University Florence of y heat work beet W Kg heat work - - PowerPoint PPT Presentation

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University Florence of y heat work beet W Kg heat work - - PowerPoint PPT Presentation

Jan 03, 2024 465 likes •807 views

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 -

slide-1
SLIDE 1

quantum

measurement

as a

thermodynamic

Resource Michele

Campisi

University

  • f
Florence

y

slide-2
SLIDE 2 heat work W beet Kg
slide-3
SLIDE 3 heat work W beet Kg
slide-4
SLIDE 4 heat work W beet Ks M " metro
  • work
, , " quantum
  • hot
, Etovdrd etat . , hpj
  • quantum info
, Z Cloth
slide-5
SLIDE 5 ( vid unitary evolution )

(

p EREOTROPY

W

W s g → Ug ut work Kg
slide-6
SLIDE 6 arXiv 1905.10262

(

METROTROPY M

µ

g → I TKSITK
slide-7
SLIDE 7 ERE W I His ] =
  • E
=
  • 2
Es rk

\

P is uni
  • stochastic
g1=UgUt If E' = Ek

4444k

) P is doubly stochastic = EKEK Rare

Birkhoff

theorem = ET . i. r Pre = KKIUIE ) 12 P = Eidir ; ri ← permutations

Wimax

IE
  • Ey
Min → p =
  • w
= E
  • min
E '
slide-8
SLIDE 8 bist . Uh ist . given a permutation matrix 5

\

permutations you can always find a unitary U such thet ri ; = Isil Ul I ' O O eid e.
  • f

! :

:)

"

:

:)

slide-9
SLIDE 9 ERGOTROPY is METROTROPY Tvo level system H = rz

W=4RHRHbz

M = Nf
slide-10
SLIDE 10 I His ] '
  • IYIETROTROPY
M

(

1Tk=1YkXHkl

ME

Max I E
  • E
' ) = E
  • min
E ' Pe*= Kellys ) 12=161011012
slide-11
SLIDE 11 1) Use Birkhoff theorem to find

mpg

;

Et . pip . r ) p = 1+21

Bf

set
  • f
Bi stochastic matrices Tz = argmin Et . htt . r 2
slide-12
SLIDE 12 2) Not all bistocastic matrices are unistochastic to bist . 1+62 I whist . Be example I (

big

) -148,191=4

!

!

← unnoitstochastic O t ti : is is

;)

slide-13
SLIDE 13 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 Theorem LAU
  • Yeong ,
Linear algebra its app e . 15C I 1991 ) )
slide-14
SLIDE 14 Is any convex combination involving
  • nly
complementary permutations Uni stochastic ? OPEN QUESTION YES : up To N E

15

! Au
  • Yeong ,
Linear algebra its appl . 15C I 1991 )
slide-15
SLIDE 15 STATEMENT the minimum
  • f
Et . Pip . r
  • ver
all convex

combinations

containing
  • nly
pairwise permutations is achieved by In = Set
  • f
symmetric permutations ( A.Sdfanelli et al ) arXiv 1905.10262
slide-16
SLIDE 16 Symmetric la ) lb ) to ) Id ) . . . K ) permutation
  • n
= ( lb

HEY

c) . . . Ix ) ) T
  • f
=
  • n
. pij-kilvlo.SI ' bist . ( Whist .

Itza

slide-17
SLIDE 17 Theorem the minimum
  • f
Et . Pip . r
  • ver
all UNI STOCHASTIC MATRICES is achieved by In = Set
  • f
symmetric permutations ( A.Sdfanelli et al ) arXiv 1905.1026
slide-18
SLIDE 18 example 4
  • level
system a- foie . ) r . . ) a

f

"% :
slide-19
SLIDE 19 Corollaries E
  • min
ETT . r
  • M
= 2
  • if
Jw is symmetric , then M= Wz
  • MEI
( LH ,gJ=o ) 2
  • MEW
I in general ) Conjecture
  • Me
Wz (in general )
slide-20
SLIDE 20 three level system

E=

E

r=(

&)

ra A

ra

an rp

  • r
, .ra

Y

rot

  • h

road

Bri

slide-21
SLIDE 21
slide-22
SLIDE 22 Wear , ' wz of Den H = Hit Hz t Htt is en s
  • et
  • x etzk
Qi g
  • g
' = E. IT , 9 IT , Q2 Tr ; H ; ( g!
  • g.)
= D Ei ) = Qi ( M ) = ( DE ) = CDE, > tCDEz7 = Q , t QL
slide-23
SLIDE 23 flat p2Qz= . DCS lls ]
  • 151911g
, It Into ' ] t

AS

70 IV . IV IV IV O O O O
  • Iyzcs
' ) g ' =

EKITI

, .TK " DES '

1¥

' ] is unital I 2 If I

DS

70 Dcgllr ] = Trfgeng
  • glnr )

Into

]
  • ESCH
  • SCH
S est
  • TrglngDS
  • Slye
]
  • SGo
]
slide-24
SLIDE 24 Pi Q , + P2 Q2 30 ( DE ) = Q , t Q2 It A. Solfanelli ( M ) B. Sc . thesis WIFI U U U U Es Es

Ee

Ee

^ A

heat

Engine A Heater A Accelerator U ✓ Ute HI IES

Ee

Ee

n n ^ n

Refrigerator

slide-25
SLIDE 25 Results 1 H A E R f ' 1 WE , PL
slide-26
SLIDE 26 Results 2 maximises y[ R ] ,
  • Qz
in [ R )
  • range
y[ E) , ( DE > in [

E)

  • range
y[ D= w¥ Wz y ⇒ = 1- w÷
slide-27
SLIDE 27 Results metro
  • work
  • utput
LE ] Maximal efficiency and ⑤

{ heat

extraction CRI can be achieved with higher rank projectors
  • e. g
: g- 14 :X tilt 145×451 92=145×451 t ly :X 491
slide-28
SLIDE 28 Results 4 Generally for two qudits 1 In
  • rder
to realize anything
  • ther
than [ H ] , some
  • f
the measurement projectors must be entangled ( cannot be written in factorised form ) 4@ However , external efficiency
  • ccurs
when gl = Z p'n MXM 1h ) = 1ns ) IND
slide-29
SLIDE 29 Results

5

let 14k 7 = Uk > Pick U randomly from the invariant

SUKN

) measure then CDEF to ⇒ [H ]

(

I =

ftp.m

, f )
slide-30
SLIDE 30 Results

⑥

Monte Carlo Sampling
  • f
SUCH
slide-31
SLIDE 31 Experiment . . . . circuit QED
  • 1
circuit QB & circuit Quantum 91=-4 . IT , 9 IT , Thermo → Pekok , Eiazotto . . . . = -4 Upkvtguput Dynamics

÷

:÷÷÷

:[

.

,

from

.in . femme

foams

. Natphys # 1%,
slide-32
SLIDE 32

thank

YOU

i