Polygamy relations of multipartite systems

Quantum Information Processing - Tập 18 Số 4 - Trang 1-14 - 2019
Jin, Zhi-Xiang1, Fei, Shao-Ming2,3, Qiao, Cong-Feng1,4
1School of Physics, University of Chinese Academy of Sciences, Beijing, China
2School of Mathematical Sciences, Capital Normal University, Beijing, China
3Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
4CAS Center for Excellence in Particle Physics, Beijing, China

Tóm tắt

We investigate the polygamy relations of multipartite quantum states. General polygamy inequalities are given in the $$\alpha $$ th $$(\alpha \ge 2)$$ power of concurrence of assistance, $$\beta $$ th $$(\beta \ge 1)$$ power of entanglement of assistance, and the squared convex-roof extended negativity of assistance (SCRENoA).

Tài liệu tham khảo

citation_title=Quantum Computation and Quantum Information; citation_publication_date=2000; citation_id=CR1; citation_author=MA Nielsen; citation_author=IL Chuang; citation_publisher=Cambridge University Press citation_journal_title=Rev. Mod. Phys.; citation_title=Quantum entanglement; citation_author=R Horodecki, P Horodecki, M Horodecki, K Horodecki; citation_volume=81; citation_publication_date=2009; citation_pages=865; citation_doi=10.1103/RevModPhys.81.865; citation_id=CR2 citation_journal_title=Phys. Rev. Lett.; citation_title=Concurrence of mixed bipartite quantum states in arbitrary dimensions; citation_author=F Mintert, M Kuś, A Buchleitner; citation_volume=92; citation_publication_date=2004; citation_pages=167902; citation_doi=10.1103/PhysRevLett.92.167902; citation_id=CR3 citation_journal_title=Phys. Rev. Lett.; citation_title=Concurrence of arbitrary dimensional bipartite quantum states; citation_author=K Chen, S Albeverio, SM Fei; citation_volume=95; citation_publication_date=2005; citation_pages=040504; citation_doi=10.1103/PhysRevLett.95.040504; citation_id=CR4 citation_journal_title=J. Phys. A Math. Gen.; citation_title=Separability criteria and bounds for entanglement measures; citation_author=HP Breuer; citation_volume=39; citation_publication_date=2006; citation_pages=11847; citation_doi=10.1088/0305-4470/39/38/010; citation_id=CR5 citation_journal_title=Phys. Rev. Lett.; citation_title=Optimal entanglement criterion for mixed quantum states; citation_author=HP Breuer; citation_volume=97; citation_publication_date=2006; citation_pages=080501; citation_doi=10.1103/PhysRevLett.97.080501; citation_id=CR6 citation_journal_title=Phys. Rev. A; citation_title=Lower bounds on concurrence and separability conditions; citation_author=JI Vicente; citation_volume=75; citation_publication_date=2007; citation_pages=052320; citation_doi=10.1103/PhysRevA.75.052320; citation_id=CR7 citation_journal_title=Phys. Rev. A; citation_title=Optimal entanglement witnesses based on local orthogonal observables; citation_author=CJ Zhang, YS Zhang, S Zhang, GC Guo; citation_volume=76; citation_publication_date=2007; citation_pages=012334; citation_doi=10.1103/PhysRevA.76.012334; citation_id=CR8 citation_journal_title=Phys. Rev. A; citation_title=Security proof for cryptographic protocols based only on the monogamy of bells inequality violations; citation_author=M Pawlowski; citation_volume=82; citation_publication_date=2010; citation_pages=032313; citation_doi=10.1103/PhysRevA.82.032313; citation_id=CR9 citation_journal_title=Phys. Rev. A; citation_title=Distributed entanglement; citation_author=V Coffman, J Kundu, WK Wootters; citation_volume=61; citation_publication_date=2000; citation_pages=052306; citation_doi=10.1103/PhysRevA.61.052306; citation_id=CR10 citation_journal_title=Phys. Rev. Lett.; citation_title=Entanglement of formation of an arbitrary state of two qubits; citation_author=WK Wootters; citation_volume=80; citation_publication_date=1998; citation_pages=2245; citation_doi=10.1103/PhysRevLett.80.2245; citation_id=CR11 citation_journal_title=Phys. Rev. A; citation_title=Deterministic entanglement of assistance and monogamy constraints; citation_author=G Gour, DA Meyer, BC