TY - JOUR
T1 - Entanglement negativity of fermions
T2 - Monotonicity, separability criterion, and classification of few-mode states
AU - Shapourian, Hassan
AU - Ryu, Shinsei
N1 - Publisher Copyright:
© 2019 American Physical Society.
PY - 2019/2/11
Y1 - 2019/2/11
N2 - We study quantum information aspects of the fermionic entanglement negativity recently introduced [H. Shapourian, Phys. Rev. B 95, 165101 (2017)10.1103/PhysRevB.95.165101] based on the fermionic partial transpose. In particular, we show that it is an entanglement monotone under the action of local quantum operations and classical communications, which preserves the local fermion-number parity, and satisfies other common properties expected for an entanglement measure of mixed states. We present fermionic analogs of tripartite entangled states such as W and Greenberger-Horne-Zeilinger states and compare the results of bosonic and fermionic partial transpose in various fermionic states, where we explain why the bosonic partial transpose fails in distinguishing separable states of fermions. Finally, we explore a set of entanglement quantities which distinguish different classes of entangled states of a system with two and three fermionic modes. In doing so, we prove that vanishing entanglement negativity is a necessary and sufficient condition for separability of N≥2 fermionic modes with respect to the bipartition into one mode and the rest. We further conjecture that the entanglement negativity of inseparable states which mix local fermion-number parity is always nonvanishing.
AB - We study quantum information aspects of the fermionic entanglement negativity recently introduced [H. Shapourian, Phys. Rev. B 95, 165101 (2017)10.1103/PhysRevB.95.165101] based on the fermionic partial transpose. In particular, we show that it is an entanglement monotone under the action of local quantum operations and classical communications, which preserves the local fermion-number parity, and satisfies other common properties expected for an entanglement measure of mixed states. We present fermionic analogs of tripartite entangled states such as W and Greenberger-Horne-Zeilinger states and compare the results of bosonic and fermionic partial transpose in various fermionic states, where we explain why the bosonic partial transpose fails in distinguishing separable states of fermions. Finally, we explore a set of entanglement quantities which distinguish different classes of entangled states of a system with two and three fermionic modes. In doing so, we prove that vanishing entanglement negativity is a necessary and sufficient condition for separability of N≥2 fermionic modes with respect to the bipartition into one mode and the rest. We further conjecture that the entanglement negativity of inseparable states which mix local fermion-number parity is always nonvanishing.
UR - http://www.scopus.com/inward/record.url?scp=85061564787&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85061564787&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.99.022310
DO - 10.1103/PhysRevA.99.022310
M3 - Article
AN - SCOPUS:85061564787
SN - 2469-9926
VL - 99
JO - Physical Review A
JF - Physical Review A
IS - 2
M1 - 022310
ER -