Quantum Information Theory with Gaussian Systems

More documents

Recommendations

Info

4 Gaussian quantum cellular automata After carrying out the reduction, this becomes ˆγ(k) ↦→ ÂT (k) · ˆγ(k) · Â(k) + ĈT (k) · ˆγ ′ (k) · Ĉ(k). (4.40) The output state of an irreversible Gaussian qca with transformation Γ and noise form g is given in (4.33) and corresponds to a transformation of the correlation function as ˆγ(k) ↦→ Γ T (k) · ˆγ(k) · Γ(k) + ˆg(k). (4.41) Comparing (4.40) and (4.41) yields for the irreversible qca T: Γ(k) = Â(k) and ˆg(k) = ĈT (k) ˆγ ′ (k) Ĉ(k). Indeed, g is real and symmetric as required, i.e. ˆg(k) = −ˆg(−k) = ˆg(k), because C is real and γ ′ is real and symmetric. So, while reversible Gaussian qcas with local ancillas can implement irreversible Gaussian qcas of type IV, the converse is unfortunately not clear: are all irreversible Gaussian qcas of type IV? The answer to this question is an important step towards the definition of Gaussian as well as general irreversible qcas. 98
Private Quantum Channels
Page 1 and 2:
Quantum Information Theory with Gau
Page 3:
Vorveröffentlichungen der Disserta
Page 6 and 7:
Contents Quantum Cellular Automata
Page 8 and 9:
List of Figures viii
Page 10 and 11:
List of Theorems x
Page 12 and 13:
Summary mum is reached by a measure
Page 14 and 15:
Summary 4
Page 16 and 17:
1 Introduction electromagnetic fiel
Page 18 and 19:
1 Introduction 8
Page 20 and 21:
2 Basics of Gaussian systems Since
Page 22 and 23:
2 Basics of Gaussian systems Theore
Page 24 and 25:
2 Basics of Gaussian systems For a
Page 26 and 27:
2 Basics of Gaussian systems for co
Page 28 and 29:
2 Basics of Gaussian systems 2.2 Ga
Page 30 and 31:
2 Basics of Gaussian systems As pur
Page 32 and 33:
2 Basics of Gaussian systems unitar
Page 34 and 35:
2 Basics of Gaussian systems In pha
Page 36 and 37:
2 Basics of Gaussian systems Remark
Page 38 and 39:
2 Basics of Gaussian systems 28
Page 41 and 42:
3 Optimal cloners for coherent stat
Page 43 and 44:
3.1 Setup 3.1 Setup A deterministic
Page 45 and 46:
f2(T) 1 0 (a) 1 f1(T) f2(T) 1 0 (
Page 47 and 48:
the expectation value of an arbitra
Page 49 and 50:
3.3 Covariance clone). A more gener
Page 51 and 52:
3.3 Covariance In the case of joint
Page 53 and 54:
3.3 Covariance where the second ide
Page 55 and 56:
3.4 Optimization search to covarian
Page 57 and 58: 3.4 Optimization Hence for the case
Page 59 and 60: 1 2 3 1 2 0 f2 1 2 (a) 2 3 1 f1 0.0
Page 61 and 62: 3.4 Optimization tained without app
Page 63 and 64: = π R 2 0 dt ǫ + R2 = π log , ǫ
Page 65 and 66: 3.4 Optimization where the bound is
Page 67 and 68: 3.4 Optimization wheren is the matr
Page 69 and 70: 3.4 Optimization Lemma 3.10: The ou
Page 71 and 72: 3.5 Optical implementation The wei
Page 73 and 74: 3.6 Teleportation criteria can be t
Page 75 and 76: 3.6 Teleportation criteria carry th
Page 77: Quantum Cellular Automata
Page 80 and 81: 4 Gaussian quantum cellular automat
Page 111 and 112: 5 Gaussian private quantum channels
Page 113 and 114: p Figure 5.1: Illustrating the encr
Page 115 and 116: characteristic function χrand(ξ)
Page 117 and 118: = − 1 2 2Nf i,j=1 where M ′ =
Page 119 and 120: p δ ξk ξ x 5.2 Security estimati
Page 121 and 122: 5.2 Security estimation where in th
Page 123 and 124: 5.3 Result and outlook 5.3 Result a
Page 125: Bibliography
Page 128 and 129: Bibliography [7] M. Reed and B. Sim
Page 130 and 131: Bibliography [37] R. F. Werner,Opti
Page 132 and 133: Bibliography [69] N. Takei, H. Yone
Page 134 and 135: Bibliography 124
show all

Quantum Information Theory with Gaussian Systems

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?