Connes Embedding Gɛlɛya ye

Connes Embedding Problem ye ɲininkali juguba dɔ ye bi jatebɔ la , min sigilen bɛ operatɛriw ka jatebɔw , kunnafoni kuantimɛw teori ani jatebɔ gɛlɛyaw cɛtigɛyɔrɔ la Faransi jatebɔla Alain Connes y’a Laɲini san 1976, k’a ɲɛnabɔ cogo dafalen na san 2020, a jaabi ye jatebɔlaw ni fizik dɔnnikɛlaw ka ɲɔgɔndanw faamuya cogo kura la, yɔrɔ danmadɔw, ani jatebɔ hakilila-jɔ-cogo yɛrɛ.

Kɔnɔnafili gɛlɛya ye mun ye tigitigi ?

A kɔnɔna na, Connes Embedding Problem ye ɲininkali nɔgɔman dɔ kɛ min bɛ mɔgɔ lafili : yala von Neumann ka algebra danma bɛɛ ni tracial state bɛ se ka don ultrapower dɔ kɔnɔ min ye hyperfinite II1 factor ye wa ? K’a fɔ k’a jɛya, a y’a sɛgɛsɛgɛ ni dantigɛli-dafalen-dafalenw bɛɛ bɛ se ka gɛrɛ ɲɔgɔn na ni jatebɔ-yɔrɔw ye minnu bɛ dantigɛ, minnu bɛ se ka ɲɛnabɔ.

Alain Connes ye miiri fɔlɔ kɛ san 1976 ko jaabi ye ɔnhɔn — ko nin doncogo in bɛ se ka kɛ tuma bɛɛ . San tan naani ni kɔ kɔnɔ, o gɛlɛya dabɔra, ka diɲɛ jatebɔla ŋana dɔw ka cɛsiriw kɛlɛ. A ɲɛnabɔli tun tɛna bɔ baarakɛla saniyalen ka aljɛbra teori la, nka a tun bɛna bɔ sira dɔ la min tun ma deli ka kɛ pewu: jatebɔ gɛlɛya min bɛ daliluw ni ɲɔgɔn cɛ quantum.

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"Connes Embedding Problem sɔsɔli tɛ jatebɔ ɲinini dɔrɔn ye — a bɛ danfara jɔnjɔn dɔ jira quantum systems bɛ se ka min kɛ ani klasiki gɛrɛgɛrɛw bɛ se ka min minɛ, ni a nɔfɛkow bɛ daminɛ kriptografi la ka se fiziki jusigilanw ma."

Jateminɛ min kɛra san 44 kɔnɔ, o labanna ka jatebɔ gɛlɛya dɔ ɲɛnabɔ cogo di ?

San 2020 , ɲininikɛla Ji, Natarajan, Vidick, Wright ani Yuen ye sɛbɛnba in bɔ min b’a jira ko MIP* = RE, MIP* bɛ gɛlɛya suguya jira min bɛ se ka ɲɛnabɔ klasiki sɛgɛsɛgɛlikɛla dɔ fɛ min bɛ jɛɲɔgɔnya kɛ ni kɔrɔlen sɛgɛsɛgɛlikɛla fila ye minnu sirilen don, wa RE ye kanw kulu ye minnu bɛ se ka jate segin-segin. O nɔ in kɛra kabako ye : a y’a jira ko quantum entanglement bɛ fanga danma di — a jɔyɔrɔba la, dan tɛ min na — ka ɲɛsin dalilu sitɛmuw ma minnu bɛ ɲɔgɔn sɔrɔ.

Jɛɲɔgɔnya min bɛ Connes ? Ekipu y’a Jira ko Connes Embedding Problem ye equivalent ni kumasen ye MIP* = MIP (classique multiprover interactive proof class). Komin MIP* y’a jira ko a ka bon kosɛbɛ ka tɛmɛ MIP kan — tiɲɛ na, a ni RE bɛ bɛn — Connes Embedding ka jateminɛ tun ye nkalon ye. Von Neumann ka aljɛbra danma bɛɛ tɛ don ultrapower dɔ kɔnɔ min ye hyperfinite II1 factor ye.

gɛlɛya kɔfɛ sariyakolo jɔnjɔn jumɛnw bɛ yen ?

