Reasonable fermionic quantum information theories require relativity. (English) Zbl 1456.81011
Summary: We show that any quantum information theory based on anticommuting operators must be supplemented by a superselection rule deeply rooted in relativity to establish a reasonable notion of entanglement. While quantum information may be encoded in the fermionic Fock space, the unrestricted theory has a peculiar feature: the marginals of bipartite pure states need not have identical entropies, which leads to an ambiguous definition of entanglement. We solve this problem, by proving that it is removed by relativity, i.e., by the parity superselection rule that arises from Lorentz invariance via the spin-statistics connection. Our results hence unveil a fundamental conceptual inseparability of quantum information and the causal structure of relativistic field theory.
MSC:
| 81P05 | General and philosophical questions in quantum theory |
| 81P45 | Quantum information, communication, networks (quantum-theoretic aspects) |
References:
| [1] | Friis N, Dunjko V, Dür W and Briegel H J 2014 Phys. Rev. A 89 030303(R) · doi:10.1103/PhysRevA.89.030303 |
| [2] | Schliemann J, Loss D and MacDonald A H 2001 Phys. Rev. B 63 085311 · doi:10.1103/PhysRevB.63.085311 |
| [3] | Schliemann J, Cirac J I, Kuś M, Lewenstein M and Loss D 2001 Phys. Rev. A 64 022303 · doi:10.1103/PhysRevA.64.022303 |
| [4] | Li Y S, Zeng B, Liu X S and Long G L 2001 Phys. Rev. A 64 054302 · doi:10.1103/PhysRevA.64.054302 |
| [5] | Eckert K, Schliemann J, Bruß D and Lewenstein M 2002 Ann. Phys.299 88-127 · Zbl 1007.81015 · doi:10.1006/aphy.2002.6268 |
| [6] | Shi Y 2003 Phys. Rev. A 67 024301 · doi:10.1103/PhysRevA.67.024301 |
| [7] | Botero A and Reznik B 2004 Phys. Lett. A 331 39-44 · Zbl 1123.81307 · doi:10.1016/j.physleta.2004.08.037 |
| [8] | Caban P, Podlaski K, Rembieliński J, Smolińksi K A and Walczak Z 2005 J. Phys. A: Math. Gen.38 L79-86 · Zbl 1065.81521 · doi:10.1088/0305-4470/38/6/L02 |
| [9] | Bañuls M C, Cirac J I and Wolf M M 2007 Phys. Rev. A 76 022311 · doi:10.1103/PhysRevA.76.022311 |
| [10] | Balachandran A P, Govindarajan T R, de Queiroz A R and Reyes-Lega A F 2013 Phys. Rev. Lett.110 080503 · doi:10.1103/PhysRevLett.110.080503 |
| [11] | Moriya H 2002 Lett. Math. Phys.60 109-21 · Zbl 1022.46037 · doi:10.1023/A:1016158125660 |
| [12] | Araki H and Moriya H 2003 Commun. Math. Phys.237 105-22 · Zbl 1041.46038 · doi:10.1007/s00220-003-0832-6 |
| [13] | Moriya H 2005 J. Math. Phys.46 033508 · Zbl 1067.82007 · doi:10.1063/1.1850995 |
| [14] | Harlow D 2016 Rev. Mod. Phys.88 015002 · doi:10.1103/RevModPhys.88.015002 |
| [15] | Friis N, Lee A R and Bruschi D E 2013 Phys. Rev. A 87 022338 · doi:10.1103/PhysRevA.87.022338 |
| [16] | Wick G C, Wightman A S and Wigner E P 1952 Phys. Rev.88 101-5 · Zbl 0046.43906 · doi:10.1103/PhysRev.88.101 |
| [17] | Christenson J H, Cronin J W, Fitch V L and Turlay R 1964 Phys. Rev. Lett.13 138 · doi:10.1103/PhysRevLett.13.138 |
