<<

. 9
( 9 .)



âÚÇÌÍË Ê‚•ÇÏ ‘ÃÏÇÐË„‚ÎË”ß Æ“–… ” Æ“–…‘Ï “ÇÊ–Îß•‚•‚ÏË
"’“ÇÆÇÎßБ •‘ÚÐÞÏ" ‘Ã΂”•âÏ Ð‚–ÍË, •‚ÍËÏ Í‚Í ÏÇ•“‘-
à•Ë˜ ‘’Ç“‚™ËÌ [20, 21, 142].
Α…Ëâ Ë Í‘Ï’ßá•Ç“Ђ⠗ËÊËÍ‚, •“–ÆБ –É˕ߔ⠔‘
¹•‘ Í‚”‚Ç•”â ÐÇÌ•“‚ÎßÐÞ˜ ‚•‘Ï‘„, •‘ „„ËÆ– ÑÎß-
”ΖڂÌБ”•ßá ’“‘™Ç””‘„ ’‘â„ÎÇÐËâ Ê‚’–•‚ÐÐÞ˜ —‘•‘Ð-
Û‘…‘ “‚ÊБ‘Ó‚ÊËâ „‘ÊÏ‘ÉÐÞ˜ ÏÇ•‘Æ‘„ ‘“…‚ÐËÊ‚™ËË
ÐÞ˜ ’‚“. °•”áÆ‚ „‘ÊÐËÍ΂ ËÆÇâ ’‘˔͂ ÆÇ•Ç“ÏËÐË”•”͢
Í‘…Ç“ÇЕБ…‘ „Ê‚ËÏ‘ÆÇÌ”•„Ëâ ÏÇÉÆ– ‚•‘Ï‚ÏË, —–ÐÆ‚-
ÏÇ•‘Æ‘„ ”‘ÊÆ‚ÐËâ Ê‚’–•‚ÐÐÞ˜ ”‘”•‘âÐËÌ. ¬‚Í ‘͂ʂΑ”ß,
ÏÇЕ‚ÎßÐÞ˜ ‘…“‚ÐËÚÇÐËÌ Ð‚ Ú˔Α Ë”’‘ÎßÊ–ÇÏÞ˜ ‚•‘-
ЂËÑÎÇÇ –Æ‘ÃÐ‘Ì Ã‚Ê‘Ì ÆÎâ “Ç‚ÎËÊ‚™ËË à•Ë˜ ÏÇ•‘Æ‘„
Ï‘„ ’‘Í‚ ÐÇ ’“‘”ÎÇÉË„‚Ç•”â. ¯‚ Æ‚ÐÐ‘Ï à•‚’Ç Ð‚ËÑÎÇÇ
â„Îâᕔ⠂•‘ÏÞ Ë Ë‘ÐÞ, Ê‚˜„‚ÚÇÐÐÞÇ „ ”‘„“ÇÏÇÐÐÞ˜
’Ç“”’ÇÍ•Ë„ÐÞÏ Ð‚Ï ’“ÇÆ”•‚„ÎâÇ•”â Æ‚ÎßÐÇÌÛÇÇ “‚Ê„Ë-
àÎÇÍ•“‘Ï‚…ÐË•ÐÞ˜ Α„–ÛÍ‚˜. ±‘ΑÉÇÐËÇÏ •‚͢ ‚•‘-
•ËÇ àÍ”’Ç“ËÏÇЕ‚ÎßÐÞ˜ ÏÇ•‘Æ‘„, ‘”Б„‚ÐÐÞ˜ Ђ Ë”’‘Îß-
Ï‘„ ‘•Ð‘”Ë•ÇÎßБ ÎÇ…Í‘ Ï‚ÐË’–ÎË“‘„‚•ß „ àÍ”’Ç“ËÏÇÐ-
Ê‘„‚ÐËË „Þ”‘͑ƑÓ‘•ÐÞ˜ “ÇʑЂ•‘“‘„ Ë “ÇʑЂДБ…‘
•‚˜, ‚ ÏÇ•‚”•‚ÃËÎßÐÞÇ „Ж•“ÇÐÐËÇ ”‘”•‘âÐËâ ’“ÇÆ‘”•‚„-
ÆË’‘Îß-ÆË’‘ÎßБ…‘ „Ê‚ËÏ‘ÆÇÌ”•„Ëâ.
Îâá• ’“‚Í•ËÚÇ”ÍË ËÆÇ‚ÎßЖá Âʖ ÆÎâ ˜“‚ÐÇÐËâ Í„‚Е‘-
£ Ê‚ÍÎáÚÇÐËÇ ‘•ÏÇ•ËÏ, Ú•‘ Ђ”•‘âÜËÌ ‘ÃÊ‘“ ÐÇ
„Þ˜ ”‘”•‘âÐËÌ, „ÍÎáÚ‚â ˘ „‘ÊÏ‘ÉÐÞÇ Í„‚Е‘„ÞÇ
Ï‘ÉÇ• ’“Ç•ÇÐÆ‘„‚•ß Ђ ’‘ÎБ•– ˜‘•â ÃÞ ’‘•‘Ï–, Ú•‘
Í‘““ÇÎâ™ËË.
