Fermionic quantum theory and superselection rules for operational probabilistic theories

Transcription

1 Fermionic quantum theory and superselection rules for operational probabilistic theories Alessandro Tosini, QUIT group, Pavia University Joint work with G.M. D Ariano, F. Manessi, P. Perinotti Supported by QPL, Oxford, July 13-17, 2015

2 Outline 1. Are fermions systems of the usual quantum theory? 2. Fermions as bricks of a new operational probabilistic theory 3. Informational features: tomography in fermionic quantum theory fermionic entanglement 4. A definition of superselection for a general probabilistic theory: fermionic and real QT as special cases 5. Future perspectives

3 1. Are fermions systems of the usual quantum theory? Simulating Physics with Computers Richard P. Feynman Department of Physics, California Institute of Technology, Pasadena, California Received May 7, 1981 The question is, if we wrote a Hamiltonian which involved only these operators, locally coupled to corresponding operators on the other space-time points, could we imitate every quantum mechanical system which is discrete and has a finite number of degrees of freedom? I know, almost certainly, that we could do that for any quantum mechanical system which involves Bose particles. I'm not sure whether Fermi particles could be described by such a system. So I leave that open. Well, that's an example of what I meant by a general quantum mechanical simulator. I'm not sure that it's sufficient, because I'm not sure that it takes care of Fermi particles.

4 1. Are fermions systems of the usual quantum theory? Simulating Physics with Computers Richard P. Feynman Department of Physics, California Institute of Technology, Pasadena, California Received May 7, 1981 The question is, if we wrote a Hamiltonian which involved only these operators, locally coupled to corresponding operators on the other space-time points, could we imitate every quantum mechanical system which is discrete and has a finite number of degrees of freedom? I know, almost certainly, that we could do that for any quantum mechanical system which involves Bose particles. I'm not sure whether Fermi particles could be described by such a system. So I leave that open. Well, that's an example of what I meant by a general quantum mechanical simulator. I'm not sure that it's sufficient, because I'm not sure that it takes care of Fermi particles. A A T B a states maps measurements

5 1. Are fermions systems of the usual quantum theory? Simulating Physics with Computers Richard P. Feynman Department of Physics, California Institute of Technology, Pasadena, California Received May 7, 1981 The question is, if we wrote a Hamiltonian which involved only these operators, locally coupled to corresponding operators on the other space-time points, could we imitate every quantum mechanical system which is discrete and has a finite number of degrees of freedom? I know, almost certainly, that we could do that for any quantum mechanical system which involves Bose particles. I'm not sure whether Fermi particles could be described by such a system. So I leave that open. Well, that's an example of what I meant by a general quantum mechanical simulator. I'm not sure that it's sufficient, because I'm not sure that it takes care of Fermi particles. Prob(, T,a) A T B a A A T B a Probabilities must be reproduced correctly states maps measurements

6 Particle physics Quantum theory

7 Particle physics Quantum theory Relativity: fermionic field Fermions are anti-commuting systems { i, j} =0 { i, i } = iji

8 Particle physics Quantum theory Relativity: fermionic field Fermions are anti-commuting systems { i, j} =0 { i, i } = iji Fermions satisfy a parity superselection rule = even particles + odd particles Wick, G. C., Wightman, A. S., and Wigner, E. P., 1952, Phys. Rev. 88,

9 Particle physics Quantum theory Relativity: fermionic field Fermions are anti-commuting systems { i, j} =0 { i, i } = iji Qubits are commuting systems Fermions satisfy a parity superselection rule = even particles + odd particles Wick, G. C., Wightman, A. S., and Wigner, E. P., 1952, Phys. Rev. 88,

10 Particle physics Quantum theory Relativity: fermionic field Fermions are anti-commuting systems { i, j} =0 { i, i } = iji Qubits are commuting systems Fermions satisfy a parity superselection rule = even particles + odd particles = No a priori superselection even particles + odd particles Wick, G. C., Wightman, A. S., and Wigner, E. P., 1952, Phys. Rev. 88,

11 Particle physics Quantum theory Relativity: fermionic field? Fermions are anti-commuting systems { i, j} =0 { i, i } = iji Qubits are commuting systems Fermions satisfy a parity superselection rule = even particles + odd particles = No a priori superselection even particles + odd particles Wick, G. C., Wightman, A. S., and Wigner, E. P., 1952, Phys. Rev. 88,

