Quantum Physics / Quant-Ph

All posts under category "Quantum Physics / Quant-Ph"

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Quantum Private Information Retrieval with Sublinear Communication Complexity

Quantum Private Information Retrieval with Sublinear Communication Complexity

๋ณธ ๋…ผ๋ฌธ์€ ์–‘์ž ๊ฐœ์ธ ์ •๋ณด ๊ฒ€์ƒ‰ ํ”„๋กœํ† ์ฝœ ์— ๋Œ€ํ•œ ์‹ฌ๋„ ์žˆ๋Š” ๋ถ„์„์„ ์ œ๊ณตํ•ฉ๋‹ˆ๋‹ค. ์ด๋Š” ์„œ๋ฒ„๋กœ๋ถ€ํ„ฐ ๋ฐ์ดํ„ฐ๋ฒ ์ด์Šค ํ•ญ๋ชฉ์„ ๋น„๊ณต๊ฐœ๋กœ ๊ฒ€์ƒ‰ํ•˜๋Š” ๋ฐฉ๋ฒ•์œผ๋กœ, Chor, Kushilevitz, Goldreich ๋ฐ Sudan์˜ ์—ฐ๊ตฌ์—์„œ ์‹œ์ž‘๋œ ๋ถ„์•ผ์ž…๋‹ˆ๋‹ค. ๋ณธ ๋…ผ๋ฌธ์€ ๊ณต๊ฐœ ๋ฐ์ดํ„ฐ๋ฒ ์ด์Šค๊ฐ€ ๋ณดํŽธํ™”๋จ์— ๋”ฐ๋ผ ๋”์šฑ ์ค‘์š”ํ•ด์ง„ ์ด ์ฃผ์ œ๋ฅผ ๋‹ค๋ฃน๋‹ˆ๋‹ค. 1. ๊ฐœ์ธ ์ •๋ณด ๊ฒ€์ƒ‰ ํ”„๋กœํ† ์ฝœ์˜ ๋ฐฐ๊ฒฝ ๋ณธ ๋…ผ๋ฌธ์€ Chor, Kushilevitz, Goldreich ๋ฐ Sudan์˜ ์—ฐ๊ตฌ์—์„œ ์‹œ์ž‘๋œ ๊ฐœ์ธ ์ •๋ณด ๊ฒ€์ƒ‰ ๋ถ„์•ผ๋ฅผ ์†Œ๊ฐœํ•ฉ๋‹ˆ๋‹ค. ์ด๋Š” ์„œ๋ฒ„๋กœ๋ถ€ํ„ฐ ๋ฐ์ดํ„ฐ๋ฒ ์ด์Šค ํ•ญ๋ชฉ์„ ๋น„๊ณต๊ฐœ๋กœ

Computational Complexity Quantum Physics Computer Science Cryptography and Security
No-go theorems for functorial localic spectra of noncommutative rings

No-go theorems for functorial localic spectra of noncommutative rings

๋ณธ ๋…ผ๋ฌธ์€ ๋น„์ปค๋ฎค๋‹ˆํ‹ฐ๋ธŒ C ๋Œ€์ˆ˜์— ๋Œ€ํ•œ ๊ฒ”ํŒ๋“œ ์ŠคํŽ™ํŠธ๋Ÿผ์˜ ์ผ๋ฐ˜ํ™”๋ฅผ ์‹œ๋„ํ•˜๋Š” ๋ฐ ์žˆ์–ด ์ค‘์š”ํ•œ ์ œํ•œ์  ๊ฒฐ๊ณผ๋ฅผ ์ œ๊ณตํ•œ๋‹ค. ์ด ์—ฐ๊ตฌ๋Š” ํŠนํžˆ ํ–‰๋ ฌ ๋Œ€์ˆ˜ M n(C) (n โ‰ฅ 3)์—์„œ ์ž๋ช…ํ•œ ๋กœ์ปฌ์„ ์ƒ์„ฑํ•œ๋‹ค๋Š” ์ ์—์„œ, ์ „ํ†ต์ ์ธ ํ† ํฌ์Šค ๊ฐœ๋…์ด ๋น„์ปค๋ฎค๋‹ˆํ‹ฐ๋ธŒ C ๋Œ€์ˆ˜์— ๋Œ€ํ•œ ์ข‹์€ ์ŠคํŽ™ํŠธ๋Ÿผ ๊ฐœ๋…์„ ํฌ์šฉํ•˜๋Š” ๋ฐ ๋ถ€์ ์ ˆํ•จ์„ ๊ฐ•๋ ฅํ•˜๊ฒŒ ๋ณด์—ฌ์ค€๋‹ค. 1. ๋ ˆ์˜ˆ์Šค ์ •๋ฆฌ์˜ ํ™•์žฅ ๋ ˆ์˜ˆ์Šค์˜ ๋…ผ๋ฌธ์€ ๋ชจ๋“  ์ปค๋ฎคํ‹ฐ๋ธŒ C ๋Œ€์ˆ˜์— ๋Œ€ํ•ด ๊ฒ”ํŒ๋“œ ์ŠคํŽ™ํŠธ๋Ÿผ์„ ํ• ๋‹นํ•˜๋Š” ํŽ‘ํ„ฐ๊ฐ€ ํ–‰๋ ฌ ๋Œ€์ˆ˜ M n(C) (n โ‰ฅ 3)์—์„œ ์ž๋ช…ํ•œ ๊ฒฐ๊ณผ๋ฅผ ์–ป๋Š”๋‹ค๋Š” ๊ฒƒ์„ ๋ณด์—ฌ์ค€๋‹ค. ๋ณธ ๋…ผ๋ฌธ์€ ์ด ์ •๋ฆฌ๋ฅผ ํ™•์žฅํ•˜