Sanders; citation_volume=72; citation_publication_date=2005; citation_pages=042329; citation_doi=10.1103/PhysRevA.72.042329; citation_id=CR12 citation_journal_title=Phys. Rev. A; citation_title=Tsallis entropy and entanglement constraints in multiqubit systems; citation_author=JS Kim; citation_volume=81; citation_publication_date=2010; citation_pages=062328; citation_doi=10.1103/PhysRevA.81.062328; citation_id=CR13 citation_journal_title=J. Phys. A Math. Theor.; citation_title=Unified entropy, entanglement measures and monogamy of multiparty entanglement; citation_author=JS Kim, BC Sanders; citation_volume=44; citation_publication_date=2011; citation_pages=295303; citation_doi=10.1088/1751-8113/44/29/295303; citation_id=CR14 citation_journal_title=J. Math. Phys.; citation_title=Dual monogamy inequality for entanglement; citation_author=G Goura, S Bandyopadhyayb, BC Sandersc; citation_volume=48; citation_publication_date=2007; citation_pages=012108; citation_doi=10.1063/1.2435088; citation_id=CR15 citation_journal_title=Phys. Rev. A; citation_title=Polygamy of distributed entanglement; citation_author=F Buscemi, G Gour, JS Kim; citation_volume=80; citation_publication_date=2009; citation_pages=012324; citation_doi=10.1103/PhysRevA.80.012324; citation_id=CR16 citation_journal_title=Phys. Rev. A; citation_title=General polygamy inequality of multiparty quantum entanglement; citation_author=JS Kim; citation_volume=85; citation_publication_date=2012; citation_pages=062302; citation_doi=10.1103/PhysRevA.85.062302; citation_id=CR17 citation_journal_title=Phys. Rev. A; citation_title=Tsallis entropy and general polygamy of multiparty quantum entanglement in arbitrary dimensions; citation_author=JS Kim; citation_volume=94; citation_publication_date=2016; citation_pages=062338; citation_doi=10.1103/PhysRevA.94.062338; citation_id=CR18 citation_journal_title=Quantum Inf. Process.; citation_title=Tighter entanglement monogamy relations of qubit systems; citation_author=ZX Jin, SM Fei; citation_volume=16; citation_publication_date=2017; citation_pages=77; citation_doi=10.1007/s11128-017-1520-3; citation_id=CR19 citation_journal_title=Phys. Rev. A; citation_title=Tighter monogamy relations in multiqubit systems; citation_author=ZX Jin, J Li, T Li, SM Fei; citation_volume=97; citation_publication_date=2018; citation_pages=032336; citation_doi=10.1103/PhysRevA.97.032336; citation_id=CR20 citation_journal_title=Phys. Rev. A; citation_title=Entanglement monogamy relations of qubit systems; citation_author=XN Zhu, SM Fei; citation_volume=90; citation_publication_date=2014; citation_pages=024304; citation_doi=10.1103/PhysRevA.90.024304; citation_id=CR21 citation_journal_title=Quantum Inf. Process.; citation_title=Quantum steering borders in three-qubit systems; citation_author=JK Kalaga, W Leoński; citation_volume=16; citation_publication_date=2017; citation_pages=175; citation_doi=10.1007/s11128-017-1627-6; citation_id=CR22 citation_journal_title=Quantum Inf. Process.; citation_title=Quantum steering and entanglement in three-mode triangle Bose–Hubbard system; citation_author=JK Kalaga, W Leoński; citation_volume=16; citation_publication_date=2017; citation_pages=265; citation_doi=10.1007/s11128-017-1717-5; citation_id=CR23 citation_journal_title=Phys. Rev. A; citation_title=Spreading of entanglement and steering along small Bose–Hubbard chains; citation_author=MK Olsen; citation_volume=92; citation_publication_date=2015; citation_pages=033627; citation_doi=10.1103/PhysRevA.92.033627; citation_id=CR24 citation_journal_title=Phys. Rev. Lett.; citation_title=Demonstration of monogamy relations for Einstein–Podolsky–Rosen steering in Gaussian cluster states; citation_author=X Deng, Y Xiang, C Tian, G Adesso, Q He; citation_volume=118; citation_publication_date=2017; citation_pages=230501; citation_doi=10.1103/PhysRevLett.118.230501; citation_id=CR25 citation_journal_title=Phys. Rev. A; citation_title=Einstein–Podolsky–Rosen steering and coherence in the family of entangled three-qubit states; citation_author=JK Kalaga, W