Ú˔Α “‚Ñ•, •‚Í ËÎË ËЂÚÇ ’‘”„âÜÇÐÐÞ˜ Ê‚’–•‚ÐÐÞÏ
©Ð‚ÚË•ÇÎßÐ–á “‘Îß „ ’‘„ÞÛÇÐËË ËЕǓǔ‚ Í Ê‚’–-
”‘”•‘âÐËâÏ, –ÉÇ Ð‚”ÚË•Þ„‚Ç• ÐÇ ‘ÆЖ •Þ”âÚ– (”Ï.
•‚ÐÐÞÏ ”‘”•‘âÐËâÏ ‚•‘ÏÐÞ˜ ”Ë”•ÇÏ ”Þ…“‚΂ Ë ’Ç“„‚â
ÃËÃÎË‘…“‚—Ëá [189]). ¬ •‘Ï– ÉÇ ’‘ ÐÇÍ‘•‘“ÞÏ Ð‚ÃÎáÆÇ-
’“ÇÆΑÉÇÐЂ⠔˜ÇÏ‚ Í„‚Е‘„‘…‘ Í‘Ï’ßá•Ç“‚, ‘”Б„‚Ð-
ÐËâÏ Ú˔Α ’–ÃÎËÍ‚™ËÌ, ’‘”„âÜÇÐÐÞ˜ Ê‚’–•‚ÐÐÞÏ
Ђâ Ђ ’“ËÏÇÐÇÐËË „Ж•“ÇÐÐ˘ Ë Í‘ÎÇ•ÇÎßÐÞ˜ ”‘”•‘â-
”‘”•‘âÐËâÏ, “‚”•Ç• ” Í‚ÉÆÞÏ …‘Æ‘Ï „ …Ç‘ÏÇ•“ËÚǔ͑Ì
ÐËÌ Ë‘Ð‘„, Ê‚˜„‚ÚÇÐÐÞ˜ „ Ë‘ÐÐ‘Ì “‚ÆË‘Ú‚”•‘•Ð‘Ì
’“‘…“Ç””ËË [190].
ÎËÐÇÌÐ‘Ì Î‘„–ÛÍÇ. ¯‚ ÂÊÇ à•‘Ì ËÆÇË „ Ë‘ÐÐÞ˜ Α-
±‘-„ËÆËÏ‘Ï–, “‚Ê„Ë•ËÇ ËЕǓǔ‚ Í Ê‚’–•‚ÐÐÞÏ
„–ÛÍ‚˜ ÃÞÎË ”‘ÊÆ‚ÐÞ Ê‚’–•‚ÐÐÞÇ ”‘”•‘âÐËâ Æ„–˜ Ë
”‘”•‘âÐËâÏ ”ÎÇÆ–Ç• Í΂””ËÚÇ”Í‘Ì ÆËЂÏËÍÇ ”Ë”•ÇÏÞ ”
ÚǕޓǘ ˑБ„, ‚ •‚ÍÉÇ ’“‘„ÇÆÇÐÞ Æ“–…ËÇ àÍ”’Ç“Ë-
’‘ΑÉË•ÇÎßÐ‘Ì ‘Ó‚•Ð‘Ì ”„âÊßá. ³ ‘ÆÐ‘Ì ”•‘“‘ÐÞ,
ÏÇÐ•Þ „ ‘Ã΂”•Ë —ËÊËÍË Í„‚Е‘„‘Ì ËЗ‘“Ï‚™ËË.
“‚”ÛË“ÇÐËÇ ‘Ã΂”•Ë ’“ËΑÉÇÐËÌ Ê‚’–•‚ÐÐÞ˜ ”‘”•‘âÐËÌ
°ÆЂ͑ ’‘’Þ•ÍË Æ‚ÎßÐÇÌÛÇ…‘ “‚Ê„Ë•Ëâ àÍ”’Ç“ËÏÇÐ-
”•ËÏ–ÎË“–Ç• “‚Ê„Ë•ËÇ ‘ÃÜÇÌ •Ç‘“ËË Ê‚’–•‚ÐÐÞ˜ ”‘”•‘â-
•‚ÎßÐ‘Ì •Ç˜ÐËÍË ”•‘ÎÍЖÎË”ß ” Æ‘„‘ÎßБ ”Ç“ßÇÊÐÞÏË
ÐËÌ Ë ”‘‘•„Ç•”•„–áܢ àÍ”’Ç“ËÏÇЕ‚ÎßÐÞ˜ ’‘Ƙ‘Æ‘„. ³
•“–ÆБ”•âÏË, Í‘•‘“ÞÇ Æ‘ ͑Й‚ ÐÇ “‚Ê“ÇÛÇÐÞ Ë ’‘
Æ“–…‘Ì ”•‘“‘ÐÞ, ’‘”•‘âÐБ “‚”•–Ü‚â ’‘’–Îâ“Б”•ß à•‘Ì
”Ç…‘ÆÐâÛÐËÌ ÆÇÐß.