Quantum Physics Mathematics
Quantum Entanglement Phase Transition in Werner State

Quantum Entanglement Phase Transition in Werner State

: ๋ณธ ๋…ผ๋ฌธ์€ ๊ณ„์‚ฐ ์—ญํ•™์„ ๊ธฐ๋ฐ˜์œผ๋กœ ํ•œ ์ƒˆ๋กœ์šด ์ ‘๊ทผ๋ฒ•์„ ํ†ตํ•ด ์–‘์ž ์‹œ์Šคํ…œ์˜ ๋ณต์žก์„ฑ์„ ์ธก์ •ํ•˜๋Š” ๋ฐฉ๋ฒ•์„ ์ œ์•ˆํ•˜๊ณ  ์žˆ์Šต๋‹ˆ๋‹ค. ์ด ์—ฐ๊ตฌ๋Š” ๊ณ ์ „์  ๋ณต์žก์„ฑ ์ธก์ • ์ง€ํ‘œ์™€ ๋‹ฌ๋ฆฌ, ์–ฝํž˜๊ณผ ๊ฐ™์€ ์–‘์ž ํšจ๊ณผ๋ฅผ ํฌ์ฐฉํ•  ์ˆ˜ ์žˆ๋Š” ์ƒˆ๋กœ์šด ์ง€ํ‘œ ๊ฐœ๋ฐœ์— ์ดˆ์ ์„ ๋งž์ถ”๊ณ  ์žˆ์Šต๋‹ˆ๋‹ค. 1. ๊ณ„์‚ฐ ์—ญํ•™์˜ ๊ธฐ์ดˆ ๊ณ„์‚ฐ ์—ญํ•™์€ Crutchfield์™€ Young์ด ์ œ์•ˆํ•œ ๊ฐœ๋…์œผ๋กœ, ๋™์—ญํ•™ ์‹œ์Šคํ…œ์˜ ๋ณต์žก์„ฑ์„ ์ธก์ •ํ•˜๋Š” ๋ฐฉ๋ฒ•์„ ์ œ๊ณตํ•ฉ๋‹ˆ๋‹ค. ์ด ์ ‘๊ทผ๋ฒ•์—์„œ๋Š” ํ™•๋ฅ ์  ์ž๋™๋ฌธ์„ ์ƒ์„ฑํ•˜์—ฌ ๋ถ„์„ ์‹œ์Šคํ…œ์˜ ๊ธฐํ˜ธ ์—ญํ•™์„ ๋ชจ๋ฐฉํ•˜๊ณ , ์ด๋ฅผ ํ†ตํ•ด ๋‚ด์žฌ์ ์ธ ๊ณ„์‚ฐ ๋ฐ ๋ณต์žก์„ฑ์„ ์ •๋Ÿ‰ํ™”ํ•ฉ๋‹ˆ๋‹ค. 2. ์–‘์ž ์ƒ

Physics Nonlinear Sciences Quantum Physics
Adversary lower bounds in the Hamiltonian oracle model

