Jaeger G. Quantum Information: An Overview
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Index 281
privacy amplification, 200, 202
private key, 192
probability
axioms of, 241
epistemic, 7
probability density function (p.d.f.), 232
probability mass function, 70
probabit, 2
problem
decision, 206, 207
easy, 205
halting, 205
hard, 205
LP, 142
measurement, 30, 31
oracle, 222
ratio, 113
separability, 93
Simon’s, 229
process
Markov, 73
quantum
type I, 33
type II, 33
projection
L¨uders, 37, 38, 83, 262
quantum state, 32, 34, 35, 37, 41,
164, 166, 209, 214
selective, 37
projection method
Schmidt, 166
projection postulate, 32, 34, 246
projector, 3, 5, 141, 236
proof
security, 201
PSPACE, 206, 213
public key, 192
purification, 107, 160
entanglement, 104
quantum state, 23
purity, 5, 31, 128, 145
PV measure, 42
QBER, 197, 199
QSAT, 214
qu-d-it, 140, 167, 174
quantum amplitude
amplification of, 223
quantum circuit, 211
quantum circuit model, 203, 211
quantum cloning, 187
quantum cloning machine
universal (UQCM), 188
quantum computing
fault-tolerant, 214
quantum copying, 186
quantum copying machine, 188
asymmetric, 189
optimal, 189
symmetric, 189
quantum dephasing, 158
quantum erasure, 160
quantum interference, 18
quantum jump, 32
quantum key distribution, 10, 14, 25,
43, 48, 63, 153–155, 191, 193–195,
197–199, 201
autocompensating, 194
quantum key expansion, 201
quantum logic
traditional, 240, 243
quantum measurement problem, 30
quantum mechanics
Hilbert-space formulation of, 237
Liouville formulation of, 248
standard postulates of, 245
quantum network, 211
quantum state
“amplification” of, 222
B class, 135
bipartite, 92
bound, 94, 105
broadcasting of, 149, 185
catalyst, 122
classicality of, 97
comparison of, 156
completeness of, 51
distillable, 94
entangled, 92
best separable approximation of, 97
factorable, 92
filtering of, 156
generic class, 135
GHZ class, 133
locally contaminated (LC), 174
mixed, 2, 3, 5, 6, 27, 31
multiseparable, 133
product, 92
282 Index
pure, 3, 5
purification, 23, 159
reduced, 39
S class, 135
separable, 92
W class, 133, 135
quantum state preparation, 20, 29
quasi-phase-matching (QPM), 116
qubit, 1–6, 8, 9, 11–14, 16, 17, 20, 21,
23–25, 40, 47, 50, 56, 58, 60, 82,
124, 130, 132, 134, 140–143, 147,
148, 153–155, 157, 160, 162, 169,
171–173, 176–178, 180, 182, 183,
188–190, 193, 197–200, 203, 211,
217, 222
ancillary, 21, 22, 41, 107, 144, 154,
155, 176, 178, 179, 181, 187–189,
201–203, 214, 223
bosonic, 215
control, 63, 211
logical, 174, 175, 178, 180, 183, 217
phase, 24
polarization,4,11
representation of, 3, 8, 11
dual-rail, 20
spatial, 19, 23, 161
target, 63
temporal, 61
qutrit, 36, 97, 101, 170
radius
Bloch vector, 12
spectral, 236
Radon–Nikodym theorem, 51
ratio problem, 113
ray, 233
read-write head, 207
readout, 26, 27, 29, 203
reality condition, 50
Redhead, M., 3
register, quantum, 30
registration, measurement, 30
repetition hypothesis
quantum measurement, 32
representation
equivalent, 239
irreducible, 239
operator sum, 40
projective, 239
spectral, 238
resource
directed, 108, 147
entanglement, 104, 108
information processing, 78, 82
quantum information, 105
undirected, 108, 147
retrodiction, 30
Rohrlich, D., 93, 109
Rosen, N., 49, 91
rotation, 13
hyperbolic, 13
RP, 208
RSA, 192
rule
Born, 12, 141, 246, 252
Born-type, 51
L¨uders, 37
Sanpera, A., 97
scheme, finite, 68
Schmidt measure, 95, 99, 101
Schmidt number, 94, 99, 119
Schmidt rank, 94
Schr¨odinger equation, 30, 39, 41, 247
Schr¨odinger picture, 247
Schr¨odinger, E., 91
Schumacher, B., 1, 87, 95, 169
Schumacher–Westmoreland–Wootters
bound, 152
secrecy capacity, 202
security
unconditional, 48, 201