Kɔnɛsi Embedding Gɛlɛya faamuyali bɛ jatebɔsen jɔnjɔn caman dɔnni de wajibiya :

• Von Neumann Algebras : Baarakɛlaw danmadɔw ka jatebɔw Hilbert yɔrɔ dɔ kan minnu datugulen don baarakɛla topidiya barikama jukɔrɔ, ka matiriyali jatebɔw caman kɛ ka se hakɛ danmadɔw ma.
• The Hyperfinite II1 Factor : von Neumann ka jatebla kɛrɛnkɛrɛnnen, kanon ye min ye danma matiriyali jatebla "dan" ye — danma-danma-danma-danma-danma-daɲɛ-sɛnɛcogo min ka bon kosɛbɛ.
• Tracial States : Baarakɛcogo sinsinni von Neumann ka alɛjibɛrɛw kan minnu bɛ u yɛrɛ kɛ i n’a fɔ taamasiyɛnw normalizelenw , minnu bɛ hakilina di « bonya » walima « hakɛ » kan jateminɛw kama.
• sebaaya camanba : Modèle-teori jɔli min bɛ jatebɔsen kura bɔ ni dantigɛliw tali ye alɛjibɛrɛw sigiyɔrɔmali la cogo kɛrɛnkɛrɛnnen na , min tɛ sariya ye .
• Jɛɲɔgɔnya kuantimɛw : Jɛɲɔgɔnya suguya min bɛ se ka sɔrɔ mɔgɔ fila fɛ minnu bɛ kuantimɛ cogoya sirilenw tila ɲɔgɔn na, o min ye kunnafoniko kuantimɛko miiriya cɛmancɛ ye ani gɛlɛya labanko ɲɛnabɔli.

Nin gɛlɛya in tariku kɔnɔko ni a jiginni ye mun ye ?

gɛlɛya in bɔyɔrɔ bɛ bɔ Kɔnɛsi ka san 1976 sɛbɛn na pikirijikɛlanw kan , o ye fɛn caman tigɛli baara ye operatɛriw ka alɛjibɛrɛw la . San tan minnu tugura o kɔ, jatebɔlaw y’a Sɔrɔ ko CEP bɛ Bɛn ni gɛlɛya tan ni caman ye minnu bɛ i n’a fɔ u ni ɲɔgɔn cɛ tɛ jatebla la — k’a ta Kirchberg ka QWEP jateminɛ na C*-algebra teori la ka se Tsirelson ka gɛlɛya ma quantum information theory la, min y’a ɲininka ni quantum correlations minnu bɛ sɔrɔ commuting operators fɛ, olu ni tensor product fɛ minnu bɛ sɔrɔ, olu ye kelen ye baarakɛlaw.

O bɛnkanw web in ye CEP kɛ cɛmancɛ labɛnni gɛlɛya ye, "hub" min bɛ foro danfaralenw siri ɲɔgɔn na. Tuma min na a binna san 2020, o ripple effects (jikuruw nɔfɛkow) ye jatebɔ, fizik ani ɔridinatɛri dɔnniya bɛɛ lajɛlen ye waati kelen na. Dalilu min b’a jira ko Tsirelson ka gɛlɛya ye jaabi jugu sɔrɔ — min bɛ jira k’a ɲɛsin MIP* = RE ma — o y’a jira ko quantum mechanics bɛ fɛn nɔgɔlenw mara minnu ka dun hali ka tɛmɛ fiziki dɔnnikɛlaw tun bɛ miiri min na.

Nin ɲɛnabɔli in nataw taabolo n' a nɔfɛkow ye mun ye ?

Kɔnɔw ka donko gɛlɛya ɲɛnabɔli bɛ ɲinini dancɛ kura da mɔgɔw ɲɛ na pewu . Kriptografi kuantimɛ na, a b’an ka faamuyali nɔgɔya, kuantimɛ jɛɲɔgɔnya sugu minnu bɛ se ka kɛ farikolo ta fan fɛ ni jatebɔ dɔrɔn ye. Complexité teori la, a b’a jira ko entangled quantum provers fanga ka bon kosɛbɛ ka tɛmɛn modeli kan fɔlɔ kan. Jatebla jusigilanw na, a bɛ ɲininkali juguw lawuli jɛɲɔgɔnya min bɛ dantigɛli danma ni jatebɔfɛnw danmadɔw cɛ.