646 ª.£. ¢¡²¤¡´ª¯, ¢.¡. ¤²ªº¡¯ª¯, £.¯. ©¡¥¬°£ [µ¶¯ 2001


34. Biolatti E et al. Phys. Rev. Lett. 85 5647 (2000)
‘Ã΂”•Ë —ËÊËÍË ’“Ë„ÎÇÍ‚Ç• Í ÐÇÌ „”Ç Ã‘ÎßÛÇÇ Í‘ÎËÚÇ”•„‘
35. http://www.archive.org; http://ru.archive.org; http://xxx.itep.ru
–ÚÇÐÞ˜, Ú•‘ „ ”„‘á ‘ÚÇ“ÇÆß ”’‘”‘Ô•„–Ç• ‘•Í“Þ•Ëá 36. Special Issue on Quantum Information Phys. World 11 (3) (1998)
Б„Þ˜ ’“ËÏÇÐÇÐËÌ Ê‚’–•‚ÐÐÞ˜ ”‘”•‘âÐËÌ. 37. ³‚ÆÃÇ“Ë ¡ ¬„‚Е‘„‚â Ïǘ‚ÐËÍ‚ Ë —ËÊËÍ‚ àÎÇÏÇЕ‚“ÐÞ˜ Ú‚”•Ë™
´ÇÏ ÐÇ ÏÇÐÇÇ, Ðǔϑ•“â Ђ ’“ÇÆ’“ËÐËÏ‚ÇÏÞÇ –”ËÎËâ (®.: ®Ë“, 1989)
38. Bennett C H et al. Phys. Rev. A 53 2046 (1996)
’‘ “Ç‚ÎßБϖ „ÐÇÆ“ÇÐËá ’“‚Í•ËÚǔ͢ ’“ËΑÉÇÐËÌ
39. Bennett C H et al. Phys. Rev. A 54 3824 (1996)
Ê‚’–•‚ÐÐÞ˜ ”‘”•‘âÐËÌ, —ËÊËÍ‚ Ê‚’–•‚ÐÐÞ˜ ”‘”•‘âÐËÌ
40. ¤“ËÛ‚ÐËÐ ¢ ¡ ¬„‚Е‘„‚â àÎÇÍ•“‘ÆËЂÏËÍ‚ ÆÎâ “‚ÆË‘—ËÊËÍ‘„
‘”•‚Ç•”â ’‘Í‚ ’“ÇËÏ–ÜÇ”•„ÇÐБ •Ç‘“Ç•ËÚÇ”Í‘Ì Ë „‘ (®.: ªÊÆ-„‘ ®‘”Í. –Ð-•‚, 1981)
ÏБ…‘Ï ”’ÇÍ–Îâ•Ë„БÌ, Ú•‘, ’‘-„ËÆËÏ‘Ï–, ”‘”•‚„ÎâÇ• ÇÇ 41. Busch P, Lahti P J, Mittelstaedt P The Quantum Theory of
Measurement 2nd rev. ed. (Berlin: Springer, 1996) 7
"ÑÎÇÊÐß “‘”•‚". ¥‚ÉÇ ‚’‘Α…Ç•Þ Ð‘„Þ˜ Ђ’“‚„ÎÇÐËÌ
42. Bennett C H et al. Phys. Rev. A 59 1070 (1999)
—ËÊËÍË Í„‚Е‘„‘Ì ËЗ‘“Ï‚™ËË ’“ËÊЂá•, Ú•‘ “Ç‚ÎßБÇ
43. Lo H-K, Popescu S Phys. Rev. A 63 022301 (2001)
”‘ÊÆ‚ÐËÇ ”‘‘•„Ç•”•„–áܢ –”•“‘Ì”•„, •‚͢, Ђ’“ËÏÇ“, 44. Bose S, Vedral V, Knight P L Phys. Rev. A 60 194 (1999)
Í‚Í Í„‚Е‘„ÞÌ Í‘Ï’ßá•Ç“, ‘”•‚Ç•”â Æ‘„‘ÎßБ Æ‚ÎÇÍ‘Ì 45. Greenberger D M, Horne M, Zeilinger A, in Bell's Theorem,
’Ç“”’ÇÍ•Ë„‘Ì. ±‘Í‚ ÉÇ – —ËÊËÍ‘„ Ç”•ß –ÐËÍ‚ÎßЂâ Quantum Theory, and Conceptions of the Universe (Ed. M Kafatos)
(Dordrecht: Kluwer Acad. Publ., 1989) p. 107
„‘ÊÏ‘ÉБ”•ß ÚÇ“’‚•ß ËÆÇË ËÊ à•‘Ì –ÆË„Ë•ÇÎßÐ‘Ì ÏÇÉ-
46. Linden N et al., quant-ph/9912039
ÆË”™Ë’ÎËЂ“Ð‘Ì ‘Ã΂”•Ë Ђ–ÍË Ë ”•‚„Ë•ß àÍ”’Ç“ËÏÇЕÞ, 47. Cohen O Phys. Rev. A 60 80 (1999)
‘•Í“Þ„‚áÜËÇ Ð‘„ÞÇ ÐÇ‘ÉËÆ‚ÐÐÞÇ ”•‘“‘ÐÞ Í„‚Е‘„‘Ì 48. DiVincenzo D P et al., in Proc. First NASA Int. Conf. on Quantum
