
lock

lock, yaa sthaaniya sanchaalan aur shaastriya sanchaar, quantum soochana siddhant mein ack vidhi haye jahan ack sthaaniya (utpaad) sanchaalan pranali key hisse parr kiya jaataa haye, aur jahan usa operation key parinam koo shaastriya roop seey dusare hisse mein "sanchaarit" kiya jaataa haye jahan aamtaur parr ack anya sthaaniya sanchaalan praapt jaankaari parr kiya jaataa haye.
ganitiya guna.
lock sanchaalan key samooh kii aupchaarik paribhasha iss tathya key kaaran jatil haye kii baad mein sthaaniya sanchaalan samanya roop seey pichhale sabhi shaastriya sanchaar parr nirbhar karate hain aur sanchaar daur kii aseemit sankhya key kaaran. kissy bhee seemit sankhya sootra key liye koee bhee sootra _ 2 koo paribhaashit curr sakata haye, lock sanchaalan kaa sett jise shaastriya sanchaar key sootra _ 3 daur key saath praapt kiya jaa sakata haye. jaba bhee sootra _ 3 badhaaya jaataa haye tou sett sakhti seey badaa hoe jaataa haye aur aseem roop seey kaee round kii seema koo paribhaashit karane key liye dhyaan rakhna padata haye. vishesh roop seey, sett locus sthalgat roop seey bund naheen haye, yaani quantum sanchaalan hain jinhen locus dwara manmaane dhang seey nikatata seey anumaanit kiya jaa sakata haye lekin joe swayam locus naheen hain.
ack "ack-goal" lock sootra _ 5 ack quantum upkaran sootra _ 6 haye, jisake liye trace-gair-badh rhaa poori tarah seey sakaratmak maanchitra (see. pee. aim. aiss.) sootra _ 7 sabhi maap parinamon key liye sthaaniya hain.ee.sootra _ 9 aur ack site sootra _ 10 aisaa haye kii kewal sootra _ 11 parr maanchitra sootra _ 12 sootra _ 13 trace-preserving naheen haye. iska matlab haye kii upkaran koo paksh dwara site sootra _ 11 parr (sthaaniya) upkaran sootra _ 15 koo lagu karke aur anya sabhi pakshon koo shaastriya parinam sootra _ 8 koo sampreshit karke mahsoos kiya jaa sakata haye, joe phir pratyek pradarshan (sootra _ 8 parr shart) trace-preservation (nirdhaarak) sthaaniya quantum sanchaalan sootra _ 18 kartaa haye.
phir sootra _ 2 koo una sanchalanon key roop mein punaraavarti roop seey paribhaashit kiya jaataa haye jinhen ack sootra _ 5-operation key saath ack operation sootra _ 20 kaa paalan karke mahsoos kiya jaa sakata haye. yahaan yeh anumati dee gaee haye kii joe dall anuvarti kaarravaai kartaa haye, vaha pichhale daur key parinam parr nirbhar kartaa haye. isake alawa, humm "motey anaaj" kii bhee anumati dete hain.ee.maap parinamon (sabhi dauron) mein kootbaddh kuchh shaastriya jaankaari koo tyagana.
sabhi sootra _ 2 sanchalanon key sangh koo sootra _ 23 dwara darshaaya jaataa haye aur isamen aise upkaran hotey hain jinhen adhik lock round key saath behtar aur behtar anumaanit kiya jaa sakata haye. isake topological closure formula _ 24 mein aise sabhi operation shamil hain.
yeh dikhaaya jaa sakata haye kii yeye sabhi sett alag-alag hainh
sabhi lock sanchaalan kaa samooh sabhi "alag karane yogya sanchaalan" key nirdhaarit sootra _ 26 mein nihit haye. sootra _ 26 mein sabhi sanchaalan hotey hain jinhen cross operators kaa upayog karke likhaa jaa sakata haye jinake sabhi utpaad roop hain, i.ee., 
sootra _ 29 key saath. sootra _ 26 mein sabhi sanchaalan sthaan naheen hain, 
aaee.ee.aise udaaharan hain jinhen sanchaar key anant daur key saath bhee sthaaniya roop seey lagu naheen kiya jaa sakata haye.
sanlagnak key sansaadhan siddhanton mein loksi "mukt sanchaalan" hainh sanlagnak koo loksi key saath alag kiye jaa sakane vaale raajyon seey utpann naheen kiya jaa sakata haye aur yadi sthaaniya paksh sabhi loksi sanchaalan karane mein saksham honey key alawa kuchh ulajhe hue raajyon key saath bhee susajjit hain, tou way akele loksi kii tulanaa mein adhik sanchaalan kaa ehsas curr sakate hain.
udaaharan.
lock sanchaalan "raajya kii taiyari", "raajya bhedbhaav" aur "ulajhaav parivartan" key liye upayogi hain.
raajya kii taiyari.