Jateminɛla minnu bɛ baara kɛ ani minnu bɛ kɛ ni fɛnɲɛnɛmaw ye, o jaabi b’a jira ko a nafa ka bon ka danfara min bɛ "sigida" ni "taama" quantum jɛɲɔgɔnyaw cɛ, o kalanni — danfara min bɛ na ni kɔlɔlɔ tilennen ye minɛnw yɛrɛmahɔrɔnyalen quantum cryptography ani quantum networks dilanni na.

Ɲininkali minnu bɛ kɛ tuma caman na

Yala Connes Embedding Conjecture jirala ko tiɲɛ don walima nkalon ?

jateminɛ in jirala nkalon san 2020 Ji , Natarajan , Vidick , Wright ani Yuen fɛ . U ka dalilu, n’o ye MIP* = RE sigi senkan, o y’a jira ko von Neumann ka aljɛbraw bɛ yen minnu tɛ se ka don ultrapowers (factor hyperfinite II1) kɔnɔ, o bɛ Connes ka jateminɛ fɔlɔ sɔsɔ k’a ɲɛsin a ma.

mun na Connes Embedding Problem nafa ka bon jatebɔ saniyalen kɔfɛ ?

gɛlɛya in bɛ tali kɛ kuanti fiziki ni ɔridinatɛri dɔnniya la. A ka ɲɛnabɔli y’a Jira ko kuantimɛ-kɛnɛya bɛ Se ka jɛɲɔgɔnyaw Lase minnu klasiki ni hali kɔrɔlen-kɔrɔ-fɔcogo kɔrɔlenw tɛ Se k’u Lasegin. O bɛ na ni nɔ ye kuantimɛ kriptografi la, quantum computing architecture la, ani quantum mechanics yɛrɛ jusigilanw na.

factor hyperfinite II1 ye mun ye ani mun na a bɛ nin gɛlɛya in cɛmancɛ la ?

Factor II1 hyperfinite, n’a bɛ fɔ tuma caman na R, o ye von Neumann ka jatebɔ kɛrɛnkɛrɛnnen ye min jɔra i n’a fɔ dancɛ-dafalen matiriyali jatebɔw dan. O ye danma-danma-danma-danma-danma-sɛnɛcogo nɔgɔman ye min ka nɔgɔn ani "a bɛ se ka "gɛrɛ" kosɛbɛ. Ɲininkali min ye ko alɛjibɛrɛ minnu ka gɛlɛn kosɛbɛ, olu bɛ don R ka ultrapowers kɔnɔ, o ye ɲininkali ye kosɛbɛ ko ni quantum systems bɛɛ bɛ nin dantigɛli danmadɔ in jɛ — wa jaabi, i n’a fɔ san 2020 jaabi b’a jira cogo min na, o ye ayi ye.

Bɔli minnu bɛ kɛ i n’a fɔ Kɔnɛsi Embedding Problem ɲɛnabɔli, olu b’a jira min bɛ kɛ ni sigida gɛlɛnw, minnu bɛ ɲɔgɔn cɛ, olu faamuyara u jugumanba la — ka jɛɲɔgɔnyaw jira minnu ma labɛn fɔlɔ ani ka seko kura bɛɛ da wuli. Mewayz la, an dalen b’a la ko o sariyakolo kelen de bɛ tali kɛ i ka jago jɔli la. An ka jagokɛcogo min bɛ ni modulu 207 ye, o bɛ baarakɛminɛnw di baarakɛla 138.000 ni kɔ ma walasa u ka se k’u ka baarakɛcogo fan bɛɛ faamuya, k’u ni ɲɔgɔn cɛ, k’u ɲɛnabɔ ka ɲɛ, k’a ta feereli ni CRM la ka se jateminɛw ma ani a kɔfɛ — o bɛɛ bɛ daminɛ dɔrɔmɛ 19 dɔrɔn na kalo kɔnɔ.

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