12 Usual approach to the problem Local fermionic mode: system ' 0 0 empty 1 fermion S. B. Bravyi and A. Y. Kitaev, Annals of Physics 298, 210 (2002)

13 Usual approach to the problem Local fermionic mode: system ' 0 0 empty 1 fermion N Local Fermionic modes (LFM) = N qubits Jordan-Wigner isomorphism S. B. Bravyi and A. Y. Kitaev, Annals of Physics 298, 210 (2002)

14 Usual approach to the problem Local fermionic mode: system ' 0 0 empty 1 fermion N Local Fermionic modes (LFM) = N qubits Jordan-Wigner isomorphism Price to pay for anti-commutation N Local Fermionic modes (LFM) isomorphism N qubits.. S. B. Bravyi and A. Y. Kitaev, Annals of Physics 298, 210 (2002)

15 Usual approach to the problem Local fermionic mode: system ' 0 0 empty 1 fermion N Local Fermionic modes (LFM) = N qubits Jordan-Wigner isomorphism Price to pay for anti-commutation N Local Fermionic modes (LFM) isomorphism N qubits.. 2 Warnings: Where does parity superselection come from? What do I map via the Jordan-Wigner map? S. B. Bravyi and A. Y. Kitaev, Annals of Physics 298, 210 (2002)

16 2. Fermions as bricks of a new operational probabilistic theory Elementary systems: local fermionic modes G. M. D Ariano, F. Manessi, P. Perinotti and A. Tosini, IJMPA (2014)

17 2. Fermions as bricks of a new operational probabilistic theory Construction of the theory: i-th local fermionic mode Elementary systems: local fermionic modes States and maps in terms of the fields ' i, ' i G. M. D Ariano, F. Manessi, P. Perinotti and A. Tosini, IJMPA (2014)

18 2. Fermions as bricks of a new operational probabilistic theory Construction of the theory: i-th local fermionic mode Elementary systems: local fermionic modes States and maps in terms of the fields ' i, ' i maps? T ( )= X i s i K i K i kraus operator field algebra states? := X j K j K j vacuum G. M. D Ariano, F. Manessi, P. Perinotti and A. Tosini, IJMPA (2014)

19 2. Fermions as bricks of a new operational probabilistic theory Construction of the theory: i-th local fermionic mode Elementary systems: local fermionic modes States and maps in terms of the fields ' i, ' i maps? T ( )= X i s i K i K i kraus operator field algebra states? := X j K j K j vacuum Operational assumptions: The field ' must be physical : Maps with single Kraus ' + ' are maps of the theory G. M. D Ariano, F. Manessi, P. Perinotti and A. Tosini, IJMPA (2014)

20 2. Fermions as bricks of a new operational probabilistic theory Construction of the theory: i-th local fermionic mode Elementary systems: local fermionic modes States and maps in terms of the fields ' i, ' i maps? T ( )= X i s i K i K i kraus operator field algebra states? := X j K j K j vacuum Operational assumptions: The field ' must be physical : Maps with single Kraus ' + ' are maps of the theory Notion of local operations: A map made of fields on some modes => Local on that modes. T. 1. N LOCAL in the operational sense } = G. M. D Ariano, F. Manessi, P. Perinotti and A. Tosini, IJMPA (2014)

21 Proposition: Fermionic states satisfy the parity superselection rule G. M. D Ariano, F. Manessi, P. Perinotti and A. Tosini, IJMPA (2014) Fock space: F = F e F o even sector odd sector never superimposed Any state is of the form: p = e 0 0 (1 p) o

22 Proposition: Fermionic states satisfy the parity superselection rule G. M. D Ariano, F. Manessi, P. Perinotti and A. Tosini, IJMPA (2014) Fock space: F = F e F o even sector odd sector never superimposed Any state is of the form: p = e 0 0 (1 p) o 2-LFM: 10i + 01i 00i + 11i

23 Proposition: Fermionic states satisfy the parity superselection rule G. M. D Ariano, F. Manessi, P. Perinotti and A. Tosini, IJMPA (2014) Fock space: F = F e F o even sector odd sector never superimposed Any state is of the form: p = e 0 0 (1 p) o 2-LFM: 10i + 01i 0i 00i + 11i 1-LFM: 1i NOTICE: LFM = classical bit