ellis aur bobb koo utpaad avastha sootra mein ack quantum pranali dee jaati haye. unakaa kaary alag karane yogya avastha sootra kaa utpaadan karna haye. akele sthaaniya sanchaalan key saath yeh praapt naheen kiya jaa sakata haye, kyonki way sootra 34 mein maujood (shaastriya) sahsambandh kaa utpaadan naheen curr sakate hain. haalaanki lock key saath (sanchaar key ack daur key saath) sootra 34 taiyar kiya jaa sakata haih ellis ack nishpaksh sikka fenkta haye (joe 50 pratishat sambhavana key saath pratyek sir yaa poonchh dikhaata haye) aur aggar sikka "poonchh" dikhaata haye tou usey palat detaa haye (sootra 36 parr), anyatha ise aparivartit chhod diyaa jaataa haye. phir vaha sikke-flip (shaastriya jaankaari) kaa parinam bobb koo bhejati haye joe sandesh "tails" praapt karane parr apane cubit koo bhee flip kartaa haye. parinami avastha sootra 34 haye. samanya roop seey, "sabhi" alag karane yogya avasthaon (aur kewal yeye) koo ack utpaad avastha seey taiyar kiya jaa sakata haye jisamen kewal sthaaniya sanchaalan hotaa haye.
raajya bhedbhaav.
dwi-yaa bahu-partite hilbert space sootra _ 39 parr dou quantum avastha sootra _ 38 diye jaane parr, kaary yeh nirdhaarit karna haye kii dou (yaa adhik) sambhaavit avastha sootra _ 40 mein seey kaun saa haye. ack saral udaaharan key roop mein, dou ghanti avasthaon parr vichaar karein.
maan leejiye kii dou-cubit pranali alag haye, jahan pahala cubit ellis koo diyaa jaataa haye aur doosara bobb koo diyaa jaataa haye. sanchaar key binaa, ellis aur bobb donon avasthaon mein antar naheen curr sakate hain, kyonki sabhi sthaaniya maapon key liye sabhi maap aankade bilkul samaan hain (donon avasthaon mein samaan cumm ghanatva matricks haye). ee.jee.maan leejiye kii ellis pahale cubit koo maapata haye, aur parinam 0 praapt kartaa haye. kyonki yeh parinam donon mamalon mein seey pratyek mein honey kii samaan sambhavana (sambhavana 50 pratishat key saath) haye, isaliye usey koee jaankaari naheen milati haye kii usey kaun see ghanti jodee dee gaee thee aur bobb key liye bhee vahee haye yadi vaha koee maap kartaa haye. lekin abb ellis koo apana parinam ack shaastriya channel parr bobb koo bhejane dein. abb bobb apane parinam kii tulanaa usake saath curr sakata haye aur yadi way samaan hain tou vaha yeh nishkarsh nikaal sakata haye kii dee gaee jodee sootra _ 43 thee, kyonki kewal yeh ack sanyukt maap parinam sootra _ 44 key liye anumati detaa haye. iss prakaar lock aur dou maapon key saath inn donon sthitiyon koo poori tarah seey alag kiya jaa sakata haye. dhyaan dein kii vaishvik (gair-sthaaniya yaa ulajhe hue) maapon key saath, ack ekal maap (sanyukt hilbert sthaan parr) inn donon (parasparik orthogonal) sthitiyon koo alag karane key liye paryaapt haye.
aise quantum avasthaaen hain jinhen lock sanchaalan key saath alag naheen kiya jaa sakata haye.
ulajhaav parivartan.
jabaki lock utpaad avasthaon seey baahar ulajhi hui avasthaon koo "utpann" naheen curr sakata haye, unakaa upayog ulajhi hui avasthaon koo anya ulajhi hui avasthaon mein badalane key liye kiya jaa sakata haye. una seemaon koo lagu karane key liye pratibandh joe parivartan sambhav hain.
ulajhaav roopaantaran.
nielson ney yeh nirdhaarit karane key liye ack samanya sthiti praapt kii haye kii kyaa dvidaliya quantum pranali kii ack shuddh sthiti koo kewal lock kaa upayog karke dusare mein parivartit kiya jaa sakata haye. puuraa vivaran pahale sandarbhit pepper mein paaya jaa sakata haye, parinam yahaan sketch kiye gaye hain.
ayam sootra key hilbert sthaan mein dou kanon parr vichaar karein-sootra 46 key saath kann avastha sootra aur sootra 47 schmitt apghatan key saath
50 key sootra koo schmitt gunank key roop mein jaanaa jaataa haye. yadi unhein sabse badey seey sabse chhote (i.ee.sootra _ 51) key saath sootra _ 46 koo kewal sthaaniya sanchaalan kaa upayog karke sootra _ 47 mein parivartit kiya jaa sakata haye yadi aur kewal tabhi jaba seema sootra _ 55 mein sabhi sootra _ 54 key liye
adhik sankshipt sanketan menh
yeh ack adhik pratibandhaatmak sthiti haye kii sthaaniya sanchaalan ulajhane key upaayon koo naheen badhaa sakate hain. yeh kaafee sambhav haye kii sootra _ 46 aur sootra _ 47 mein samaan matra mein ulajhan hoe lekin ack koo dusare mein parivartit karna sambhav naheen haye aur yahaan taka kii donon dishaaon mein roopaantaran bhee asambhav haye kyonki schmitt gunank kaa koee bhee sett dusare koo pramukh naheen banaata haye. badey sootra key liye yadi sabhi schmitt gunank gair-shoonya hain tou gunank key ack samooh key dusare koo pramukh banaane kii sambhavana nagany hoe jaati haye. isaliye, badey sootra _ 45 key liye kissy bhee manmaane dhang seey sthiti key lock key madhyam seey dusare mein parivartit honey kii sambhavana nagany hoe jaati haye.