—ËÊËÍË. °”•‚Ç•”â •‘ÎßÍ‘ ’‘ÉÇ΂•ß, Ú•‘ÃÞ Í„‚Е‘„‚â Computing and Quantum Communications (Springer-Verlag Lecture
Notes in Computer Science, Vol. 1509) (Heidelberg: Springer-
•Ç‘“Ëâ, ÐÇÆ‚„Б ‘•ÏÇ•Ë„Û‚â ”„‘Ç ”•‘ÎÇ•ËÇ, Ë „ ÖƖÜÇÏ
Verlag, 1999)
‘”•‚„‚΂”ß Ë”•‘ÚÐËÍ‘Ï „Æ‘˜Ð‘„ÇÐËâ Í‚Í „ —–ÐÆ‚ÏÇÐ- 49. Vedral V et al. Phys. Rev. A 56 4452 (1997)
•‚ÎßÐÞ˜, •‚Í Ë „ ’“ËÍ΂ÆÐÞ˜ ‘Ã΂”•â˜ —ËÊËÍË. 50. Eisert J, Plenio M B J. Mod. Opt. 46 145 (1999)
²‚Ñ•‚ „Þ’‘ÎÐÇЂ ’“Ë ’‘ÆÆÇ“ÉÍÇ ²‘””Ë̔͑…‘ —‘ÐÆ‚ 51. Wootters W K Phys. Rev. Lett. 80 2245 (1998)
52. Deutsch D et al. Phys. Rev. Lett. 77 2818 (1996)
—–ÐÆ‚ÏÇЕ‚ÎßÐÞ˜ Ë””ÎÇÆ‘„‚ÐËÌ (…“‚Е 01-02-16311),
53. Maneva E N, Smolin J A, quant-ph/0003099
¤‘”–Æ‚“”•„ÇÐÐÞ˜ Ђ–ÚБ-•Ç˜ÐËÚǔ͢ ’“‘…“‚ÏÏ ²‘””ËÌ- 54. Thew R T, Munro W J, quant-ph/0012049
”Í‘Ì ¶ÇÆÇ“‚™ËË "¶–ÐÆ‚ÏÇЕ‚ÎßЂâ ÏÇ•“‘Α…Ëâ" Ë 55. Horodecki M, Horodecki P, Horodecki R Phys. Rev. Lett. 84 2014
"¯‚Б•Ç˜Ð‘Α…ËË", …“‚Е‚ INTAS ¦„“‘’Ç̔͑…‘ ”‘‘Ã- (2000)
56. Nielsen M A Phys. Rev. Lett. 83 436 (1999)
ÜÇ”•„‚ (“Ç…. å 479, 2001 ….), ‚ •‚ÍÉÇ —‘ÐÆ‚ Volkswagen
57. Smolin J A, quant-ph/0001001 (v1)
Stiftung (…“‚Е å 1/72944). 58. Lewenstein M et al., quant-ph/0006064 (v1); J. Mod. Opt. 47 2841
(2000)
³’Ë”‘Í ÎË•Ç“‚•–“Þ 59. Lewenstein M et al., quant-ph/0005014 (v1)
60. Terhal B M, quant-ph/0101032
1. Einstein A, Podolsky B, Rosen N Phys. Rev. 47 777 (1935) [±Ç“Ç„‘Æ
61. Parker S, Bose S, Plenio M B Phys. Rev. A 61 032305 (2000)
Ђ “–””ÍËÌ âÊÞÍ: µ¶¯ 16 440 (1936)]
62. Acin A et al. Phys. Rev. Lett. 85 1560 (2000)
2. Schrodinger E Naturwissenschaften 23 807, 823, 844 (1935) [±Ç“Ç-
È
63. Eisert J, Briegel H-J, quant-ph/0007081 (v1)
„‘Æ Ð‚ “–””ÍËÌ âÊÞÍ: µ”’Ç˜Ë ˜ËÏËË 5 390 (1936)]
64. Bennett C H et al. Phys. Rev. A 63 012307 (2001)
3. ¢ÇΑ͖“‘„ £ £, ´ËÏ‘—ÇÇ„”Í‚â ° ¥, ·“–”•‚ÎÇ„ ° ¡ ¬„‚Е‘„‚â
65. Collins D, Linden N, Popescu S, quant-ph/0005102
•ÇÎÇ’‘“•‚™Ëâ ¬ ‘ÃÞÍБ„ÇÐÐ‘Ç Ú–Æ‘ (ªÉÇ„”Í: ¯ª¸ "²Ç…–Îâ“-
66. Bell J S Physics 1 195 (1964)
Ђâ Ë ˜‚‘•ËÚǔ͂â ÆËЂÏËÍ‚", 2000)
67. Bouwmeester D et al. Phys. Rev. Lett. 82 1345 (1999)
