measurement quantum thermodynamic Resource as a Michele Campisi University Florence of y
heat work beet W Kg
heat work beet W Kg
heat work beet W Ks M " metro work , , - " hot quantum - , Etovdrd - quantum info etat Cloth , hpj Z , .
( vid unitary ( evolution ) W EREOTROPY p Ug ut → g W s work Kg
arXiv 1905.10262 ( METROTROPY µ M → I TKSITK g
W ERE I His ] \ o = -2 E Es rk = Wimax P stochastic uni is - g1=UgUt If P stochastic doubly E' is 4444k Ek ) = Birkhoff EKEK Rare = theorem ET i. r = . P ← permutations Eidir ri ) 12 Pre KKIUIE = ; = p Min ow → = IE Ey - ' E min E = -
bist . ist Uh . \ a permutation matrix 5 given permutations always find unitary U thet such you can a ' Isil Ul I ri ; = eid of :) :) ! : O O e. " :
METROTROPY ERGOTROPY is H level rz system Tvo = W=4RHRHbz = Nf M
I His ] ( o ' M IYIETROTROPY 1Tk=1YkXHkl ' ) ME I E Max E - ' E E min = - Kellys ) 12=161011012 Pe*=
1) Use Birkhoff theorem r ) to find mpg ; pip = 1+21 Et . . p Bf set of Bi stochastic matrices Et htt Tz argmin r = . . 2
2) all bistocastic Not to unistochastic matrices are bist . 1+62 Be I whist . example ) -148,191=4 I ( big ! ! unnoitstochastic ← t ti O 0 ;) is is :
Theorem I 1991 ) ) - Yeong , LAU 15C its Linear algebra app e . Any convex combination of permutation matrices which is unistochastic, is such that it involves only permutations that are pairwise complementary. Two N × N matrices A and B are said to be complementary if, for any 1 ≤ i, j, h, k ≤ N, A_ij = A_hk = B_ik = 1 implies B_hj = 1. Any permutation that is complementary to the identity is symmetric
Is combination only permutations involving complementary convex any Uni stochastic ? OPEN QUESTION ! 15 YES : up To N E - Yeong , Au its appl I 1991 ) 15C Linear algebra .
STATEMENT Pip Et combinations the all r over of minimum . . containing pairwise only permutations achieved is convex by In Set symmetric permutations of = A. Sdfanelli et al ( ) arXiv 1905.10262
= ( lb lb ) to ) la ) Id ) HEY K ) Symmetric . . Ix ) ) . permutation on c) . . . T . ( of = on . Itza ' bist pij-kilvlo.SI Whist . •
Theorem Pip Et the all r over of minimum . . UNI MATRICES STOCHASTIC achieved is by In Set symmetric permutations of = A. Sdfanelli et al ( ) arXiv 1905.1026
example level system 4 - a- foie f . ) "% : . ) r a .
ETT Corollaries E r min - . M • = 2 M= • if , then symmetric Jw is Wz ( LH ,gJ=o ) • MEI 2 I in general ) MEW • Conjecture Me ( in general ) • Wz
. ra oh an Y ra rp or A rot r=( E= Bri & ) three level system E road ra ,
wz of ' Wear , H Hit Hz Htt t = Den - et ox etzk is s en - Qi ' E. IT IT g 0 9 g = - , , Q2 g.) Tr ; ( g ! D Ei H Qi ) = ; = - ( DE ) CDE , > tCDEz7 ( M ) = = t QL Q = ,
flat p2Qz= EKITI ] DCS It lls SCH - Slye - Trglng DS Into S Go DS AS 1¥ . ' Into ] t 70 , ESCH IV IV IV IV O . O O O - -151911g - ' ) Iyzcs ' g = .TK " ' ] , DES unital ' is 2 I I If 70 Trfgeng Dcgllr ] glnr ) = - ] - - - est S ] ] - -
heat Q2 Q P2 + 30 Pi , Q2 Q ( DE t ) = , It U te A. Solfanelli Refrigerator ( M ) thesis B. WIFI Sc . U U U Ee Ee U Es Es Ee Ee ^ A A A Heater Accelerator Engine U ✓ HI IES n ^ n n
Results � 1 � H A E R 1 f 0 WE ' PL ,
Results � 2 � maximises R ] - Qz - range y[ [ R ) in , E) - range E) ( DE > y[ [ in , D= w¥ y[ Wz ⇒ y 1- w÷ =
Results output LE ] { heat metro work and Maximal - efficiency ⑤ extraction CRI with be achieved higher projectors can rank tilt 145×451 14 :X e. g g- : 92=145×451 ly :X 491 t
Results � 4 � Generally two for qudits 1 of the other than [ H ] In order projectors to realize measurement anything some , be entangled must ( cannot be written form ) in factorised 4@ However external when efficiency occurs , gl Z MXM = p 'n 1h ) 1ns ) IND =
Results let Uk 14k 7 > = � 5 � Pick U from the invariant randomly ) measure SUKN then ftp.m CDEF [ H ] to ⇒ f ) I ( = ,
Results Monte ⑥ Sampling Carlo SUCH of
circuit QB Experiment circuit QED -1 . . . . & Quantum circuit Pekok , Eiazotto Thermo 91=-4 → IT IT 9 . . . . . , Dynamics , = -4 Upkvtguput foams :[ ÷ :÷÷÷ , from .in . . Natphys # 1% , . femme
thank YOU i
Recommend
More recommend
