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- Nathaniel Johnston, David W. Kribs
- Quantum Information & Computation
- 2011

We consider the problem of computing the family of operator norms recently introduced in [1]. We develop a family of semidefinite programs that can be used to exactly compute them in small dimensionsâ€¦ (More)

- Jianxin Chen, Hillary Dawkins, +4 authors Bei Zeng
- 2013

Jianxin Chen,1, 2 Hillary Dawkins,1 Zhengfeng Ji,2, 3 Nathaniel Johnston,1, 2 David Kribs,1, 2 Frederic Shultz,4 and Bei Zeng1, 2 Department of Mathematics & Statistics, University of Guelph, Guelph,â€¦ (More)

- Nathaniel Johnston, David W. Kribs, Vern I. Paulsen
- Quantum Information & Computation
- 2009

The diamond and completely bounded norms for linear maps play an increasingly important role in quantum information science, providing fundamental stabilized distance measures for differences ofâ€¦ (More)

- Carmine De Napoli, Thomas R. Bromley, Marco Cianciaruso, Marco Piani, Nathaniel Johnston, Gerardo Adesso
- Physical review letters
- 2016

Quantifying coherence is an essential endeavor for both quantum foundations and quantum technologies. Here, the robustness of coherence is defined and proven to be a full monotone in the context ofâ€¦ (More)

- Nathaniel Johnston
- Game of Life Cellular Automata
- 2010

We show that the multiplicative domain of a completely positive map yields a new class of quantum error correcting codes. In the case of a unital quantum channel, these are precisely the codes thatâ€¦ (More)

We consider a family of vector and operator norms which we refer to as Schmidt norms. We show that these norms have several uses in quantum information theory â€“ they can be used to help classifyâ€¦ (More)

It is known that, in an (m âŠ— n)-dimensional quantum system, the maximum dimension of a subspace that contains only entangled states is (m âˆ’ 1)(n âˆ’ 1). We show that the exact same bound is tight if weâ€¦ (More)

A long-standing open question asks for the minimum number of vectors needed to form an unextendible product basis in a given bipartite or multipartite Hilbert space. A partial solution was found byâ€¦ (More)

- Nathaniel Johnston
- Discrete Mathematics
- 2013

We examine the open problem of finding the shortest string that contains each of the n! permutations of n symbols as contiguous substrings (i.e., the shortest superpermutation on n symbols). It hasâ€¦ (More)