4. Whitaker M A B Prog. Quantum Electron. 24 1 (2000)
68. Haroche S Phys. Today 51 (7) 36 (1998)
5. Percival I C, quant-ph/0008097; submitted to Nature
69. Horodecki M, Horodecki P, Horodecki R Phys. Lett. A 223 1 (1996)
6. ¬ÎÞÛÍ‘ ¥ ¯ µ¶¯ 168 975 (1998)
70. Terhal B M Phys. Lett. A 271 319 (2000)
7. ®ÇДÍËÌ ® ¢ µ¶¯ 170 631 (2000)
71. Tittel W et al. Phys. Rev. Lett. 81 3563 (1998)
8. ¬‚ƑϙDŽ ¢ ¢ µ¶¯ 164 449 (1994)
72. Szabo L E, Fine A, quant-ph/0007102 (v1)
9. ¬‚ƑϙDŽ ¢ ¢ ¥ËЂÏËÍ‚ Ë ËЗ‘“Ï‚™Ëâ (®.: ²ÇÆ‚Í™Ëâ É–“Ђ΂
73. Zurek W H Phil. Trans. Roy. Soc. Lond. A 356 1793 (1998)
µ¶¯, 2000)
74. ®ÇДÍËÌ ® ¢ µ¶¯ 168 1017 (1998)
10. Scarani V et al., quant-ph/0007008
75. Brandt H E Prog. Quantum Electron. 22 257 (1998)
11. Gisin N et al., quant-ph/0101098; submitted to Rev. Mod. Phys.
76. De Martini F, Mussi V Fortschr. Phys. 48 413 (2000)
12. Preskill J, in Lecture notes on Physics 229: Quantum information and
77. Sackett C A et al. Nature 404 256 (2000)
computation, http://www.theory.caltech.edu/people/preskill/ph229/
78. Myatt C J et al. Nature 403 269 (2000)
13. Steane A Rep. Prog. Phys. 61 117 (1998)
79. Monroe C et al. Science 272 1131 (1996)
14. Jozsa R, Abrams D S Phys. Rev. Lett. 85 2010 (2000)
80. Brune M et al. Phys. Rev. Lett. 77 4877 (1996)
15. Chuang I L Phys. Rev. Lett. 85 2006 (2000)
81. Kitagawa M, Ueda M Phys. Rev. A 47 5138 (1993)
16. Clauser J F, Shimony A Rep. Prog. Phys. 41 1881 (1978)
82. Hald J et al. Phys. Rev. Lett. 83 1319 (1999)
17. ¬ÎÞÛÍ‘ ¥ ¯ ¶‘•‘ÐÞ Ë ÐÇÎËÐÇÌЂ⠑’•ËÍ‚ (®.: ¯‚–Í‚, 1980)
83. Wineland D J et al. Phys. Rev. A 50 67 (1994)
18. Kwiat P G et al. Phys. Rev. Lett. 75 4337 (1995)
84. Huelga S F et al. Phys. Rev. Lett. 79 3865 (1997)
19. Turchette Q A et al. Phys. Rev. Lett. 81 3631 (1998)
85. ¬ÎÞÛÍ‘ ¥ ¯, ±ÇÐËÐ ¡ ª µ¶¯ 152 653 (1987)
20. Steane A M, Lucas D M, quant-ph/0004053
86. Deutsch D, Barenco A, Ekert A Proc. Roy. Soc. Lond. A 449 669