abb taka varnit sanchaalan nirdhaarak hain, i.ee.way sambhavana 100% key saath safal hotey hain. yadi koee "sambhaavit" parivartanon seey santusht haye, tou lock kaa upayog karke kaee aur parivartan sambhav hain. inn karyon koo "stockestic" lock (slock) kahaa jaataa haye. vishesh roop seey bahu-pakshiya raajyon key liye slock key tahat parivartaniyata kaa adhyayan shamil raajyon key ulajhane key gunon mein gunaatmak antardrishti praapt karane key liye kiya jaataa haye.
lock seey parey jaanah utprerak roopaantaran.
yadi ulajhi hui avasthaaen ack sansaadhan key roop mein upalabdh hain, tou yeye sthaaniya sthaan key saath milkar parivartan key ack bahut badey varg kii anumati dete hain. yeh mamla taba bhee haye jaba inn sansaadhan avasthaon kaa upbhog prakriya mein naheen kiya jaataa haye (udaaharan key liye, quantum teleportation mein). iss prakaar parivartanon koo "ulajhaav utpreran" kahaa jaataa haye. iss prakriya mein, ack praarambhik avastha kaa antim avastha mein roopaantaran joe lock key saath asambhav haye, ack "utprerak avastha" sootra _ 62 key saath praarambhik avastha key ack tensor utpaad koo laker sambhav kiya jaataa haye aur yeh aavashyak hotaa haye kii yeh sthiti abhee bhee roopaantaran prakriya key anta mein upalabdh hoe. aaee.ee.utprerak avastha koo roopaantaran dwara aparivartit chhod diyaa jaataa haye aur phir kewal vaanchhit antim sthiti koo chhodate hue ise hataaya jaa sakata haye. raajyon parr vichaar karein,
yeye avasthaaen schmitt apghatan key roop mein aur avrohi crum mein likhi jaati hain. humm sootra _ 46 aur sootra _ 47 key gunank key yog kii tulanaa karate hain.
talika mein, yadi sootra _ 68 mein laal rung rakhaa jaataa haye, yadi sootra _ 69 mein haraa rung rakhaa jaataa haye, aur yadi sootra _ 70 mein safed rung banaa rahata haye, tou talika banaane key baad, sootra _ 46 aur sootra _ 47 koo formula _ 54 disha mein dekhkar aasaani seey pataa lagaaya jaa sakata haye kii kyaa way parivartit hoe sakate hain. yadi sabhi rung harey yaa safed hain tou sootra _ 46 koo sootra _ 47 mein parivartit kiya jaa sakata haye, aur sootra _ 47 koo sootra _ 46 mein parivartit kiya jaa sakata haye yadi sabhi rung laal yaa safed hain. jaba talika laal aur haraa donon rung prastut karati haye, tou avasthaaen parivartaniya naheen hoti hain.
abb humm utpaad avastha sootra _ 78 aur sootra _ 79 parr vichaar karate hainh
isi tarah, humm talika banaate hainh
sootra _ 54 disha mein rung sabhi harey yaa safed hain, isaliye, nielson kii pramey key anusaar, sootra _ 78 koo lock dwara sootra _ 79 mein parivartit kiya jaa sakata haye. utprerak" avastha sootra _ 62 koo roopaantaran key baad hataa diyaa jaataa haye. anta mein humm lock dwara sootra _ 86 paate hain.
yadi pranali aur utprerak key beach sahsambandh kii anumati dee jaati haye, tou dvidaliya shuddh avasthaon key beach utprerak parivartanon koo ulajhaav entropy key madhyam seey chihnit kiya jaataa haye. adhik vistaar seey, ack shuddh avastha sootra _ 87 koo utprerak sthaan key madhyam seey ack anya shuddh avastha sootra _ 88 mein parivartit kiya jaa sakata haye yadi aur kewal yadi 
sootra _ 89,
jahan sootra 90 wonn neuman entropy haye, aur sootra 91 aur sootra 92 kramshah sootra 87 aur sootra 88 kii cumm avasthaaen hain. samanya taur parr, roopaantaran sateek naheen haye, lekin manmaane dhang seey sateekta key saath kiya jaa sakata haye. pranali aur utprerak key beach sahsambandh kii matra koo bhee manmaane dhang seey chhota kiya jaa sakata haye.