Quantum complementarity: A novel resource for unambiguous exclusion and encryption (2309.11968v1)
Abstract: Complementarity is a phenomenon explaining several core features of quantum theory, such as the well-known uncertainty principle. Roughly speaking, two objects are said to be complementary if being certain about one of them necessarily forbids useful knowledge about the other. Two quantum measurements that do not commute form an example of complementary measurements, and this phenomenon can also be defined for ensembles of states. Although a key quantum feature, it is unclear whether complementarity can be understood more operationally, as a necessary resource in some quantum information task. Here we show this is the case, and relates to a novel task which we term $\eta$-unambiguous exclusion. As well as giving complementarity a clear operational definition, this also uncovers the foundational underpinning of unambiguous exclusion tasks for the first time. We further show that a special type of measurement complementarity is equivalent to advantages in certain encryption tasks. Finally, our analysis suggest that complementarity of measurement and state ensemble can be interpreted as strong forms of measurement incompatibility and quantum steering, respectively.
- P. Busch, P. Lahti, and R. F. Werner, Colloquium: Quantum root-mean-square error and measurement uncertainty relations, Rev. Mod. Phys. 86, 1261 (2014).
- M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, 10th ed. (Cambridge University Press, 2010).
- J. Watrous, The Theory of Quantum Information (Cambridge University Press, 2018).
- P. Skrzypczyk and D. Cavalcanti, Semidefinite Programming in Quantum Information Science, 2053-2563 (IOP Publishing, 2023).
- H. K. Mishra, M. Nussbaum, and M. M. Wilde, On the optimal error exponents for classical and quantum antidistinguishability (2023), arXiv:2309.03723 .
- V. c. v. Havlíček and J. Barrett, Simple communication complexity separation from quantum state antidistinguishability, Phys. Rev. Res. 2, 013326 (2020).
- V. Russo and J. Sikora, Inner products of pure states and their antidistinguishability, Phys. Rev. A 107, L030202 (2023).
- M. Pusey, J. Barrett, and T. Rudolph, On the reality of the quantum state, Nat. Phys. 8, 475 (2012).
- A. F. Ducuara and P. Skrzypczyk, Operational interpretation of weight-based resource quantifiers in convex quantum resource theories, Phys. Rev. Lett. 125, 110401 (2020).
- L. Wang and R. Renner, One-shot classical-quantum capacity and hypothesis testing, Phys. Rev. Lett. 108, 200501 (2012).
- D. Cavalcanti and P. Skrzypczyk, Quantum steering: a review with focus on semidefinite programming, Rep. Prog. Phys. 80, 024001 (2016).
- M. F. Pusey, Verifying the quantumness of a channel with an untrusted device, J. Opt. Soc. Am. B 32, A56 (2015).
- I. Šupić and J. Bowles, Self-testing of quantum systems: a review, Quantum 4, 337 (2020).
- C.-Y. Hsieh, P. Skrzypczyk, and R. Uola, in preparation.
- A. F. Ducuara and P. Skrzypczyk, Fundamental connections between utility theories of wealth and information theory (2023), arXiv:2306.07975 .
- A. F. Ducuara and P. Skrzypczyk, Characterization of quantum betting tasks in terms of Arimoto mutual information, PRX Quantum 3, 020366 (2022).
- H.-Y. Ku, C.-Y. Hsieh, and C. Budroni, Measurement incompatibility cannot be stochastically distilled (2023), arXiv:2308.02252 .
- C.-Y. Hsieh, H.-Y. Ku, and C. Budroni, Characterisation and fundamental limitations of irreversible stochastic steering distillation (2023), arXiv:2309.06191 .
- C.-Y. Hsieh, Resource preservability, Quantum 4, 244 (2020).
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