21. Cirac J I et al. Phys. Rev. Lett. 78 3221 (1997)
(1995)
22. Lloyd S, Shahriar M S, Hemmer P R, quant-ph/0003147 (v1)
87. Beige A et al. J. Mod. Opt. 47 401 (2000)
23. ¬ËÎËÐ ³ Á µ¶¯ 169 507 (1999)
88. Linden N, Popescu S, quant-ph/9906008 (v1)
24. Huelga S F et al. Appl. Phys. B 67 723 (1998)
89. Braunstein S L, Pati A K, quant-ph/0008018
25. Bouwmeester D, Ekert A K, Zeilinger A (Eds) The Physics of
90. Knill E et al., quant-ph/9908051
Quantum Information: Quantum Cryptography, Quantum Teleporta-
91. Schack R, Caves C M Phys.Rev. A 60 4354 (1999)
tion, Quantum Computation (New York: Springer, 2000)
92. Shor P W, Preskill J Phys. Rev. Lett. 85 441 (2000)
26. £‚ÎËÇ„ ¬ ¡, ¬‘ÍËÐ ¡ ¡ ¬„‚Е‘„ÞÇ Í‘Ï’ßá•Ç“Þ: ЂÆÇÉÆÞ Ë
93. Aschauer H, Briegel H J, quant-ph/0008051 (v1)
“Ç‚ÎßБ”•ß (ªÉÇ„”Í: ¯ª¸ "²Ç…–Îâ“Ђâ Ë ˜‚‘•ËÚǔ͂â ÆËЂÏË-
Í‚", 2001)
27. ¢ÇÎËДÍËÌ ¡ £, ¬ÎÞÛÍ‘ ¥ ¯ µ¶¯ 163 (8) 1 (1993)
7 ©‚ÏÇ•ËÏ, Ú•‘ ’‘Ðâ•ËÇ ÐÇ‘“•‘…‘ЂÎßБ…‘ Í„‚Е‘„‘…‘ ËÊÏÇ“ÇÐËâ
28. Mandel L Rev. Mod. Phys. 71 S274 (1999)
ÃÞΑ „’Ç“„ÞÇ „„ÇÆÇÐБ „ “‚Ñ•Ç: Helstrom C W, Liu J W S, Gordon J P
29. Zeilinger A Rev. Mod. Phys. 71 S288 (1999)
Opt. Commun. 58 1578 (1970), ‚ „ ЂËÑÎÇÇ ‘ÃÜÇÌ —‘“ÏÇ ÐÇ‘“•‘…‘-
30. DiVincenzo D P, quant-ph/0002077 (v1)
31. Cory D G et al., quant-ph/0004104 ЂÎßБ…‘ “‚ÊΑÉÇÐËâ ÇÆËÐË™Þ (’‘ΑÉË•ÇÎßÐ‘Ì ‘’Ç“‚•‘“Ð‘Ì ÏÇ“Þ,
32. Kane B E Nature 393 133 (1998) POVM) ¬ ‘ÆÐËÏ ËÊ Ð‚” „ “‚Ñ•Ç: ¤“ËÛ‚ÐËÐ ¢ ¡ ´Ç˜ÐËÚǔ͂â
33. Tanamoto T Phys. Rev. A 61 022305 (2000) ÍËÃÇ“ÐÇ•ËÍ‚ 5 127 (1973)
647
´. 171, å 6] ©¡±µ´¡¯¯½¦ ¬£¡¯´°£½¦ ³°³´°Á¯ªÁ ¡´°®¯½· ³ª³´¦®


94. Wootters W K, Zurek W H Nature 299 802 (1982) 145. Steane A et al. Phys. Rev. A 62 042305 (2000)
95. Ribordy G et al., quant-ph/0008039 (v1) 146. Balykin V I, Minogin V G, Letokhov V S Rep. Prog. Phys. 63 1429
96. Bennett C H, Brassard G, in Proc. IEEE Int. Conf. on Computers, (2000)
Systems, and Signal Processing (New York: IEEE Publ., 1985) p. 175 147. Grimm R, Weidemuller M, Ovchinnikov Yu B Adv. Atom. Mol.
