The no-cloning theorem is a cornerstone result in quantum mechanics that forbids copying of general quantum information. More quantitatively, even given $N$ copies of an unknown state, any channel producing an $(N+1)$-copy state incurs a nonzero trace-distance error on some inputs. Turning this around, one can ask abou...
Yaroslav Herasymenko, Jun-Qiao Lin, P. Lunel et al.· 0 citations
Two new approaches to QFT circuit construction are developed, based on Mackey theory and Clifford theory, respectively, and used to show exponential improvement in circuit cost for specific group families.
Carli Bruinsma, P. M. Posta, Joppe Stokvis et al.· 0 citations
We consider the problem of approximate cloning of quantum states: given $n$ copies of an unknown state $\rho \in \mathbb{C}^{d \times d}$, prepare an $(n+k)$-copy state with high fidelity to $\rho^{\otimes (n+k)}$. Werner's pure state cloner is the optimal channel for the pure state case, and shows that $n = \Theta(kd/...
Marco Fanizza, Dmitry Grinko, Thilo Scharnhorst et al.· 0 citations
Quantum Fourier transforms (QFTs) are essential primitives in quantum algorithms. While abelian groups admit efficient QFT circuits, with circuit size polynomial in the logarithm of the group order, efficient constructions are known for relatively few non-abelian families. We develop two new approaches to QFT circuit c...
Carli Bruinsma, P. M. Posta, Joppe Stokvis et al.· 0 citations
This work establishes the first rigorous finite-$n bounds on quantum resource testing and hence quantum resource manipulation, thus strengthening the GQSL and providing explicit estimates on the number of copies needed to achieve a prescribed performance.
Dmitry Grinko, Ludovico Lami· arXiv.org· 0 citations
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