security proof, 201
selection, 30
self-interference, 23, 57, 61, 82
separability, degree of, 97
sequences, typical
theorem of, 70
Sergienko, A. V., xi
Shaknov, I., 55
Shannon coding, 79
Shannon, C., 67
Shannon–Hartley theorem, 74
Shimony, A., 3, 53, 54, 97, 114
Shor code, 179
Shor, P., 224
sifting
quantum key, 196
Index 283
sigma algebra, 41, 240
simplex
Choquet, 7
singlet state, 50
singular values, 106
SL(2,C), 14
SO(3), 9
solvability
recursive, 207
source
entanglement, 55
single-photon, 194
spectral norm, 236
spectral theorem, 36
nuclear, 36
spectroscopy
quantum state, 126
spectrum
eigenvalue, 36, 145
speedup
quantum, 2, 220, 228
superpolynomial, 213
stabilizer, 130, 182, 214
automorphism group of, 214
stabilizer code, 181
state
Bell-correlated, 93
Bell-gem, 136
classical, 7
complete, 46, 50
control, 206
dispersion-free, 47–49, 52
EPR-correlated, 93
GHZ, 95, 123, 134, 135, 180, 181, 183
machine, 206
accepting, 206
initial, 206
rejecting, 206
quantum, 5
quantum-code, 178
vacuum, 215
W, 135
Werner, 97
state discrimination
ambiguous, 153
unambiguous, 154
state inversion
universal, 127
state space
classical, 7
quantum, 3
state specification
completeness of, 46
statistical operator, 3, 139, 174, 237
separability of, 100
statistical state, 3
statistics
quantum
Bose-Einstein, 161
Steane code, 183
Steane, A., 181, 215
Steinberg, A., 175
Stern–Gerlach apparatus, 34
Stokes four-vector, 14
Stokes parameters, 11–14, 98, 124,
140–143
two-particle, 98
two-qubit, 98
Stokes tensor
multiple-qubit, 125, 127
two-qubit, 98, 99
Stokes vector, 12
Stokes, G. G., 140
string
bit, 67
SU(2), 9
subalgebra
Boolean, 241
subensemble, 33, 37, 103, 111, 153
sublattice
Boolean, 241
suborthoposet, 241
subspace
vector, 233
subspaces
logic of, 243
measurement and, 33
subsystem, 23
dismissal of, 39
superbroadcasting
quantum state, 186
superoperator, 39, 122, 127, 143, 150,
248
superposition
coherent, 6, 31
superpositionprinciple,1,2,4,8,245
surprisal, 68
symbol
284 Index
Levi–Civita, 133
symmetry, 85, 114, 124, 126, 128, 136,
161, 175, 199, 260
tangle, 124, 126, 134, 146
I-, 107
residual, 133
tape
Turing machine, 207
teleportation
quantum state, 91, 104, 108, 147, 162,
187, 216, 217
tensor product, 239
Terhal, B., 104
thermodynamics
laws of, 111
time complexity, 207
Toffoli, T., ix, 65, 135, 209
tomography
quantum process, 143
quantum state, 139, 140, 144, 146
TP map, 40
trace, 236
cyclic invariance of, 5
partial, 38
trace relation, 125
transducer, 23, 57, 58
transformation
Boolean, 212
conditional sign-flip, 216
local unitary (LUT), 95, 121
nonlinear sign change, 216
transformations
group of, 239
transition matrix, 238
transposition, 40, 145
partial, 99
trap door, 192
Tukey, J. W., 67, 225
Turing machine, 204, 210
m-tape, 208
deterministic, 206
probabilistic, 207
quantum, 211
Turing, A., 70
two-slit experiment, 18
Uhlmann’s relation, 106
uncertainty relation
Heisenberg–Robertson, 2, 191, 193,
247
unitality, 40
unitarity, 5, 235
value space, 42
vector
norm of, 233
unit, 233
vector space, 233
basis for, 233
complete, 234
separable, 234
subspace of, 233
vectors
orthogonal, 233
orthonormal, 233
Vernam, G., 192
virtual slit, 57
visibility
entanglement, 60
single-particle interference, 21
two-particle interference, 57
von Neumann chain, 32
von Neumann equation, 247
von Neumann, J., xii, 3, 32, 35, 48, 49,
51, 243
wavefunction, 3
weight of evidence, 70
welcher-weg determination, 19
Werner state, 93
Wheeler, J., 32, 113
which-way determination, 19
Wiesner, S., 160
Wigner inequality, 56
Wigner’s theorem, 237
Wigner, E., 55
Wootters, W., 106, 160
word, 206
empty, 207
work, 111
Wu,C.S.,55
Zeilinger, A., 134, 164
Zurek, W. H., 260