Index
- a
- Abelian symmetry 629–630
- absolutely maximally entangled states 317
- absorption 691, 810–811
- accuracy 805, 814
- active transformations 48
- additivity 224
- adiabatic approximation 477, 478
- adiabatic computation 104–105
- adiabatic theorem 105
- alphabet 403
- Anderson localization 599
- angular momentum 635
- annihilation operator 196
- anti‐Jaynes–Cummings Hamiltonian 488
- approximate quantum cloning
- area law 311
- asymmetric cloning 69–70
- asymptotic activation effect 273
- asymptotic continuity 223
- asymptotic superactivation 277, 284
- atom‐cavity microscope 680
- atom chip 684
- atomic ensemble 702, 724, 731
- atomic frequency comb 725–727
- atomic kaleidoscope 680
- atomic spin operator 704
- atomic trajectory 679
- atom–light interaction 802–805
- atoms in a cavity 661
- attenuated laser pulses 360
- Aunt Martha 369
- authentication 357
- axioms of probability 405
- b
- base norm 226
- BB84 protocol 278, 355, 369
- BBPSSW protocol 242
- beam splitters 199, 201, 371, 409–410, 681
- Bell
- Bell inequalities
- communication complexity reduction 285–286
- Bell states 242, 336, 424
- Berry phase 477
- binary symmetric channel (BSC) 9
- binding entanglement channel 281–282
- binomial coefficient 64
- bipartite 195
- bipartite entanglement distillation
- bipartite system 233
- biseparable 308
- bit‐flip error 116
- Bloch ball 42
- Bloch band 497
- Bloch equation 634
- Bloch–Messiah reduction 846
- Bloch sphere 417
- Bloch vector 42
- block code 10
- Boolean function 404, 432
- bosonic system 613, 614
- bosons, Gaussian state 314
- bound entanglement
- activation effects 284–285
- applications 275–277
- asymptotic activation 277–278
- asymptotic irreversibility 272
- asymptotic regime 277
- Bell inequalities and communication complexity reduction 285–286
- binding entanglement channel 281–282
- bipartite 238
- continuous variables 287
- enhanced probabilistic quantum teleportation 276–277
- feedback to classical theory 286–287
- information phenomenon 281
- multipartite 248
- quantum cryptography 278–280
- remote quantum information concentration 285
- states 206
- bound information 281
- bound states 600
- branching diagram 610, 613
- breeding 246
- Brownian motion 593
- Bures distance 219
- bus mode 490
- by‐product operator 452
- c
- Calderbank–Shor–Stean code (CSS) 358
- Caley's hyperdeterminant 300
- canonical commutation relations 45
- canonical transformations 717
- Cartan decomposition 653
- Cauchy–Schwarz inequality 203
- cavity 678, 698
- CD‐decomposition 464
- centraliser 610, 634
- channel 75
- binary symmetric 9
- classical 83–84
- covariant 88
- dephasing 113
- depolarizing 87, 112
- discrete 4
- entanglement breaking 87
- expansion 77
- forgetful 86
- Gaussian 89
- Heisenberg picture 77
- ideal 86–87
- with memory 83–84
- memoryless 85
- noiseless 4
- noisy 4
- noisy time evolution 77–78
- product 113
- restriction 77
- Schrödinger picture 77
- unitary time evolution 77
- channel capacity
- channel noise 358, 691
- characteristic function 46
- charge qubit 644, 656
- Choi–Jamiolkowski isomorphism 78–80, 277
- Cirac–Zoller 95, 490
- classical–classical state 180
- classical Gaussian noise 50
- classical regime 811
- Clifford gates 428
- Clifford group 453, 459–461
- cluster state 249, 449, 838
- cluster states 849
- CNOT gate 653, 656, 676
- multiply controlled 653
- C‐numerical range 614
- code
- coherent attack 360
- coherent evolution 593
- coherent pulses 372
- coherent quantum control 493
- coherent spin state 705, 712
- coherent states 45, 47, 783–786
- coherent superposition 677
- collective attack 360
- collective controls 633
- coloring 27–28
- commutant 610
- commutation relations
- angular momentum 704
- commutator 196
- compact Lie algebra 614
- completely positive map 75–78
- complete positivity 44
- composability 357
- compositeness 26–27
- composition 44
- concurrence 154
- conditional entropy 8, 223
- conditional probability distribution 182
- conditional variance 348
- connection 693
- constrained optimisation 616
- continuous variables 195
