TY - JOUR
T1 - Entangling capacities and the geometry of quantum operations
AU - Kao, Jhih Yuan
AU - Chou, Chung Hsien
N1 - Funding Information:
This work is partly supported by Ministry of Science and Technology of Taiwan under the Grant number MOST 107-2627-E-006-001, and by Headquarters of University Advancement at the National Cheng Kung University, which is sponsored by the Ministry of Education, Taiwan.
Publisher Copyright:
© 2020, The Author(s).
PY - 2020/12/1
Y1 - 2020/12/1
N2 - Quantum operations are the fundamental transformations on quantum states. In this work, we study the relation between entangling capacities of operations, geometry of operations, and positive partial transpose (PPT) states, which are an important class of states in quantum information. We show a method to calculate bounds for entangling capacity, the amount of entanglement that can be produced by a quantum operation, in terms of negativity, a measure of entanglement. The bounds of entangling capacity are found to be associated with how non-PPT (PPT preserving) an operation is. A length that quantifies both entangling capacity/entanglement and PPT-ness of an operation or state can be defined, establishing a geometry characterized by PPT-ness. The distance derived from the length bounds the relative entangling capability, endowing the geometry with more physical significance. We also demonstrate the equivalence of PPT-ness and separability for unitary operations.
AB - Quantum operations are the fundamental transformations on quantum states. In this work, we study the relation between entangling capacities of operations, geometry of operations, and positive partial transpose (PPT) states, which are an important class of states in quantum information. We show a method to calculate bounds for entangling capacity, the amount of entanglement that can be produced by a quantum operation, in terms of negativity, a measure of entanglement. The bounds of entangling capacity are found to be associated with how non-PPT (PPT preserving) an operation is. A length that quantifies both entangling capacity/entanglement and PPT-ness of an operation or state can be defined, establishing a geometry characterized by PPT-ness. The distance derived from the length bounds the relative entangling capability, endowing the geometry with more physical significance. We also demonstrate the equivalence of PPT-ness and separability for unitary operations.
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U2 - 10.1038/s41598-020-72881-z
DO - 10.1038/s41598-020-72881-z
M3 - Article
C2 - 32994512
AN - SCOPUS:85091713889
SN - 2045-2322
VL - 10
JO - Scientific reports
JF - Scientific reports
IS - 1
M1 - 15978
ER -