficient tomography via Pauli MeasurementsWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2020Year of publication
- Publication date
-
2020-09-10Full publication date if available
- Authors
-
Nengkun YuList of authors in order
- Landing page
-
https://arxiv.org/abs/2009.04610Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2009.04610Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2009.04610Direct OA link when available
- Concepts
-
Pauli exclusion principle, Quantum tomography, Trace distance, Qubit, Physics, Quantum state, Pauli matrices, Quantum, State (computer science), SIC-POVM, Quantum mechanics, Mathematics, Combinatorics, Algorithm, Quantum operation, Open quantum systemTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
6Total citation count in OpenAlex
- Citations by year (recent)
-
2024: 1, 2022: 2, 2021: 1, 2020: 2Per-year citation counts (last 5 years)
- References (count)
-
13Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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| corresponding_author_ids | https://openalex.org/A5088217238 |
| countries_distinct_count | 0 |
| institutions_distinct_count | 1 |
| citation_normalized_percentile |