Adversary lower bounds in the Hamiltonian oracle model

Catchy Title KO: ํ•˜๋ฏธํ„ด ์˜ค๋ผํด ๋ชจ๋ธ์—์„œ ์ ๋Œ€์ž ๋ฐฉ๋ฒ•์„ ํ†ตํ•œ ์–‘์ž ์ฟผ๋ฆฌ ๋ณต์žก๋„ ๋ถ„์„ Abstract KO: ์ด ๋…ผ๋ฌธ์€ ์–‘์ž ์ฟผ๋ฆฌ ๋ชจ๋ธ์—์„œ ํ•จ์ˆ˜ ๊ณ„์‚ฐ์˜ ๋ณต์žก์„ฑ์„ ๋ถ„์„ํ•˜๋Š” ๋ฐ ์‚ฌ์šฉ๋˜๋Š” ์ ๋Œ€์ž ๋ฐฉ๋ฒ•์— ์ดˆ์ ์„ ๋งž์ถ”๊ณ  ์žˆ๋‹ค. ํŠนํžˆ, ์ด ๋…ผ๋ฌธ์—์„œ๋Š” ํ•˜๋ฏธํ„ด ์˜ค๋ผํด ๋ชจ๋ธ์ด๋ผ๋Š” ์—ฐ์† ์‹œ๊ฐ„ ๋ชจ๋ธ์„ ํ†ตํ•ด ์ด๋Ÿฌํ•œ ๋ฐฉ๋ฒ•๋ก ์„ ์ ์šฉํ•˜๊ณ , ์ด๋ฅผ ํ†ตํ•ด ์–‘์ž ์•Œ๊ณ ๋ฆฌ์ฆ˜์˜ ์ฟผ๋ฆฌ ๋ณต์žก๋„๋ฅผ ๋ถ„์„ํ•œ๋‹ค. ์ด๋Š” ์ด์‚ฐ ์ฟผ๋ฆฌ ๋ชจ๋ธ๊ณผ ๋ถ„์ˆ˜ ์ฟผ๋ฆฌ ๋ชจ๋ธ์—์„œ ์‚ฌ์šฉ๋˜๋Š” ์ ๋Œ€์ž ๋ฐฉ๋ฒ•๊ณผ ์œ ์‚ฌํ•˜์ง€๋งŒ, ์—ฐ์† ์‹œ๊ฐ„ ๋ชจ๋ธ์—์„œ๋Š” ํ•˜๋ฏธํ„ด ์˜ค๋ผํด์„ ํ†ตํ•ด ํ•จ์ˆ˜ ๊ณ„์‚ฐ์ด ์ˆ˜ํ–‰๋œ๋‹ค. Deep Ana

Model Computational Complexity Quantum Physics Computer Science
On the Simulation of Adaptive Measurements via Postselection

On the Simulation of Adaptive Measurements via Postselection

๋ณธ ๋…ผ๋ฌธ์€ ์–‘์ž ๊ณ„์‚ฐ ๋ชจ๋ธ์—์„œ ์ ์‘ ์ธก์ •์ด ํฌ์ŠคํŠธ์„ ํƒ์„ ํ†ตํ•ด ์‹œ๋ฎฌ๋ ˆ์ด์…˜๋  ์ˆ˜ ์žˆ๋Š”์ง€์— ๋Œ€ํ•œ ํƒ๊ตฌ๋ฅผ ์ค‘์‹ฌ์œผ๋กœ ์ง„ํ–‰๋ฉ๋‹ˆ๋‹ค. ์ด ์—ฐ๊ตฌ๋Š” ์–‘์ž ์ปดํ“จํŒ… ๋ถ„์•ผ์—์„œ ์ค‘์š”ํ•œ ์˜๋ฏธ๋ฅผ ์ง€๋‹ˆ๋ฉฐ, ํŠนํžˆ P ๋ฌธ์ œ ํ•ด๊ฒฐ ๋Šฅ๋ ฅ๊ณผ ๊ฐ™์€ ์ž ์žฌ์ ์ธ ํ˜์‹ ์  ๊ฒฐ๊ณผ๋ฅผ ์ œ์‹œํ•ฉ๋‹ˆ๋‹ค. 1. ์„œ๋ก  ์„œ๋ก ์—์„œ๋Š” ํฌ์ŠคํŠธBQP(PostBQP) ๋ณต์žก์„ฑ ํด๋ž˜์Šค์— ๋Œ€ํ•œ ์†Œ๊ฐœ์™€ ์•„๋ก ์†์ด ์ œ๊ธฐํ•œ ํฅ๋ฏธ๋กœ์šด ์งˆ๋ฌธ์„ ๋‹ค๋ฃน๋‹ˆ๋‹ค. ํฌ์ŠคํŠธBQP๋Š” ํฌ์ŠคํŠธ์„ ํƒ๊ณผ ์ œํ•œ๋œ ์˜ค์ฐจ๋ฅผ ๊ฐ€์ง„ ์–‘์ž ํŠœ๋ง ๋จธ์‹ ์—์„œ ํ•ด๊ฒฐ ๊ฐ€๋Šฅํ•œ ๋ชจ๋“  ๊ณ„์‚ฐ ๋ฌธ์ œ๋ฅผ ํฌํ•จํ•˜๋Š” ๋ณต์žก์„ฑ ํด๋ž˜์Šค์ž…๋‹ˆ๋‹ค. ๋˜ํ•œ, ํฌ์ŠคํŠธBQP๊ฐ€ ํ™•๋ฅ ์  ํŠœ๋ง ๋จธ์‹ ์— ์˜ํ•ด