Leoński; citation_volume=97; citation_publication_date=2018; citation_pages=042110; citation_doi=10.1103/PhysRevA.97.042110; citation_id=CR26 citation_journal_title=Phys. Rev. A; citation_title=Negativity and tight constraints of multiqubit entanglement; citation_author=JS Kim; citation_volume=97; citation_publication_date=2018; citation_pages=012334; citation_doi=10.1103/PhysRevA.97.012334; citation_id=CR27 citation_journal_title=Phys. Rev. A; citation_title=Weighted polygamy inequalities of multiparty entanglement in arbitrary-dimensional quantum systems; citation_author=JS Kim; citation_volume=97; citation_publication_date=2018; citation_pages=042332; citation_doi=10.1103/PhysRevA.97.042332; citation_id=CR28 citation_journal_title=Quantum Inf. Process.; citation_title=Any entanglement of assistance is polygamous; citation_author=Y Guo; citation_volume=17; citation_publication_date=2018; citation_pages=222; citation_doi=10.1007/s11128-018-1996-5; citation_id=CR29 citation_journal_title=Phys. Rev. A; citation_title=Fidelity and concurrence of conjugated states; citation_author=A Uhlmann; citation_volume=62; citation_publication_date=2000; citation_pages=032307; citation_doi=10.1103/PhysRevA.62.032307; citation_id=CR30 citation_journal_title=Phys. Rev. A; citation_title=Universal state inversion and concurrence in arbitrary dimensions; citation_author=P Rungta, V Buz̆ek, CM Caves, M Hillery, GJ Milburn; citation_volume=64; citation_publication_date=2001; citation_pages=042315; citation_doi=10.1103/PhysRevA.64.042315; citation_id=CR31 citation_journal_title=J. Opt. B Quantum Semiclass. Opt.; citation_title=A note on invariants and entanglements; citation_author=S Albeverio, SM Fei; citation_volume=3; citation_publication_date=2001; citation_pages=223; citation_doi=10.1088/1464-4266/3/4/305; citation_id=CR32 citation_journal_title=Quantum Inf. Comput.; citation_title=Local vs. joint measurements for the entanglement of assistance; citation_author=T Laustsen, F Verstraete, SJ Van Enk; citation_volume=3; citation_publication_date=2003; citation_pages=64; citation_id=CR33 citation_journal_title=Phys. Rev. A; citation_title=Entanglement monogamy of tripartite quantum states; citation_author=CS Yu, HS Song; citation_volume=77; citation_publication_date=2008; citation_pages=032329; citation_doi=10.1103/PhysRevA.77.032329; citation_id=CR34 citation_journal_title=Phys. Rev. Lett.; citation_title=General monogamy inequality for bipartite qubit entanglement; citation_author=TJ Osborne, F Verstraete; citation_volume=96; citation_publication_date=2006; citation_pages=220503; citation_doi=10.1103/PhysRevLett.96.220503; citation_id=CR35 citation_journal_title=Phys. Rev. A; citation_title=Entanglement monogamy and entanglement evolution in multipartite systems; citation_author=YK Bai, MY Ye, ZD Wang; citation_volume=80; citation_publication_date=2009; citation_pages=044301; citation_doi=10.1103/PhysRevA.80.044301; citation_id=CR36 citation_journal_title=J. Phys. A; citation_title=Concurrence vectors in arbitrary multipartite quantum systems; citation_author=SJ Akhtarshenas; citation_volume=38; citation_publication_date=2005; citation_pages=6777; citation_doi=10.1088/0305-4470/38/30/011; citation_id=CR37 citation_journal_title=Phys. Rev. A; citation_title=Polygamy of entanglement in multipartite quantum systems; citation_author=JS Kim; citation_volume=80; citation_publication_date=2009; citation_pages=022302; citation_doi=10.1103/PhysRevA.80.022302; citation_id=CR38 citation_journal_title=New J. Phys.; citation_title=Experimental quantum cryptography with qutrits; citation_author=S Groblacher, T Jennewein, A Vaziri, G Weihs, A Zeilinger; citation_volume=8; citation_publication_date=2006; citation_pages=75; citation_doi=10.1088/1367-2630/8/5/075; citation_id=CR39 citation_journal_title=Phys. Rev. A.; citation_title=Computable measure of entanglement; citation_author=G Vidal, RF Werner; citation_volume=65; citation_publication_date=2002; citation_pages=032314; citation_doi=10.1103/PhysRevA.65.032314; citation_id=CR40