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Operational transformation rates of quantum states

  • Giulia Mazzola
  • Renato Renner
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Abstract

Typically, multiple copies of a quantum state are described by a tensor power of that state. However, from an operational point of view, an experimentalist cannot, in general, rule out imperfections at unknown positions or correlations between copies, so assuming independent and identically distributed (iid) copies is not justified a priori. In the following, we relax the iid assumption by considering a whole set of resource states that are fundamentally indistinguishable from a tensor power state, and in that sense look like many copies of the quantum state to the experimentalist. Using a de Finetti-type argument, we show that this operational set of states can asymptotically be represented by almost-iid states. As an application, we introduce operational analogues of asymptotic transformation rates, such as entanglement cost and distillation. This raises the question of whether these rates coincide with their iid counterparts.

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Cite

BibTeXRIS
BibTeX
@misc{mazzola2026operational,
  title = {{Operational transformation rates of quantum states}},
  author = {Giulia Mazzola and Renato Renner},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.02025},
  eprint = {2610.02025},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.02025},
}
RIS
TY  - UNPB
TI  - Operational transformation rates of quantum states
AU  - Giulia Mazzola
AU  - Renato Renner
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.02025
UR  - https://arxiv.org/abs/2610.02025
AB  - Typically, multiple copies of a quantum state are described by a tensor power of that state. However, from an operational point of view, an experimentalist cannot, in general, rule out imperfections at unknown positions or correlations between copies, so assuming independent and identically distributed (iid) copies is not justified a priori. In the following, we relax the iid assumption by considering a whole set of resource states that are fundamentally indistinguishable from a tensor power state, and in that sense look like many copies of the quantum state to the experimentalist. Using a de Finetti-type argument, we show that this operational set of states can asymptotically be represented by almost-iid states. As an application, we introduce operational analogues of asymptotic transformation rates, such as entanglement cost and distillation. This raises the question of whether these rates coincide with their iid counterparts.
ER  -