- control engineering 607
- controllability 607, 628
- controllability criteria 608
- controlled NOT 407, 429
- operation 242
- controlled reversible inhomogeneous broadening 724
- controlled Sign gate (CSIGN) 445
- controlled unitary gate cU 658
- controlled‐Z‐gate 313
- control system 608
- control theory 651
- convex roof construction 224
- Cooper pair boxes 684
- correlation matrix 198, 199
- correlation operator 241, 249
- coset 651, 653
- leader 15
- coupling topology 653–655
- covariance matrix 136, 315
- criterion of separability 138
- creation operator 207
- cross norm 227
- criterion of separability 135
- cryogenic environment 673
- cryptography 33
- CSS code 122
- d
- decoherence 411, 597, 677, 716
- free coding 377
- DEJMPS protocol 243
- dense coding capacity 160
- density matrix 427
- density operator 647
- thermal 647
- dephasing channel 113
- depolarization 241
- depolarizing channel 112
- depumping rate 706
- designer atom 820
- detection 589, 590
- Deutsch–Josza algorithm 94–96, 645, 648, 653, 661
- Deutsch's algorithm 93
- dipole‐blockade 508
- dipole–dipole interaction 507
- discrete log 101
- discrete‐time quantum walk 593
- discretization 588
- displacement 811
- operator 46
- distillability 252–253
- distillable entanglement 155, 220, 236
- Rains' bound 226
- distillation 232
- distributed‐phase‐reference 373
- divide‐and‐conquer 22
- Doppler cooling 802
- dual code 14
- dual‐rail encoding 440
- Duan separability criterion 712
- dynamical trapping 523–524
- dynamic disorder 599
- dynamic group 633
- dynamic system algebra 610, 614
- e
- eavesdropping 354, 360
- effective Rabi frequency 816
- eigenvalue 418, 419
- symplectic 315
- eigenvector 418
- Einstein–Podolski–Rosen (EPR) 195, 675
- electron spin 563, 643
- electro‐optic modulator 598
- element distinctness 104
- encoded operator 119
- energy constraint 41–42
- ensemble quantum 643
- computing 648
- ensemble states 661
- entangled mixed states 131
- entangled pure states 130, 294
- entangled states 392, 396, 712, 794
- of atomic ensembles 712
- entanglement 195, 231, 334–336
- entanglement measures 305
- additivity 224
- additivity on pure states 223
- asymptotic continuity 223
- axioms for 221
- convex roof construction 224
- cross norm measure 227
- distillable entanglement 220
- entanglement cost 219
- entanglement monotones 222
- entanglement of formation 224
- entropy of entanglement 220, 223
- extremality of distillation and cost 223
- logarithm of the negativity 225
- norm based monotones 226
- ordering of 223
- pure states 616
- regularization 223, 224
- relative entropy of entanglement 225
- robustness of entanglement 226
- squashed entanglement 228
- uniqueness on pure states 223
- entanglement of formation 153, 224
- entropy
- error
- Eulerian path 20
- exchange coupling 554–556
- expectation value 615, 616
- quantum computer 644
- experimental control 644
- experimental quantum cloning 70–71
- extension field 12
- extrinsic constraints 620
- f
- Fabry–Perot 678
- factoring 97
- factorization 32
- faint pulse QKD
- Faraday mirror 372, 373
- fast Fourier transform (FFT) 98
- feedback loop 597, 598
- feed‐forward 389–390
- fermionic system 610
- fermions
- Gaussian state 314
- fidelity 240, 241, 339, 676
- entanglement 113
- field
- field‐ionization 673
- filtering 239
- operation 299
- five‐qubit quantum computer 646
- flux qubit 644
- focal Hamiltonian 311
- free atom limit 811
- free‐space QKD 373–375
- frequency combs 837
- full controllability 644, 645
- symmetry condition 612
- g
- gain 345, 346
- Galilei group 635
- gapped phase 311
- gate
- Gaussian measurements 51–52
- Gaussian operations 199–200
- Gaussian quantum cloning 51
- Gaussian states 47, 200–202
- Gaussian transformations 387–389
- generator matrix 13
- genuine entanglement 845
- genuine multipartite entanglement 162
- geodesic 651, 655
- geometric 654
- GHZ‐class 164
- GHZ game 318
- GHZ state 235
- GKS‐Lindblad generator 622
- glass fiber 371
- GMon 624
- Gottesman/Chuang trick 438–439
- gradient echo memory 724
- gradient flow 617
- graph isomorphism 33, 102
