TY - JOUR
T1 - The Platypus of the Quantum Channel Zoo
AU - Leditzky, Felix
AU - Leung, Debbie
AU - Siddhu, Vikesh
AU - Smith, Graeme
AU - Smolin, John A.
N1 - This work was supported in part by Army Research Offce Multidisciplinary University Research Initiative (ARO MURI) Quantum Network Science under Contract W911NF2120214; in part by NSF under Grant CCF 1652560, Grant PHY 1915407, and Grant 2137953; and in part by Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant.
PY - 2023/6/1
Y1 - 2023/6/1
N2 - Understanding quantum channels and the strange behavior of their capacities is a key objective of quantum information theory. Here we study a remarkably simple, low-dimensional, single-parameter family of quantum channels with exotic quantum information-theoretic features. As the simplest example from this family, we focus on a qutrit-to-qutrit channel that is intuitively obtained by hybridizing together a simple degradable channel and a completely useless qubit channel. Such hybridizing makes this channel's capacities behave in a variety of interesting ways. For instance, the private and classical capacity of this channel coincide and can be explicitly calculated, even though the channel does not belong to any class for which the underlying information quantities are known to be additive. Moreover, the quantum capacity of the channel can be computed explicitly, given a clear and compelling conjecture is true. This 'spin alignment conjecture,' which may be of independent interest, is proved in certain special cases and additional numerical evidence for its validity is provided. Finally, we generalize the qutrit channel in two ways, and the resulting channels and their capacities display similarly rich behavior. In a companion paper, we further show that the qutrit channel demonstrates superadditivity when transmitting quantum information jointly with a variety of assisting channels, in a manner unknown before.
AB - Understanding quantum channels and the strange behavior of their capacities is a key objective of quantum information theory. Here we study a remarkably simple, low-dimensional, single-parameter family of quantum channels with exotic quantum information-theoretic features. As the simplest example from this family, we focus on a qutrit-to-qutrit channel that is intuitively obtained by hybridizing together a simple degradable channel and a completely useless qubit channel. Such hybridizing makes this channel's capacities behave in a variety of interesting ways. For instance, the private and classical capacity of this channel coincide and can be explicitly calculated, even though the channel does not belong to any class for which the underlying information quantities are known to be additive. Moreover, the quantum capacity of the channel can be computed explicitly, given a clear and compelling conjecture is true. This 'spin alignment conjecture,' which may be of independent interest, is proved in certain special cases and additional numerical evidence for its validity is provided. Finally, we generalize the qutrit channel in two ways, and the resulting channels and their capacities display similarly rich behavior. In a companion paper, we further show that the qutrit channel demonstrates superadditivity when transmitting quantum information jointly with a variety of assisting channels, in a manner unknown before.
KW - Quantum communication
KW - quantum channels
KW - quantum information science
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U2 - 10.1109/TIT.2023.3245985
DO - 10.1109/TIT.2023.3245985
M3 - Article
AN - SCOPUS:85149394678
SN - 0018-9448
VL - 69
SP - 3825
EP - 3849
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 6
ER -