97. Jennewein T et al. Phys. Rev. Lett. 84 4729 (2000) Opt. Phys. 42 95 (2000)
98. Naik D S et al. Phys. Rev. Lett. 84 4733 (2000) 148. Mandel L, Wolf E Optical Coherence and Quantum Optics (New
99. Tittel W et al. Phys. Rev. Lett. 84 4737 (2000) York: Cambridge Univ. Press, 1995) [±Ç“Ç„‘Æ Ð‚ “–””ÍËÌ âÊÞÍ:
100. ¤‚Î΂…Ç“ ² ¥É ´Ç‘“Ëâ ËЗ‘“Ï‚™ËË Ë Ð‚ÆÇÉЂ⠔„âÊß (®.: ³‘„. ®‚ÐÆÇÎß ­, £‘Îß— ¿ °’•ËÚǔ͂â Í‘…Ç“ÇЕБ”•ß Ë Í„‚Е‘„‚â
“‚ÆË‘, 1974) ‘’•ËÍ‚ (®.: ¶ËÊÏ‚•ÎË•, 2000)]
101. Hausladen P et al. Phys. Rev. A 54 1869 (1996) 149. Wallis H Phys. Rep. 255 203 (1995)
102. Holevo A S IEEE Trans. Inf. Theory 44 269 (1998) 150. Kuppens S J M et al. Phys. Rev. A 62 013406 (2000)
103. Werner R F, quant-ph/0101061 151. Townsend C G et al. Phys. Rev. A 52 1423 (1995)
104. Schumacher B, Nielsen M A Phys. Rev. A 54 2629 (1996) 152. Briegel H-J et al. J. Mod. Opt. 47 415 (2000)
105. Barnum H, Nielsen M A, Schumacher B Phys. Rev. A 57 4153 (1998) 153. Frese D et al. Phys. Rev. Lett. 85 3777 (2000)
106. Barnum H, Knill E, Nielsen M A IEEE Trans. Inf. Theory 46 1317 154. DePue M T, McCormick C, Winoto S L Phys. Rev. Lett. 82 2262
(2000) (1999)
107. Barnum H Phys. Rev. A 62 042309 (2000) 155. Hamann S E et al. Phys. Rev. Lett. 80 4149 (1998)
108. Grishanin B A, Zadkov V N Phys. Rev. A 62 032303 (2000) 156. Anderson B P, Kasevich M A Science 282 1686 (1998)
109. Bennett C H et al. Phys. Rev. Lett. 70 1895 (1993) 157. Stenger J et al. Nature 396 345 (1998)
110. Boschi D et al. Phys. Rev. Lett. 80 1121 (1998) 158. Jaksch D et al. Phys. Rev. Lett. 82 1975 (1999)
111. Bouwmeester D et al. Nature 390 575 (1997) 159. Weiner J et al. Rev. Mod. Phys. 71 1 (1999)
112. Furusawa A et al. Science 282 706 (1998) 160. Berman P R (Ed.) Cavity Quantum Electrodynamics (Boston:
113. Kim Y-H, Kulik S P, Shih Y, quant-ph/0010046; Phys. Rev. Lett. 86 Academic Press, 1994)
1370 (2001) 161. Mabuchi H, Ye J, Kimble H J Appl. Phys. B 68 1095 (1998)
114. Mattle K et al. Phys. Rev. Lett. 76 4656 (1996) 162. Domokos P et al. Phys. Rev. A 52 3554 (1995)
115. Bennett C H et al. Phys. Rev. Lett. 83 3081 (1999) 163. Pellizzari T et al. Phys. Rev. Lett. 75 3788 (1995)
116. Yurke B, Stoler D Phys. Rev. Lett. 68 1251 (1992) 164. Bergmann K, Theuer H, Shore B W Rev. Mod. Phys. 70 1003 (1998)
117. Sokolov I V et al., quant-ph/0007026 165. ¡ÐÆ“ÇÇ„ ¡ £, ¦ÏÇÎßâБ„ £ ª, ªÎßËДÍËÌ À ¡ ¬‘‘’Ç“‚•Ë„ÐÞÇ
118. Gorbachev V N et al., quant-ph/0011124 â„ÎÇÐËâ „ ‘’•ËÍÇ (®.: ¯‚–Í‚, 1988)
119. Ghosh S et al., quant-ph/0012110 166. DeVoe R G, Brewer R G Phys. Rev. Lett. 76 2049 (1996)
120. Pan J-W et al. Phys. Rev. Lett. 80 3891 (1998) 167. Barenco A et al. Phys. Rev. Lett. 74 4083 (1995)
121. Meyer D A Phys. Rev. Lett. 82 1052 (1999); 84 789, 790 (2000) 168. Brennen G K et al. Phys. Rev. Lett. 82 1060 (1999)
122. Du J et al., quant-ph/0010050 169. Lukin M D et al., quant-ph/0011028
123. Eisert J, Wilkens M, Lewenstein M Phys. Rev. Lett. 83 3077 (1999) 170. Bargatin I V, Grishanin B A, Zadkov V N Fortschr. Phys. 48 637
124. ¦ÎßâÛÇ„ËÚ ® ¡ ¡•‘ÏЂâ Ë Ï‘ÎÇÍ–Îâ“Ђ⠔’ÇÍ•“‘”Í‘’Ëâ 2-Ç (2000)
ËÊÆ. (®.: ¿ÆË•‘“Ë‚Î µ²³³, 2001) 171. Seminara F, Leonardi C Phys. Rev. A 42 5695 (1990)
125. Wineland D J et al. J. Res. Natl. Inst. Stand. Tech. 103 259 (1998) 172. Goldstein E V, Meystre P Phys. Rev. A 56 5135 (1997)
126. Happer W Rev. Mod. Phys. 44 169 (1972) 173. Bargatin I V, Grishanin B A, Zadkov V N Phys. Rev. A 61 052305
