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Quantum no-deleting principle and some of its implications

Arun K. Pati·Samuel L. Braunstein
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Abstract

Unmeasureability of a quantum state has important consequences in practical implementation of quantum computers. Like copying, deleting of an unknown state from among several copies is prohibited. This is called no-deletion prinicple. Here, we present a no deleting principle for qudits. We obtain a bound on $N$-to-$M$ deleting and show that the quality of deletion drops exponentially with the number of copies to be deleted. In addition, we investigate conditional, state-dependent and approximate quantum deleting of unknown states. We prove that unitarity does not allow us to delete copies from an alphabet of two non-orthogonal states exactly. Further, we show that no-deleting principle is consistent with no-signalling.

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Arun K. Pati, Samuel L. Braunstein. 2000-07-31. Quantum no-deleting principle and some of its implications. https://arxiv.org/abs/quant-ph/0007121

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