- graph state 249, 449
- Greenberger–Horne–Zeilinger (GHZ) 820
- group orbit 614
- Grover's algorithm 103
- Grover's search 102
- h
- Hadamard gate 92, 416, 425
- Hahn–Banach theorem 141
- Hamiltonian 419, 421
- Hamming code 14–15
- Hamming distance 10
- Hamming weight 10
- Hanbury Brown and Twiss 681
- hashing 245, 252, 256
- inequality 224
- Heisenberg algebra 624
- Heisenberg–Langevin equations 707
- Heisenberg limit 780, 782, 791
- Heisenberg picture 704
- Hermitian conjugate 413
- hidden subgroup problem 101, 653
- abelian 653
- hidden translation problem 102
- higher dimensions, cloning 68
- high‐finesse cavity 683
- highly charged ions 822
- Hilbert space 57, 343
- Holevo bound 159
- Holevo's theorem 316
- holonomic quantum computation
- holonomy 478
- homodyne detection 389–390
- homodyne detector 344, 346
- homodyne method 677
- Hubbard model 501
- Huffman coding 7
- hyperdeterminant 300
- hyperpolarisation 648
- i
- incomparable states 218
- individual attack 360
- individual controls 632
- infinite‐dimensional 195
- inhomogeneous walk 598–600
- inseparability criteria 202–209
- inseparable
- fully 308
- inseparable 202, 203
- instance 19
- intensity correlation 681
- interaction phase 506
- interference 414–416
- interferometer 780–783
- internal state preparation 807–808
- intrinsic constraints 620
- intrinsic information 281
- invariants 296
- ion
- Ising interaction 645, 653
- l
- Lagrange multiplier 62
- Lamb–Dicke 803
- Landau symbols 21
- Langevin stochastic forces 707
- laser beam 829
- laser‐cooling 679
- laser diodes 373
- laser spectroscopy (LS) 799
- Lie algebra 653, 656, 661
- Lie semialgebra 622
- Lie semigroup 622
- Lie wedge 623
- light–atoms interface 701
- light force 683
- light pulses 372
- light source 680
- Lindblad‐generator 622
- linear optics 440
- linear spin chain 653
- linear transformations 199
- local broadcasting 184–186
- local C‐numerical range 616
- local coherence 187–188
- local operations and classical communication (LOCC) 131, 190, 216, 217, 234, 297
- local oscillator 707
- local unitary (LU) 295
- logarithmic negativity 157, 225, 272
- logical Heisenberg picture 456–457
- logical qubit 119
- logic gates 414
- Lorentz group 635
- lossy channel 50, 360
- m
- Mach–Zehnder interferometer 411–412
- macroscopic superposition 512
- magnetic resonance 643
- majorization 218, 620
- majorization criterion of separability 134
- Markov condition 624
- master equation 620
- matrix
- maximally entangled set 298
- maximally entangled states 217
- Maxwell–Bloch equations 705
- measurement 421–422
- measurement‐based quantum computation (MBQC) 319, 450, 466, 837, 852–853
- Mermin GHZ game 318
- Mermin–Klyshko inequalities 285
- metrology 320
- micromaser 674
- millennium problems 31
- minimal reversible entanglement generating set (MREGS) 304
- minimum distance 11
- quantum 119–120
- minimum spanning tree 34
- mixed state 427
- entanglement 235–236
- mixing 42
- molecule 815
- monogamy of entanglement 164, 302
- motional eigenfrequencies 528
- motional eigenmodes 520
- motional sideband 488
- multimode quantum light 837
- multipartite 210
- multipartite bound information 286
- multi‐partite entanglement 845
- multipartite entanglement distillation 268–269
- multipartite fully‐separable states 162
- multipartite k‐separable states 162
- multipartite pure state entanglement 235
- multipartite quantum secret sharing 851–852
- multiparty entanglement purification 249
- multiparty quantum channels 287
- multiphoton path representation 761–766
- multiplexed homodyne detection 842, 843
- multiplexing, spatial 588, 590
- multiplexing, temporal 589, 590
- multiply‐controlled NOT gate 653, 655
- multiscale entanglement renormalization ansatz (MERA) 312
- mutual information 8, 316
- n
- near‐field image 833
- negative partial transpose (NPT) 237
- negative Wigner functions 849
- negativity 157, 225
- network 587
- Nielsen's theorem 298
- N→M purification protocol 245
- NMR quantum computer 646, 648
- no‐broadcasting theorem 72
- no‐cloning theorem 56–57, 116, 335, 340, 370