24 Proposition: Fermionic states satisfy the parity superselection rule G. M. D Ariano, F. Manessi, P. Perinotti and A. Tosini, IJMPA (2014) Fock space: F = F e F o even sector odd sector never superimposed Any state is of the form: p = e 0 0 (1 p) o 2-LFM: 10i + 01i 0i 00i + 11i 1-LFM: 1i NOTICE: LFM = classical bit NOTICE: no conserved quantity Wick, G. C., Wightman, A. S., and Wigner, E. P., 1952, Phys. Rev. 88, N fermions M N fermions

25 3. Informational features: tomography for fermionic quantum theory L. Hardy and W. K. Wootters, Foundations of Physics 42, 454 (2012)

26 3. Informational features: tomography for fermionic quantum theory Local tomography: A Alice Alice and Bob determine the state by local measurements unknown state? B?= Bob D AB = D A D B L. Hardy and W. K. Wootters, Foundations of Physics 42, 454 (2012)

27 3. Informational features: tomography for fermionic quantum theory Local tomography: A Alice Alice and Bob determine the state by local measurements unknown state? B?= Bob D AB = D A D B Non-local tomography: local measurements are not enough D AB >D A D B L. Hardy and W. K. Wootters, Foundations of Physics 42, 454 (2012)

28 Quantum theory Fermionic quantum theory? A B?= Local tomography D AB = D A D B G. M. D Ariano, F. Manessi, P. Perinotti and A. Tosini, IJMPA (2014)

29 Quantum theory Fermionic quantum theory A? A B?=?? B Local tomography D AB = D A D B G. M. D Ariano, F. Manessi, P. Perinotti and A. Tosini, IJMPA (2014)

30 Quantum theory Fermionic quantum theory A? A B?=? B +?= A? B Local tomography D AB = D A D B G. M. D Ariano, F. Manessi, P. Perinotti and A. Tosini, IJMPA (2014)

31 Quantum theory Fermionic quantum theory A? A B?=? B +?= A? B Local tomography D AB = D A D B Bilocal tomography L. Hardy and W. K. Wootters, Foundations of Physics 42, 454 (2012) D AB >D A D B D ABC 6 f(d A,D B,D C,D AB,D AC,D BC ) G. M. D Ariano, F. Manessi, P. Perinotti and A. Tosini, IJMPA (2014) NOTICE: this bound is saturated

32 3. Informational features: fermionic entanglement 1) Fix a notion of entanglement: non-separability 2) Quantify amount of entanglement in operational terms: we choose Entanglement of formation G. M. D Ariano, F. Manessi, P. Perinotti and A. Tosini, IJMPA (2014)

33 3. Informational features: fermionic entanglement 1) Fix a notion of entanglement: non-separability 2) Quantify amount of entanglement in operational terms: we choose Entanglement of formation How much entanglement in? Quantum entanglement of formation Fermionic entanglement of formation G. M. D Ariano, F. Manessi, P. Perinotti and A. Tosini, IJMPA (2014)

34 3. Informational features: fermionic entanglement 1) Fix a notion of entanglement: non-separability 2) Quantify amount of entanglement in operational terms: we choose Entanglement of formation How much entanglement in? Quantum entanglement of formation Fermionic entanglement of formation N res N resource states LOCC M M copies of E( )= lim M!1 N(M) M G. M. D Ariano, F. Manessi, P. Perinotti and A. Tosini, IJMPA (2014)

35 3. Informational features: fermionic entanglement 1) Fix a notion of entanglement: non-separability 2) Quantify amount of entanglement in operational terms: we choose Entanglement of formation How much entanglement in? Quantum entanglement of formation Fermionic entanglement of formation N res N resource states LOCC M M copies of E( )= lim M!1 N(M) M E( )=0, E( )=1, separable maximally entangled G. M. D Ariano, F. Manessi, P. Perinotti and A. Tosini, IJMPA (2014)

36 3. Informational features: fermionic entanglement 1) Fix a notion of entanglement: non-separability 2) Quantify amount of entanglement in operational terms: we choose Entanglement of formation How much entanglement in? Quantum entanglement of formation Fermionic entanglement of formation N res N resource states E( )= lim M!1 LOCC N(M) M M M copies of N res E F ( )= Ferm. LOCC lim M!1 N(M) M M E( )=0, E( )=1, separable maximally entangled G. M. D Ariano, F. Manessi, P. Perinotti and A. Tosini, IJMPA (2014)

