Fermionic mode entanglement in quantum information

We analyze fermionic modes as fundamental entities for quantum information processing. To this end we construct a density operator formalism on the underlying Fock space and demonstrate how it can be naturally and unambiguously equipped with a notion of subsystems in the absence of a global tensor product structure. We argue that any apparent similarities between fermionic modes and qubits are superficial and can only be applied in limited situations. In particular, we discuss the ambiguities that arise from different treatments of this subject. Our results are independent of the specific context of the fermionic fields as long as the canonical anti-commutation relations are satisfied, e.g., in relativistic quantum fields, or fermionic trapped ions.

[1]  E. Martín-Martínez,et al.  Residual entanglement of accelerated fermions is not nonlocal , 2011, 1107.3235.

[2]  Fermionic entanglement ambiguity in noninertial frames , 2011, 1104.2307.

[3]  E. Martín-Martínez,et al.  Redistribution of particle and antiparticle entanglement in noninertial frames , 2011, 1102.4759.

[4]  David Edward Bruschi,et al.  Kinematic entanglement degradation of fermionic cavity modes , 2011, 1110.6756.

[5]  I. Fuentes,et al.  Entanglement of Dirac fields in an expanding spacetime , 2010, 1007.1569.

[6]  K. Bradler,et al.  Comment on “Fermionic entanglement ambiguity in noninertial frames” , 2012, 1201.1045.

[7]  David Edward Bruschi,et al.  Motion generates entanglement , 2012, 1201.0549.

[8]  L. You,et al.  Quantum correlations in two-boson wave functions , 2001 .

[9]  M. Montero,et al.  Reply to "Comment on 'Fermionic entanglement ambiguity in noninertial frames' " , 2012 .

[10]  Entanglement in relativistic quantum field theory , 2004, hep-th/0408062.

[11]  Yu Shi.  Quantum entanglement of identical particles , 2003 .

[12]  Convergence of fermionic-field entanglement at infinite acceleration in relativistic quantum information , 2011, 1111.6070.

[13]  GianCarlo Ghirardi,et al.  General criterion for the entanglement of two indistinguishable particles (10 pages) , 2004 .

[14]  Robert B. Mann,et al.  Persistence of tripartite nonlocality for noninertial observers , 2011, 1107.4633.

[15]  G. Vidal,et al.  Computable measure of entanglement , 2001, quant-ph/0102117.

[16]  P. Zanardi.  Quantum entanglement in fermionic lattices , 2002 .

[17]  Bei Zeng,et al.  Entanglement in a two-identical-particle system , 2001 .

[18]  A. Wightman,et al.  Proof of the charge superselection rule in local relativistic quantum field theory , 1974 .

[19]  W. Marsden.  I and J , 2012 .

[20]  F. Illuminati,et al.  Gaussian measures of entanglement versus negativities: Ordering of two-mode Gaussian states , 2005, quant-ph/0506124.

[21]  Daniel Loss,et al.  Double-occupancy errors, adiabaticity, and entanglement of spin qubits in quantum dots , 2001 .

[22]  H M Wiseman,et al.  Entanglement of indistinguishable particles shared between two parties. , 2003, Physical review letters.

[23]  B. Moor,et al.  A comparison of the entanglement measures negativity and concurrence , 2001, quant-ph/0108021.

[24]  N. D. Birrell,et al.  Quantum fields in curved space , 2007 .

[25]  M. Lewenstein,et al.  Quantum Correlations in Systems of Indistinguishable Particles , 2002, quant-ph/0203060.

[26]  David Edward Bruschi,et al.  Unruh effect in quantum information beyond the single-mode approximation , 2010, 1007.4670.

[27]  J. Ignacio Cirac,et al.  Quantum correlations in two-fermion systems , 2001 .

[28]  P. Alsing,et al.  Entanglement of Dirac fields in noninertial frames , 2006, quant-ph/0603269.

[29]  Charles H. Bennett,et al.  Mixed-state entanglement and quantum error correction. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[30]  Benni Reznik,et al.  BCS-like modewise entanglement of fermion Gaussian states , 2004 .

[31]  Michael M. Wolf,et al.  Entanglement in fermionic systems , 2007, 0705.1103.

[32]  V. Vedral,et al.  Natural mode entanglement as a resource for quantum communication. , 2009, Physical review letters.