Quantum Physics Computational Complexity Computer Science
Comment on 'There is No Quantum World' by Jeffrey Bub

Comment on 'There is No Quantum World' by Jeffrey Bub

์ด ๋…ผํ‰์€ ์–‘์ž ๋…ผ๋ฆฌ์™€ ํ™•๋ฅ  ์ด๋ก  ์‚ฌ์ด์˜ ๊นŠ์€ ๊ตฌ์กฐ์  ์—ฐ๊ด€์„ฑ์„ ๊ฐ•์กฐํ•œ๋‹ค. ์ง๊ต ๊ณต๊ฐ„(orthogonal space)์€ ํž๋ฒ ๋ฅดํŠธ ๊ณต๊ฐ„์˜ ํ•œ ํ˜•ํƒœ๋กœ, ์–‘์ž์—ญํ•™์—์„œ ์ƒํƒœ๋ฒกํ„ฐ๊ฐ€ ์„œ๋กœ ์ง๊ตํ•  ๋•Œ ์„œ๋กœ ๋ฐฐํƒ€์ ์ธ ๋ฌผ๋ฆฌ์  ์ƒํƒœ๋ฅผ ๋‚˜ํƒ€๋‚ธ๋‹ค. ์ด๋Ÿฌํ•œ ๊ณต๊ฐ„์— ๋Œ€ํ•ด โ€œ์ง๊ต์„ฑ์„ ๋ณด์กดํ•˜๋Š” ์‚ฌ์ƒโ€์ด๋ผ ํ•จ์€ ๋‘ ๋ฒกํ„ฐ๊ฐ€ ์ง๊ต์ผ ๋•Œ ๊ทธ ์ด๋ฏธ์ง€ ์—ญ์‹œ ์ง๊ต๊ฐ€ ๋˜๋Š” ์„ ํ˜• ํ˜น์€ ๋ฐ˜์„ ํ˜• ๋ณ€ํ™˜์„ ์˜๋ฏธํ•œ๋‹ค. Uhlhorn ์ •๋ฆฌ๋Š” ์ด๋Ÿฌํ•œ ์‚ฌ์ƒ์ด ์‹ค์ œ๋กœ๋Š” ์ „์ฒด ๋‚ด์ ์„ ๋ณด์กดํ•˜๋Š”(์ฆ‰, ์œ ๋‹ˆํ„ฐ๋ฆฌ ํ˜น์€ ๋ฐ˜์œ ๋‹ˆํ„ฐ๋ฆฌ) ๋ณ€ํ™˜์— ํ•œ์ •๋œ๋‹ค๋Š” ๊ฐ•๋ ฅํ•œ ๊ฒฐ๊ณผ๋ฅผ ์ œ๊ณตํ•œ๋‹ค. ์ฆ‰, ์ง๊ต์„ฑ์„ ๋ณด์กดํ•˜๋ฉด ์ž๋™์ 

Quantum Physics
On the impossibility of non-static quantum bit commitment between two parties