37 3. Informational features: fermionic entanglement 1) Fix a notion of entanglement: non-separability 2) Quantify amount of entanglement in operational terms: we choose Entanglement of formation How much entanglement in? Quantum entanglement of formation N res N resource states E( )= lim M!1 LOCC E( )=0, E( )=1, N(M) M M copies of separable M maximally entangled Fermionic entanglement of formation N res E F ( )= Proposition: Ferm. LOCC lim M!1 N(M) M p e e + p o o M E F ( ) p e E( e )+p o E( o ) G. M. D Ariano, F. Manessi, P. Perinotti and A. Tosini, IJMPA (2014)

38 Mixed states with maximal entanglement of formation e = 1 p 2 ( ) o 1 p 2 ( )? = 1 2 eih e oih o e o D Ariano, G.M., Manessi, F., Perinotti, P., Tosini, A. EPL 107(2), 20,009 (2014)

39 Mixed states with maximal entanglement of formation e = 1 p 2 ( ) o 1 p 2 ( )? = 1 2 eih e oih o e o As qubits state it has no entanglement E(? )=0 ± = 1 p 2 ( 0 ± 1 )? = D Ariano, G.M., Manessi, F., Perinotti, P., Tosini, A. EPL 107(2), 20,009 (2014)

40 Mixed states with maximal entanglement of formation e = 1 p 2 ( ) o 1 p 2 ( )? = 1 2 eih e oih o e o As qubits state it has no entanglement E(? )=0 ± = 1 p 2 ( 0 ± 1 )? = As Fermionic state has max entanglement D Ariano, G.M., Manessi, F., Perinotti, P., Tosini, A. EPL 107(2), 20,009 (2014)

41 Mixed states with maximal entanglement of formation e = 1 p 2 ( ) o 1 p 2 ( )? = 1 2 eih e oih o e o As qubits state it has no entanglement E(? )=0 ± = 1 p 2 ( 0 ± 1 )? = As Fermionic state has max entanglement p e e + p o o E F ( ) p e E( e )+p o E( o ) D Ariano, G.M., Manessi, F., Perinotti, P., Tosini, A. EPL 107(2), 20,009 (2014)

42 Mixed states with maximal entanglement of formation e = 1 p 2 ( ) o 1 p 2 ( )? = 1 2 eih e oih o e o As qubits state it has no entanglement E(? )=0 ± = 1 p 2 ( 0 ± 1 )? = As Fermionic state has max entanglement p e e + p o o E F ( ) p e E( e )+p o E( o ) E F (? ) 1 2 E( e)+ 1 2 E( o) 1 1 D Ariano, G.M., Manessi, F., Perinotti, P., Tosini, A. EPL 107(2), 20,009 (2014)

43 Fermionic entanglement is not monogamous Quantum entanglement is monogamous Alice Bob 3-qubits: ABC Charlie D Ariano, G.M., Manessi, F., Perinotti, P., Tosini, A. EPL 107(2), 20,009 (2014)

44 Fermionic entanglement is not monogamous Quantum entanglement is monogamous Alice Max. Ent Bob 3-qubits: ABC = AB C Charlie D Ariano, G.M., Manessi, F., Perinotti, P., Tosini, A. EPL 107(2), 20,009 (2014)

45 Fermionic entanglement is not monogamous Quantum entanglement is monogamous Alice Max. Ent Bob 3-qubits: ABC = AB C E( AB )+E( AC ) V. Coffman, J. Kundu and W. K. Wootters, Phys. Rev. A 61, (2000) Charlie D Ariano, G.M., Manessi, F., Perinotti, P., Tosini, A. EPL 107(2), 20,009 (2014)

46 Fermionic entanglement is not monogamous Quantum entanglement is monogamous Alice Max. Ent Bob 3-qubits: ABC = AB C E( AB )+E( AC ) V. Coffman, J. Kundu and W. K. Wootters, Phys. Rev. A 61, (2000) Charlie Fermionic entanglement is not monogamous Alice Bob 3-LFMs: ABC = 1 2 ( ) Charlie D Ariano, G.M., Manessi, F., Perinotti, P., Tosini, A. EPL 107(2), 20,009 (2014)

47 Fermionic entanglement is not monogamous Quantum entanglement is monogamous Alice Max. Ent Bob 3-qubits: ABC = AB C E( AB )+E( AC ) V. Coffman, J. Kundu and W. K. Wootters, Phys. Rev. A 61, (2000) Charlie Fermionic entanglement is not monogamous Alice? Bob 3-LFMs: ABC = 1 2 ( ) AB = AC = BC =? E F (? )=1?? Charlie D Ariano, G.M., Manessi, F., Perinotti, P., Tosini, A. EPL 107(2), 20,009 (2014)

