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docs/src/resources/bibliography.bib

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@book{Nielsen-Chuang2011,
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Author = {Michael A. Nielsen and Isaac L. Chuang},
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Title = {Quantum Computation and Quantum Information: 10th Anniversary Edition},
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Publisher = {Cambridge University Press},
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Year = {2011},
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ISBN = {9781107002173},
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URL = {https://www.amazon.com/Quantum-Computation-Information-10th-Anniversary/dp/1107002176?SubscriptionId=AKIAIOBINVZYXZQZ2U3A&tag=chimbori05-20&linkCode=xm2&camp=2025&creative=165953&creativeASIN=1107002176}
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}
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@article{Jozsa1994,
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author = {Richard Jozsa},
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title = {Fidelity for Mixed Quantum States},
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journal = {Journal of Modern Optics},
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volume = {41},
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number = {12},
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pages = {2315--2323},
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year = {1994},
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publisher = {Taylor \& Francis},
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doi = {10.1080/09500349414552171},
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URL = {https://doi.org/10.1080/09500349414552171},
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}
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@article{gravina2024adaptive,
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title = {{Adaptive variational low-rank dynamics for open quantum systems}},
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author = {Gravina, Luca and Savona, Vincenzo},

docs/src/users_guide/states_and_operators.md

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a = destroy(5)
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```
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Now lets apply the lowering operator `\hat{a}` to our vacuum state `vac`:
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Now lets apply the lowering operator ``\hat{a}`` to our vacuum state `vac`:
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```@example states_and_operators
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a * vac
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fidelity(x, y)
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```
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Note that the definition of [`fidelity`](@ref) here is from **Nielsen & Chuang, "Quantum Computation and Quantum Information"**. It is the square root of the fidelity defined in **R. Jozsa, Journal of Modern Optics, 41:12, 2315 (1994)**. We also know that for two pure states, the trace distance (``T``) and the fidelity (``F``) are related by ``T = \sqrt{1-F^2}``:
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Note that the definition of [`fidelity`](@ref) here is from [Nielsen-Chuang2011](@cite). It is the square root of the fidelity defined in [Jozsa1994](@cite). We also know that for two pure states, the trace distance (``T``) and the fidelity (``F``) are related by ``T = \sqrt{1-F^2}``:
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```@example states_and_operators
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tracedist(x, y) ≈ sqrt(1 - (fidelity(x, y))^2)

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