Index

1-sensitive, 8 coherent states, 196 -biased oracle, 20 coincidence, 270, 271 n-partite, 125, 129 collective channel noise, 218 collective measurement, 190, 225 aerial fiber cable, 255 column flip, 8 afterpulse, 245, 253 compression, 55, 121 Akaike’s information criterion (AIC), concurrence, 52, 121 57 controlled-unitary operation, 262 amplitude amplification, 23 convex roof, 137 asymmetric channel noise, 210 coset sampling method, 177, 179 asymmetric quantum cloning machine, counting rate, 201–204 105 covariant, 48 avalanche photodiode (APD), 246 cover data, 235 balanced matrix, 13 dark count, 245 BB84, 186, 218, 220, 221, 224, 227, 230 decoy-state method, 200 beam splitter (BS), 50, 114 detection efficiency, 245 beam splitter entangler, 114 dispersion, 266 Bell state, 112, 120, 126, 264, 265 embedder, 236 Bell state measurement (BSM), 128, entangled photon, 265 264 entangled state, 126, 128 Bell type inequality, 123 entanglement, 52, 57, 114, 124, 265 Bernstein–Vazirani problem, 4 entanglement concentration, 55, 112 biCNOT, 193–195 entanglement cost, 137 bipartite, 129 entanglement distillation, 111, 119 bipartite,entanglement,infinite- entanglement of formation (EoF), 121, dimensional space, 126 137 birefringence, 250, 263, 266 entanglement purification, 188, 190 bit-flip, 191, 194, 196, 211, 215, 220 entropy of entanglement, 137 Bloch vector, 69 equivalence (EQ), 22 Boson–Fock space, 49, 114, 126 error correction, 187, 189, 195 error rejection, 216, 220, 225 channel coding, 55 error test, 189 channel state, 139 exact learning, 15 cloning machine, 49, 65 extractor, 236 CNOT, 193, 194, 220 coherence time, 271 Faraday mirror (FM), 251 coherent information, 119 fidelity, 64, 118 278 Index

final key, 195 one-way function, 168, 185 four-state protocol, 214, 225 one-way permutation, 169–171 optimal average input, 153 Gaiger mode, 246 oracle, 3 gated mode, 246 oracle computation, 3 Gaussian state, 49, 114 oracle identification, 3 GHZ state, 126, 129 oracle identification problem, 5, 20 Goldreich–Levin (GL) problem, 21 graph automorphism problem, 177 Peres–Horodecki criterion, 93 Grover search, 4, 19 periodically-poled potassium titanyl phosphate (PPKTP), 270 Hadamard gate, 256 phase covariant, 81 halving algorithm, 11 phase estimation, 256 hard-core predicate, 169 phase matching, 270 hashing, 188 phase-flip, 191, 194, 196, 197, 211, 215, hidden subgroup problem, 179 220, 225 Holevo capacity, 134 phase-matching, 266 hybrid argument, 5, 180 planar lightwave circuit (PLC), 248 hybrid matrix, 13 plug-and-play, 248, 251 hyperdeterminant, 125 PNS attack, 199, 254 polynomial method, 5 imperfect oracle, 15 POVM (positive operator-valued imperfect source, 196 measure), 46, 54 individual measurement, 190 prepare-and-measure, 187, 195 inner product (IP), 22 privacy amplification, 187, 195 input oracle, 5 probabilistic quantum cloning machine, interference fringe, 271 106 interferometer, Mach–Zehnder, 249 pseudo identity operator, 172 interferometer, Michelson, 269, 271 pseudo reflection operator, 172 interferometer, Sagnac, 256, 269 pseudorandom generator, 169 public key, 185 key rate, 196, 198, 206, 209 public-key cryptosystem, 176 kick-back effect, 262 QECC (quantum error correcting linear cost constraint, 140 code), 118–120 LOCC (local operation and classical quantum adversary argument, 5 communication), 47, 54, 55, 112 quantum adversary method, 5 loop mirror, 252 quantum bit error rate (QBER), 245, 250 majority voting, 258, 260 quantum capacity, 119 maximally entangled state, 111, 265 quantum computation, 5 minimal output entropy, 136 quantum dot, 264 minimum output entropy, 135 quantum Fourier transform followed by multipartite, 124 measurement (MQFT), 256 multipartite,entangled state, 128 quantum key distribution (QKD), 120, multiphoton pulses, 196, 199 186, 244 multitarget Grover search, 9 quantum key generation field trial, 255 quantum learning theory, 11 no-cloning theorem, 63 quantum query complexity, 19 Index 279 quantum state computational distin- state entangled, 53 guishability, 176 steganography, 235 quantum state tomography, 267 stego-data, 235 quantum teleportation, 264, 265 stochastic local operation and classical quantum adversary argument, 21 communication (SLOCC), 124 quasi-phase matching (QPM), 270 Strong superadditivity, 137 query complexity, 3, 5 strongly quantum one-way permuta- tion, 172 reliability function, 118 symplectic code, 119 remote state preparation (RSP), 128 robust, 20 tagged bits, 196, 199, 200, 205 robust quantum algorithm, 16 TP-CP (trace-preserving completely RSA, 186 positive) map, 117 trapdoor property, 178 Schwinger representation, 75 two-photon absorption (TPA), 264 secure private communication, 185 two-photon interference, 268, 269 separable, 134, 262 shrinking factor, 67 unconditional security, 187, 206, 216, Simultaneous Schmidt decomposition, 230 123 universal test, 169, 175 single-photon detector, 245 UQCM, 63, 65 six-state protocol, 213, 217, 225 SLOCC convertibility, 126 visibility, 245, 248, 250, 267, 268 spontaneous parametric down conver- sion (SPDC), 56, 223, 225, 230, W state, 126 265 weakly quantum one-way permutation, squeezed state, 48 171 Topics in Applied Physics

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