48 4. Definition of superselection for probabilistic theory Prob. theory superselection How to define? Prob. theory D Ariano, G.M., Manessi, F., Perinotti, P., Tosini, A. EPL 107(2), 20,009 (2014)

49 4. Definition of superselection for probabilistic theory Prob. theory superselection How to define? Prob. theory system A 2 fully specified by its set of states St(A) D Ariano, G.M., Manessi, F., Perinotti, P., Tosini, A. EPL 107(2), 20,009 (2014)

50 4. Definition of superselection for probabilistic theory Prob. theory superselection Prob. theory How to define? system system A 2 Ā 2 fully specified by its set of states St(A) St(Ā) linear section of St(A) D Ariano, G.M., Manessi, F., Perinotti, P., Tosini, A. EPL 107(2), 20,009 (2014)

51 4. Definition of superselection for probabilistic theory Prob. theory superselection Prob. theory How to define? system system A 2 Ā 2 fully specified by its set of states St(A) St(Ā) linear section of St(A) :! (A, St(A)) 7! (Ā, St(Ā)) St(Ā) := { St(A) (s i )=0, i =1,...,V A } D Ariano, G.M., Manessi, F., Perinotti, P., Tosini, A. EPL 107(2), 20,009 (2014)

52 4. Definition of superselection for probabilistic theory Prob. theory superselection Prob. theory How to define? system system A 2 Ā 2 fully specified by its set of states St(A) St(Ā) linear section of St(A) :! (A, St(A)) 7! (Ā, St(Ā)) St(Ā) := { St(A) (s i )=0, i =1,...,V A } D Ariano, G.M., Manessi, F., Perinotti, P., Tosini, A. EPL 107(2), 20,009 (2014) linear constraint

53 4. Definition of superselection for probabilistic theory Prob. theory superselection Prob. theory How to define? system system A 2 Ā 2 fully specified by its set of states St(A) St(Ā) linear section of St(A) :! (A, St(A)) 7! (Ā, St(Ā)) number of constraints St(Ā) := { St(A) (s i )=0, i =1,...,V A } D Ariano, G.M., Manessi, F., Perinotti, P., Tosini, A. EPL 107(2), 20,009 (2014) linear constraint

54 Superselection-holism tradeoff Open question: how does the tomography of the theory change after superselection? D Ariano, G.M., Manessi, F., Perinotti, P., Tosini, A. EPL 107(2), 20,009 (2014)

55 Superselection-holism tradeoff Open question: how does the tomography of the theory change after superselection? Question: local tomographic tomography of? D Ariano, G.M., Manessi, F., Perinotti, P., Tosini, A. EPL 107(2), 20,009 (2014)

56 Superselection-holism tradeoff The intuition A Open question: how does the tomography of the theory change after superselection?? B Question: local tomographic tomography of? D Ariano, G.M., Manessi, F., Perinotti, P., Tosini, A. EPL 107(2), 20,009 (2014)

57 Superselection-holism tradeoff The intuition A Open question: how does the tomography of the theory change after superselection?? B Question: local tomographic tomography of? less local measures D Ariano, G.M., Manessi, F., Perinotti, P., Tosini, A. EPL 107(2), 20,009 (2014)

58 Superselection-holism tradeoff The intuition A Open question: how does the tomography of the theory change after superselection?? B Question: local tomographic tomography of? less states less local measures D Ariano, G.M., Manessi, F., Perinotti, P., Tosini, A. EPL 107(2), 20,009 (2014)

59 Superselection-holism tradeoff The intuition A Open question: how does the tomography of the theory change after superselection?? B Question: local tomographic tomography of? less states tradeoff less local measures D Ariano, G.M., Manessi, F., Perinotti, P., Tosini, A. EPL 107(2), 20,009 (2014)

60 Superselection-holism tradeoff The intuition A Open question: how does the tomography of the theory change after superselection?? B Question: local tomographic tomography of? less states tradeoff less local measures Lemma: number of constraints on composite systems L(, A, B) 6 V AB 6 U(, A, B) D Ariano, G.M., Manessi, F., Perinotti, P., Tosini, A. EPL 107(2), 20,009 (2014)