| [18] | Alavi-Harati A et al (KTeV Collaboration) 1999 Phys. Rev. Lett.83 22-7 · doi:10.1103/PhysRevLett.83.22 |
| [19] | Lüders G 1954 Dan. Mat. Fys. Medd.28 1 |
| [20] | Pauli W et al (ed) 1955 Niels Bohr and the Development of Physics (London: Pergamon) · Zbl 0067.21007 |
| [21] | Lüders G 1957 Ann. Phys.2 1-5 · Zbl 0080.42002 · doi:10.1016/0003-4916(57)90032-5 |
| [22] | Hegerfeldt G C, Kraus K and Wigner E P 1968 J. Math. Phys.9 2029 · Zbl 0172.27304 · doi:10.1063/1.1664539 |
| [23] | Chiribella G, D’Ariano G M and Perinotti P 2010 Phys. Rev. A 81 062348 · doi:10.1103/PhysRevA.81.062348 |
| [24] | Chiribella G, D’Ariano G M and Perinotti P 2011 Phys. Rev. A 84 012311 · doi:10.1103/PhysRevA.84.012311 |
| [25] | Chiribella G, D��Ariano G M and Perinotti P 2012 Entropy14 1877-93 · Zbl 1296.81017 · doi:10.3390/e14101877 |
| [26] | Aharonov Y and Susskind L 1967 Phys. Rev.155 1428-31 · doi:10.1103/PhysRev.155.1428 |
| [27] | Yoshihuku Y 1972 Prog. Theor. Phys.47 2085-9 · doi:10.1143/PTP.47.2085 |
| [28] | Strocchi F and Wightman A S 1974 J. Math. Phys.15 2198 · doi:10.1063/1.1666601 |
| [29] | Verstraete F and Cirac J I 2003 Phys. Rev. Lett.91 010404 · doi:10.1103/PhysRevLett.91.010404 |
| [30] | Bartlett S D and Wiseman H M 2003 Phys. Rev. Lett.91 097903 · doi:10.1103/PhysRevLett.91.097903 |
| [31] | Schuch N, Verstraete F and Cirac J I 2004 Phys. Rev. Lett.92 087904 · doi:10.1103/PhysRevLett.92.087904 |
| [32] | Skotiniotis M, Toloui B, Durham I T and Sanders B C 2013 Phys. Rev. Lett.111 020504 · doi:10.1103/PhysRevLett.111.020504 |
| [33] | Skotiniotis M, Toloui B, Durham I T and Sanders B C 2014 Phys. Rev. A 90 012326 · doi:10.1103/PhysRevA.90.012326 |
| [34] | Friis N 2013 Cavity mode entanglement in relativistic quantum information PhD Thesis University of Nottingham (arXiv:1311.3536) |
| [35] | Wiseman H M and Vaccaro J A 2003 Phys. Rev. Lett.91 097902 · doi:10.1103/PhysRevLett.91.097902 |
| [36] | Wiseman H M, Bartlett S D and Vaccaro J A 2004 Laser Spectroscopy Proc. 25th Int. Conf. (Singapore: World Scientific) pp 307-14 (arXiv:quant-ph/0309046) · doi:10.1142/9789812703002_0047 |
| [37] | Pauli W 1940 Phys. Rev.58 716 · Zbl 0027.18904 · doi:10.1103/PhysRev.58.716 |
| [38] | Schwinger J 1951 Phys. Rev.82 914-27 · Zbl 0043.42202 · doi:10.1103/PhysRev.82.914 |
| [39] | Peskin M E and Schroeder D V 1995 An Introduction to Quantum Field Theory (Reading, MA: Westview) |
| [40] | Eisler V and Zimborás Z 2015 New J. Phys.17 053048 · Zbl 1452.81177 · doi:10.1088/1367-2630/17/5/053048 |
| [41] | Barends R et al 2015 Nat. Commun.6 7654 · doi:10.1038/ncomms8654 |
| [42] | Iorio A and Lambiase G 2014 Phys. Rev. D 90 025006 · doi:10.1103/PhysRevD.90.025006 |
| [43] | Iorio A 2015 Int. J. Mod. Phys. D 4 1530013 · Zbl 1314.81002 · doi:10.1142/S021827181530013X |
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