- noiseless coding theorem 6–7
- noisy apparatus 252–257
- noisy coding theorem 9
- noisy operation 253–254
- non Abelian quantum Fourier transform 102
- nonclassical states 819–821
- nondestructive state detection 815–819
- nondeterministic polynomial 25
- non‐Gaussian operations 52–53, 849, 853
- non‐Gaussian transformations 390–391
- nonlinear‐sign‐shift gate (NSS) 445
- non‐local games 318
- non‐locality 318, 675
- nonseparable state 335
- nonunity gain teleportation 347
- normal form 296
- normal modes 801
- NP 24
- n‐positive map 79
- nuclear magnetic resonance (NMR) 71
- nuclear spin 573–574
- nullifiers 850
- number states 45
- numerical optimal control 624, 651
- numerical range 614
- NV centers 661
- o
- observable 615
- all expectation values 634
- occupation‐number qubit 439
- one‐time pad 354
- one‐way function 33
- one‐way pattern 452
- open system 683
- optical amplification 831
- optical clocks 805–806
- optical density 706
- optical dipole 815
- optical experiments 678
- optical Feshbach resonance 514
- optical frequency combs 838
- optical lattice 496
- optical potential 496
- optical qubits 439–440
- optimal control 655
- theory 643
- optimization 34–37
- oscillator algebra 634
- p
- Pancharatnam phase 476
- para‐hydrogen 661
- parallel computing 661
- parallel transport condition 476
- parametric fluorescence 681
- parity check matrix 13
- partial transpose 205, 208
- partial transposition 132, 206, 208, 225–226, 237
- criterion of separability 133
- partition 308
- passive transformations 48
- Pauli group 122
- Pauli matrices 59, 60, 420
- percolation 594
- period finding 97
- phase conjugation 50
- phase‐covariant cloning 63–65
- phase distribution 677
- phase gate 428
- phase space 45
- phase‐space variables 197
- photon 698
- photonic band‐gap 684
- photon‐number resolving detection 589–592
- photon‐number splitting attack 360
- physical qubit 119
- plug&play‐system 372
- Pockels cells 369
- polarizing beam splitter (PBS) 378
- polynomial reduction 29–30
- positive maps 144
- positive operator valued measure (POVM) 66
- positive partial transposition (PPT) 237
- positive Shannon entropy 181
- primality 27
- prime field 12
- Prim's algorithm 35
- privacy amplification 359
- probabilistic cloning 70
- probabilistic gates 444
- probability amplitudes 410–414
- product channel 113
- product state 294
- proof checking 33
- proof existence 33
- pseudo‐pure state 647, 648
- pseudo‐spin system 644, 656, 661
- pulse shaping 842
- pure product states 130
- pure states 43, 427, 661
- entanglement 233
- purification loop 695
- purification step 240
- q
- QND interaction 706
- quadrature covariance matrix 842
- quadrature operators 706
- of atomic ensemble 705
- quadratures 345
- quantized motion 801
- quantized radiation field 761
- quantum
- bits 175
- channel capacity 114
- channels 43, 370, 691
- circuit 428–433, 561, 578
- code 114
- coherence 175
- computation 259–260
- control 643, 651, 661
- Cramer‐Rao bound 792, 853
- cryptography 278–280
- Darwinism 186
- defined 175
- dense coding 158, 376–377, 391–393
- discord 180–184
- dot 553, 564, 698
- error correction 259
- gate operation 521, 526
- harmonic oscillator 196
- information theory 265
- interface 672
- laser pointer 828–830
- logic gates 377
- logic spectroscopy 806
- memories 683
- messengers 683
- metrology 853–854
- microlithography 828
- mutual information 182
- neural network 661
- noise 707, 827
- non demolition 676, 706
- operation 43
- phase gate 676
- regime 811
- repeaters 691, 713
- secret sharing 317
- sensing 793, 795
- Shannon theory 316
- simulator 595
- systems theory 607
- teleportation 333
- walk 104, 593–595
- quantum algorithm 521, 544, 817
- quantum‐beat 682
- quantum‐classical boundary
- quantum‐classical state 180
- quantum cloning 720
- quantum communication 232, 257, 691
- quantum compiler
- quantum correlations
- quantum cryptography 70, 71
- quantum error correction code (QECC) 114, 358
- quantum Fisher information 780, 792
- quantum Fourier sampling 96
- quantum Fourier transform 98, 653, 654
- quantum gate