127. ºÇÐ ª ² ±“ËÐ™Ë’Þ ÐÇÎËÐÇÌÐ‘Ì ‘’•ËÍË (®.: ¯‚–Í‚, 1989) (2000)
128. ±‚–Îß £ µ¶¯ 160 (12) 109 (1990) 174. Plenio M B et al. Phys. Rev. A 59 2468 (1999)
129. Ghosh P K Ion Traps (Oxford: Clarendon Press, 1995) 175. Cabrillo C et al. Phys. Rev. A 59 1025 (1999)
130. Birkl G, Kassner S, Walther H Europhys. News 23 (8) 143 (1992) 176. Konopka M, Buzek V, quant-ph/9901069
131. Leibfried D et al., quant-ph/0009105 177. Rauschenbeutel A et al. Science 288 2024 (2000)
132. Monroe C et al. Phys. Rev. Lett. 75 4011 (1995) 178. Hood C J et al. Science 287 1447 (2000)
133. Cirac J I, Zoller P Phys. Rev. Lett. 74 4091 (1995) 179. Pinkse P W H et al. Nature 404 365 (2000)
134. Monroe C et al. Phys. Rev. Lett. 75 4714 (1995) 180. Hennrich M et al. Phys. Rev. Lett. 85 4872 (2000)
135. Sancho J M G, Huelga S F Phys. Rev. A 61 042303 (2000) 181. Ye J, Vernooy D W, Kimble H J Phys. Rev. Lett. 83 4987 (1999)
136. Sùrensen A, Mùlmer K Phys. Rev. A 62 022311 (2000) 182. van Enk S J et al., quant-ph/0005133 (v1)
137. Turchette Q A et al. Phys. Rev. A 61 063418 (2000) 183. Meschede D et al., in Tech. Digest XVII Intern. Conf. on Coherent
138. Monroe C et al. "Scalable entanglement of trapped ions", in Atomic and Nonlinear Optics (Minsk, Belarus, 2001)
Physics 17: Proc. of the 17th Intern. Conf. (AIP Conf. Proc., Vol. 184. Brennen G K, Deutsch I H, Jessen P S, quant-ph/9910031
551, Eds E Arimondo, P De Natle, M Inguscio) (Melville, N.Y.: 185. Haycock D L et al., quant-ph/0005091 (v1); submitted to Phys. Rev.
AIP, 2001) p. 173; http://www.bldrdoc.gov/timefreq/ion/qucomp/ Lett.
papers.htm 186. Sorensen A et al., quant-ph/0006111 (v1); Nature 409 63 (2001)
139. Roos Ch et al. Phys. Rev. Lett. 83 4713 (1999) 187. Ketterle W Phys. Today 52 (12) 30 (1999)
140. Arimondo E, in Progress in Optics Vol. 35 (Amsterdam: Elsevier, 188. Schrodinger E Proc. Cambridge Philos. Soc. 31 555 (1935)
È
1996) p. 257 189. Cabello A, quant-ph/0012089 (v1)
141. James D F V, quant-ph/0003122; submitted to Fortschr. Phys. 190. Bjork G, in Opening Speech at Swedish-Russian Workshop on
È
142. Cirac J I, Zoller P Nature 404 579 (2000) Entangled Quantum Systems (St. Petersburg, Russia, May 19 ± 21,
143. Childs A M, Chuang I L Phys. Rev. A 63 012306 (2001) 2000)
144. Jonathan D, Plenio M B, Knight P L, quant-ph/0002092 (v1); Phys.
Rev. A 62 42307 (2000)

Entangled states of atomic systems
I.V. Bargatin, B.A. Grishanin, V.N. Zadkov
M V Lomonosov Moscow State University, Department of Physics and International Laser Center, Russian Federation
Tel. (7-095) 939-51 73. Fax (7-095) 939-31 13
E-mail: zadkov@comsim1.phys.msu.su

The current status of the physics of the entangled states of atomic systems Ð an interdisciplinary field involving quantum optics,
quantum information, and foundations of quantum mechanics Ð is reviewed. In the first part of the review, an introduction to the
theory of entangled states is given and their properties and applications are described. In the second part, experiments and experimental
proposals for the creation and detection of entangled states in atomic systems are discussed. Today's most advanced experimental
technique for entangling ions in an ion trap is examined, and methods showing promise for the entanglement of neutral atoms are
analyzed.

PACS numbers: 03.65.Bz, 03.65.Ud, 03.65.Yz, 03.67. ± a, 32.80.Qk
Bibliography Ð 190 references Received 25 January 2001, revised 26 February 2001 \

<<

. 9
( 9 .)