On the impossibility of non-static quantum bit commitment between two parties

๋ณธ ๋…ผ๋ฌธ์€ ์–‘์ž ๋น„ํŠธ ์ปค๋ฐ‹๋จผํŠธ(QBC) ํ”„๋กœํ† ์ฝœ์˜ ๋ณด์•ˆ์„ฑ๊ณผ ํ•œ๊ณ„์— ๋Œ€ํ•ด ์‹ฌ๋„ ์žˆ๊ฒŒ ๋ถ„์„ํ•ฉ๋‹ˆ๋‹ค. QBC๋Š” ์•”ํ˜ธํ™”์—์„œ ์ค‘์š”ํ•œ ์—ญํ• ์„ ํ•˜๋Š”๋ฐ, ์ด๋Š” ์ „์†ก์ž๊ฐ€ ์ˆ˜์‹ ์ž์—๊ฒŒ 0 ๋˜๋Š” 1 ์ค‘ ํ•˜๋‚˜์˜ ๋น„ํŠธ๋ฅผ ์•ฝ์†ํ•˜๋Š” ๊ณผ์ •์ž…๋‹ˆ๋‹ค. ์ด ํ”„๋กœ์„ธ์Šค๋Š” ๋ฐ”์ธ๋”ฉ ์†์„ฑ๊ณผ ๊ฐ์ถ”๋Š” ์†์„ฑ์„ ๋™์‹œ์— ์ถฉ์กฑํ•ด์•ผ ํ•ฉ๋‹ˆ๋‹ค. ๋ฐ”์ธ๋”ฉ ์†์„ฑ์€ ์ „์†ก์ž๊ฐ€ ์ปค๋ฐ‹๋จผํŠธ ๋‹จ๊ณ„ ์ดํ›„์— ์•ฝ์†ํ•œ ๋น„ํŠธ ๊ฐ’์„ ๋ณ€๊ฒฝํ•  ์ˆ˜ ์—†์Œ์„ ์˜๋ฏธํ•˜๋ฉฐ, ๊ฐ์ถ”๋Š” ์†์„ฑ์€ ์ˆ˜์‹ ์ž์—๊ฒŒ ์ปค๋ฐ‹๋จผํŠธ ๋‹จ๊ณ„ ์ด์ „์—๋Š” ์•ฝ์†๋œ ๋น„ํŠธ ๊ฐ’์ด ์•Œ๋ ค์ง€์ง€ ์•Š์Œ์„ ๋‚˜ํƒ€๋ƒ…๋‹ˆ๋‹ค. ์ด๋Ÿฌํ•œ ๋‘ ๊ฐ€์ง€ ์†์„ฑ์„ ๋™์‹œ์— ์ถฉ์กฑํ•˜๋Š” ๊ณ ์ „์  ๋น„ํŠธ ์ปค๋ฐ‹๋จผํŠธ ํ”„๋กœํ† ์ฝœ

Quantum Physics Computer Science Cryptography and Security
Superiority of exact quantum automata for promise problems

Superiority of exact quantum automata for promise problems

: ๋ณธ ๋…ผ๋ฌธ์€ ์–‘์ž ์ปดํ“จํŒ…๊ณผ ๊ณ ์ „์  ์ปดํ“จํŒ…์˜ ์„ฑ๋Šฅ ์ฐจ์ด์— ๋Œ€ํ•œ ์‹ฌ๋„ ์žˆ๋Š” ๋ถ„์„์„ ์ œ๊ณตํ•ฉ๋‹ˆ๋‹ค. ํŠนํžˆ, ์–‘์ž ์˜คํ† ๋งˆํƒ€์™€ ๊ฒฐ์ •์  ์œ ํ•œ ์˜คํ† ๋งˆํƒ€(DFA)๋ฅผ ๋น„๊ตํ•˜์—ฌ ์–‘์ž์˜ ์šฐ์›”์„ฑ์„ ์ž…์ฆํ•˜๊ณ  ์žˆ์Šต๋‹ˆ๋‹ค. 1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ์–‘์ž ๊ณ„์‚ฐ์€ ๋ถ€๋ถ„ ํ•จ์ˆ˜์™€ ์ „์ฒด ํ•จ์ˆ˜์— ๋Œ€ํ•œ ๊ด‘๋ฒ”์œ„ํ•œ ์—ฐ๊ตฌ๊ฐ€ ์ด๋ฃจ์–ด์ ธ ์™”์Šต๋‹ˆ๋‹ค. ๊ทธ๋Ÿฌ๋‚˜ ์ž๋™ํ™” ์ด๋ก ์—์„œ๋Š” ์–‘์ž ์œ ํ•œ ์˜คํ† ๋งˆํƒ€(QFA)์˜ ์„ฑ๋Šฅ์„ ๋ถ„์„ํ•˜๋Š” ๊ฒฐ๊ณผ๋Š” ๋งค์šฐ ์ œํ•œ์ ์ด์—ˆ์Šต๋‹ˆ๋‹ค. Klauck

Formal Languages Quantum Physics Computational Complexity Computer Science

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