- quantum imaging
- quantum key distribution (QKD) 357, 393–396
- faint pulse 371–375
- quantum map
- quantum memory 712, 728
- quantumness 2
- quantum protocol
- multi‐party 317
- quantum teleportation 375, 718
- of light onto atoms 719
- quasifree states 47
- quaternion 634
- qubits 65–68, 804
- r
- Rabi flopping 803
- Rabi frequency 680, 803
- Rabi pulse 675
- Radon–Nikodym theorem 82–83
- Rains' bound 226
- Raman process 680
- random walk 593
- range criterion of separability 148
- rank
- tensor 300
- rare‐earth ion 728–730
- reachable set 620, 645
- realtime measurements 678
- receiver 4
- recoil kicks 683
- recurrence protocol 240, 250
- reduced density matrix 427
- reduction 29–30
- regularization 223, 224
- relative C‐numerical range 616
- relative entropy
- relative entropy of entanglement 156
- remote quantum information concentration 285
- repeater 691
- rephased amplified spontaneous emission 727–728
- resources 696
- state 319
- retarded time 705
- reversible classical computation 92
- reversible computation 405, 431
- Riemannian exponential map 618
- Riemannian manifold 617
- Riemannian metric 617
- Riemannian symmetric space 653
- robustness of entanglement 226, 302
- rotating wave approximation (RWA) 743, 761, 803
- rotational state 816
- RSA 33
- Rydberg atoms 672
- s
- satisfiability 29
- scalability 648, 649, 654, 661
- Schmidt
- Schrödinger cat 676
- Schrödinger‐cat states 821
- secure function evaluation 318
- secure links 374
- secure state distribution 258–259
- self‐homodyning 707
- semi‐simple Lie algebra 614
- separable 201, 202
- Shannon entropy 5–6, 177, 181
- Shannon's theorem 432
- Shor's algorithm 98
- shot noise 827
- sidebands 707
- transitions 804
- sifting 356
- sign‐flip error 116
- Simon's algorithm 96
- simple Lie algebra 610
- simulability 613
- single‐atom transistor 512
- single photon processes in cavity 767
- single‐photon source 682
- solid‐state 553
- spatially multimode beams 838
- spectrum estimation 295
- spin
- spin‐1/2 675
- spontaneous emission 674, 680
- squashed entanglement 228
- squeezed states 196, 200, 386, 393, 711, 786–792
- of atomic ensemble 711
- squeezing 196
- stability 805
- diagram 523–524
- stabilizer code 123
- stabilizer formalism 455
- stabilizer group 122
- standard array 15
- standard form 209
- Stark effect 673
- Stark eigenstate 507
- state‐dependent cloning 57–63
- state preparation 819
- states 42
- static disorder 599
- Stinespring dilation theorem 80
- Stinespring representation 80
- stochastic local operations and classical communication (SLOCC) 298
- stochastic matrices 404, 405
- Stokes vector 704
- strip‐line resonators 684
- strong‐binding 811
- strong controllability 628
- strong coupling 678
- strong phase reference pulse 363
- strong subadditivity 316
- subgroup orbit 614, 619, 620
- super additivity 114
- superconducting 672
- qubits 575–582
- supermodes 840, 847
- superradiance 683
- super‐resolution techniques 834
- switchable noise 623
- symmetry 610
- symplectic transformations 199
- synchronously pumped optical parametric oscillators (SPOPOs) 838
- system algebra 634
- systems theory
- t
- tangent space 619
- 3‐tangle 307
- technical noise 707
- tensor 296
- thermal state 648, 661
- threshold 254
- time complexity 643, 654, 655, 661
- time‐optimal 645, 651, 653–655
- time reversal 206
- Toffoli gate 429, 432, 656
- topological order 311
- topological quantum computing 657
- trace distance 219
- transmitter 4
- traveling salesman problem 36
- tripartite 202
- T‐transform 623
- T‐V diagram 348
- two‐colorable graph 250
- 2D quantum walks 600
- 2π pulse 675
- two qubit gate 505
- u
- unbalanced interferometer 371–372
- uncertainty relation 198
- unconditional security 359
- unitary matrix 423, 430
- unitary operation 44
- unitary orbit 645
- unitary transformations 199
- unity gain teleportation 347
- universal cloning 65–69
- universal control 634
- universal gate set 91, 428
- universal quantum gates 635
- universal quantum simulators 508
- z
- Zeeman level 680
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