ENTANGLEMENT OF GAUSSIAN STATES Gerardo Adesso

xii Contents
7.2.3. Tripartite entanglement of pure three-mode Gaussian states 132
7.2.3.1. Residual contangle and distillability of mixed states 133
7.3. Sharing structure of tripartite entanglement: promiscuous Gaussian
states 134
7.3.1. CV finite-squeezing GHZ/W states 134
7.3.2. T states with zero reduced bipartite entanglement 135
7.3.3. Promiscuous continuous-variable entanglement sharing 137
7.4. Promiscuous entanglement versus noise and asymmetry 138
7.4.1. Decoherence of three-mode states and decay of tripartite
entanglement 138
7.4.1.1. Basics of decoherence theory for Gaussian states 138
7.4.1.2. Robustness of tripartite entangled states 140
7.4.2. Entanglement distribution in noisy GHZ/W states 142
7.4.2.1. Separability properties 142
7.4.2.2. Sharing structure 143
7.4.3. Basset hound states: a ‘traditional’ sharing of entanglement 145
7.4.3.1. Tripartite entanglement 145
7.4.3.2. Sharing structure 146
7.4.4. The origin of tripartite entanglement promiscuity? 146
Chapter 8. Unlimited promiscuity of multipartite Gaussian entanglement 147
8.1. Continuous variables versus qubits 147
8.2. Entanglement in partially symmetric four-mode Gaussian states 148
8.2.1. State definition 148
8.2.2. Structure of bipartite entanglement 148
8.2.3. Distributed entanglement and multipartite sharing structure 150
8.2.3.1. Monogamy inequality 150
8.2.3.2. Tripartite entanglement estimation 151
8.2.3.3. Genuine four-partite entanglement: promiscuous beyond limits 153
8.2.4. Discussion 154
Part IV Quantum state engineering of entangled Gaussian states 157
Chapter 9. Two-mode Gaussian states in the lab 159
9.1. Schemes to realize extremally entangled states in experimental settings 160
9.1.1. GMEMS state engineering 160
9.1.2. GLEMS state engineering 161
9.2. Experimental production and manipulation of two-mode entanglement 162
9.2.1. Entangling power of passive optical elements on symmetric Gaussian
states 163
9.2.2. Effects of mode coupling on the entanglement generation 164
9.2.3. Experimental setup and homodyne measurement 166
9.2.4. Experimental measures of entanglement by the negativity 169
9.2.5. Experimental non standard form and optimization by linear optics 171
9.2.6. Summary of the experiment 173
Chapter 10. Tripartite and four-partite state engineering 175
10.1. Optical production of three-mode Gaussian states 175