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This research advances odd-prime-dimensional magic resource theory by quantifying the cost of enhancing classically simulable measurements through added magic resources. The study establishes that while consumable magic can boost discrimination power, finite-dimensional quantum catalysts and memories cannot improve success probabilities for states with positive Wigner functions. These findings clarify fundamental limits on simulating specific measurement channels using free operations within restricted resource theories.
How to improve the discrimination power of classically simulable measurements?
arXiv:2607.19070v1 Announce Type: new Abstract: Classically simulable measurements (CSMs) constitute an important class of restricted measurements in the odd-prime-dimensional magic resource theory, referring to those measurements with positive discrete Wigner functions. Since their discrimination power is weaker than that of global measurements, it is necessary to study how to improve the discrimination power of CSMs. In this paper, we consider three methods to improve the discrimination power of CSMs, including adding magic resources, using quantum catalysts, and using quantum memories. Specifically, we relate measurements with positive discrete Wigner functions to completely positive Wigner-preserving measurement channels, thereby transforming the problem of improving the discrimination power of CSMs into the problem of determining how many magic resources are required to simulate quantum channels using free operations. Based on this, we derive the lower and upper bounds of the simulation cost. Moreover, we provide a concrete example for which these bounds coincide and prove that consumable magic resources can enhance the discrimination power of CSMs. Finally, we establish a no-go theorem, which shows that for discriminating a pair of states with positive Wigner functions, neither finite-dimensional quantum catalysts nor finite-dimensional quantum memories can improve the optimal success probability of discrimination using CSMs.
Title:How to improve the discrimination power of classically simulable measurements?
Abstract:Classically simulable measurements (CSMs) constitute an important class of restricted measurements in the odd-prime-dimensional magic resource theory, referring to those measurements with positive discrete Wigner functions. Since their discrimination power is weaker than that of global measurements, it is necessary to study how to improve the discrimination power of CSMs. In this paper, we consider three methods to improve the discrimination power of CSMs, including adding magic resources, using quantum catalysts, and using quantum memories. Specifically, we relate measurements with positive discrete Wigner functions to completely positive Wigner-preserving measurement channels, thereby transforming the problem of improving the discrimination power of CSMs into the problem of determining how many magic resources are required to simulate quantum channels using free operations. Based on this, we derive the lower and upper bounds of the simulation cost. Moreover, we provide a concrete example for which these bounds coincide and prove that consumable magic resources can enhance the discrimination power of CSMs. Finally, we establish a no-go theorem, which shows that for discriminating a pair of states with positive Wigner functions, neither finite-dimensional quantum catalysts nor finite-dimensional quantum memories can improve the optimal success probability of discrimination using CSMs.
arXiv:2607.19070 [quant-ph]
(or arXiv:2607.19070v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2607.19070 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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