61 Superselection-holism tradeoff The intuition A Open question: how does the tomography of the theory change after superselection?? B Question: local tomographic tomography of? less states tradeoff less local measures Lemma: number of constraints on composite systems L(, A, B) 6 V AB 6 U(, A, B) Proposition: If satisfies local tomography then V AB = L(, A, B) V AB = U(, A, B) i) minimal SSR bilocal tomographic ii) maximal SSR D Ariano, G.M., Manessi, F., Perinotti, P., Tosini, A. EPL 107(2), 20,009 (2014) local tomographic

62 Fermionic and Real quantum theory Rebit Qubit bit

63 Fermionic and Real quantum theory Rebit Qubit 1 linear constraint Tr[ y ]=0 bit

64 Fermionic and Real quantum theory Rebit Qubit 1 linear constraint Tr[ y ]=0 bit 2 linear constraints Tr[ y ]=0 Tr[ x ]=0

65 Fermionic and Real quantum theory Rebit Extend minimally to composite systems Qubit 1 linear constraint Tr[ y ]=0 Real quantum theory bit 2 linear constraints Tr[ y ]=0 Tr[ x ]=0 Extend minimally to composite systems Fermionic quantum theory

66 Fermionic and Real quantum theory Rebit Extend minimally to composite systems Qubit 1 linear constraint Tr[ y ]=0 Real quantum theory bit 2 linear constraints Tr[ y ]=0 Tr[ x ]=0 Extend minimally to composite systems Fermionic quantum theory Real and Fermionic quantum theory are (the only two) minimal SSR of QT

67 Fermionic and Real quantum theory Rebit Extend minimally to composite systems Qubit 1 linear constraint Tr[ y ]=0 Real quantum theory bit 2 linear constraints Tr[ y ]=0 Tr[ x ]=0 Extend minimally to composite systems Fermionic quantum theory Real and Fermionic quantum theory are (the only two) minimal SSR of QT minimal SSR => bilocal tomography G. M. D Ariano, F. Manessi, P. Perinotti and A. Tosini, IJMPA (2014) L. Hardy and W. K. Wootters, Foundations of Physics 42, 454 (2012)

68 5. Future perspectives

69 5. Future perspectives Quantum Theory has been proved to be an operational theory of information processing Hardy, L. quant-ph/ (2001) CPD. Phys. Rev. A 84, (2011) Masanes, L., Muller, M.P. New J. Phys. 13(6), (2011) Dakic, B., Brukner, C. In: Halvorson, H. (ed.) Deep Beauty pp CUP (2011) + Axioms regarding how information can or cannot be manipulated

70 5. Future perspectives Quantum Theory has been proved to be an operational theory of information processing Hardy, L. quant-ph/ (2001) CPD. Phys. Rev. A 84, (2011) Masanes, L., Muller, M.P. New J. Phys. 13(6), (2011) Dakic, B., Brukner, C. In: Halvorson, H. (ed.) Deep Beauty pp CUP (2011) + Axioms regarding how information can or cannot be manipulated Question: informational derivation of Fermionic quantum theory? What is missing??

71 5. Future perspectives Quantum Theory has been proved to be an operational theory of information processing Hardy, L. quant-ph/ (2001) CPD. Phys. Rev. A 84, (2011) Masanes, L., Muller, M.P. New J. Phys. 13(6), (2011) Dakic, B., Brukner, C. In: Halvorson, H. (ed.) Deep Beauty pp CUP (2011) + Axioms regarding how information can or cannot be manipulated Question: informational derivation of Fermionic quantum theory? What is missing?? Spacetime? Dynamical quantities? Equation of their evolution? mechanical side?

72 5. Future perspectives Quantum Theory has been proved to be an operational theory of information processing Hardy, L. quant-ph/ (2001) CPD. Phys. Rev. A 84, (2011) Masanes, L., Muller, M.P. New J. Phys. 13(6), (2011) Dakic, B., Brukner, C. In: Halvorson, H. (ed.) Deep Beauty pp CUP (2011) + Axioms regarding how information can or cannot be manipulated Question: informational derivation of Fermionic quantum theory? What is missing?? Spacetime? Dynamical quantities? Equation of their evolution? mechanical side? Question: extend the operational informational framework to Quantum Field Theory Alternative to Algebraic Quantum Field theory Haag, R., Local quantum physics, volume 2, Springer Berlin, 1996.