In certain situations the state of a quantum system, after transmission through a quantum channel, can be perfectly restored. This can be done by “coding” the state space of the system before transmission into a “protected” part of a larger state space, and by applying a proper “decoding” map afterwards. By a version of the Heisenberg Principle, which we prove, such a protected space must be “dark” in the sense that no information leaks out during the transmission. We explain the role of the Knill–Laflamme condition in relation to protection and darkness, and we analyze several degrees of protection, whether related to error correction, or to state restauration after a measurement. Recent results on higher rank numerical ranges of operators are used to construct examples. In particular, dark spaces are constructed for any map of rank 2, for a biased permutations channel and for certain separable maps acting on multipartite systems. Furthermore, error correction subspaces are provided for a class of tri-unitary noise models.
Quantum Information Processing – Springer Journals
Published: Sep 23, 2009
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera