Universal Dynamical Control of Open Quantum Systems

<table>Fidelity of the IIP symmetry for two TLS coupled to zero-temperature baths. The initial state is entangled, <svg height="21.3125" id="M797" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 242.8 21.3125" width="242.8" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,77.737,13.425)"><path d="M782 703l-309 -950l-231 505l-91 -47l-18 35l147 78l194 -431h2l264 810h42z" id="x221A"></path></g><g transform="matrix(.017,-0,0,-.017,.625,16.25)"><path d="M162 -163h-61v866h61v-866z" id="x7C"></path></g><g transform="matrix(.017,-0,0,-.017,5.096,16.25)"><path d="M642 419q-50 -36 -71 -94q-28 -78 -68 -170q-39 -89 -114 -135q-34 -21 -83 -31l-45 -219l-31 -31q-8 7 -15 29.5t-2 45.5l35 172q-153 10 -153 169q0 28 6 84q7 68 7 88q0 48 -27 48q-18 0 -51 -28l-7 26q62 75 118 75q49 0 49 -90q0 -47 -5 -81q-10 -72 -10 -108
q0 -117 82 -133l87 455l62 19l7 -2l-99 -478q91 12 131 120q34 93 51 154q20 73 36 88q42 40 103 56z" id="x1D713"></path></g><g transform="matrix(.017,-0,0,-.017,16.213,16.25)"><path d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" id="x28"></path></g><g transform="matrix(.017,-0,0,-.017,22.094,16.25)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g><g transform="matrix(.017,-0,0,-.017,30.254,16.25)"><path d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" id="x29"></path></g><g transform="matrix(.017,-0,0,-.017,36.135,16.25)"><path d="M307 267l-192 -430h-62l193 433l-193 433h62l192 -430v-6z" id="x27E9"></path></g><g transform="matrix(.017,-0,0,-.017,47.865,16.25)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,62.568,16.25)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g><g transform="matrix(.017,-0,0,-.017,70.728,16.25)"><path d="M368 703l-264 -866h-60l265 866h59z" id="x2F"></path></g>
<g transform="matrix(1.25,0,0,-1.25,90,90)">
<path d="m 0.58,70.48 6.53,0" style="fill:none;stroke:#000000;stroke-width:0.68000001;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path>
</g>
<g transform="matrix(.017,-0,0,-.017,90.725,16.25)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g><g transform="matrix(.017,-0,0,-.017,98.884,16.25)"><path d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" id="x28"></path></g><g transform="matrix(.017,-0,0,-.017,104.766,16.25)"><path d="M162 -163h-61v866h61v-866z" id="x7C"></path></g><g transform="matrix(.017,-0,0,-.017,109.237,16.25)"><path d="M546 430q-14 -33 -37.5 -140t-38.5 -209q-29 -195 -156 -289q-29 -21 -70 -37t-78 -16q-62 0 -102.5 37t-40.5 69q0 27 26 48q19 15 25 -3q13 -43 46.5 -69t87.5 -26q55 0 83 21q29 22 50 65t43 140q14 64 29 163h-2q-55 -81 -149 -152q-59 -44 -102 -44q-23 0 -43.5 30
t-20.5 85q0 74 32.5 145.5t84.5 117.5q40 35 100 58.5t117 23.5q21 0 65 -8q30 -6 44 -6zM456 386q-40 16 -81 16q-29 0 -64 -13q-42 -17 -85 -97q-19 -36 -31.5 -86t-12.5 -86q0 -64 30 -64q20 0 52.5 21t60.5 52q74 81 95 123q26 62 36 134z" id="x1D454"></path></g><g transform="matrix(.017,-0,0,-.017,118.909,16.25)"><path d="M307 267l-192 -430h-62l193 433l-193 433h62l192 -430v-6z" id="x27E9"></path></g>
<g transform="matrix(.012,-0,0,-.012,125.925,20.338)"><path d="M716 28l-8 -28h-254l8 28q55 5 66 17.5t5 47.5l-30 145h-232l-74 -138q-21 -43 -11 -54.5t72 -17.5l-6 -28h-235l8 28q53 7 73.5 21t53.5 70l319 540l33 8q6 -43 33 -176l80 -381q10 -49 26.5 -63t72.5 -19zM495 281l-49 264h-2l-149 -264h200z" id="x1D434"></path></g>
<g transform="matrix(.017,-0,0,-.017,135.275,16.25)"><path d="M162 -163h-61v866h61v-866z" id="x7C"></path></g><g transform="matrix(.017,-0,0,-.017,139.746,16.25)"><path d="M391 364q0 -28 -20.5 -53.5t-50 -43.5t-70 -34t-73.5 -25t-68 -17v-29q0 -48 20 -81t65 -33q73 0 157 76l16 -23q-107 -113 -221 -113q-21 0 -40.5 6.5t-39 22t-31.5 47t-12 75.5q0 69 33.5 139.5t95.5 114.5q77 55 143 55q42 0 69 -24.5t27 -59.5zM313 350
q0 26 -14.5 40.5t-37.5 14.5q-32 0 -44 -7q-82 -46 -104 -175q200 49 200 127z" id="x1D452"></path></g><g transform="matrix(.017,-0,0,-.017,146.783,16.25)"><path d="M307 267l-192 -430h-62l193 433l-193 433h62l192 -430v-6z" id="x27E9"></path></g>
<g transform="matrix(.012,-0,0,-.012,153.8,20.338)"><path d="M594 511q0 -122 -171 -157l1 -2q158 -33 158 -159q0 -52 -34.5 -95t-90.5 -65q-76 -33 -217 -33h-223l8 28q63 5 79.5 19t26.5 72l83 426q9 48 -2.5 60t-77.5 17l6 28h259q195 0 195 -139zM499 509q0 59 -37 83t-91 24q-36 0 -51 -9q-17 -9 -22 -44l-35 -195h62
q82 0 128 37t46 104zM481 199q0 71 -48 102.5t-121 31.5h-56l-37 -201q-11 -58 7.5 -77t80.5 -19q76 0 125 44.5t49 118.5z" id="x1D435"></path></g>
<g transform="matrix(.017,-0,0,-.017,165.55,16.25)"><path d="M535 230h-212v-233h-58v233h-213v50h213v210h58v-210h212v-50z" id="x2B"></path></g><g transform="matrix(.017,-0,0,-.017,179.285,16.25)"><path d="M162 -163h-61v866h61v-866z" id="x7C"></path></g><g transform="matrix(.017,-0,0,-.017,183.756,16.25)"><path d="M391 364q0 -28 -20.5 -53.5t-50 -43.5t-70 -34t-73.5 -25t-68 -17v-29q0 -48 20 -81t65 -33q73 0 157 76l16 -23q-107 -113 -221 -113q-21 0 -40.5 6.5t-39 22t-31.5 47t-12 75.5q0 69 33.5 139.5t95.5 114.5q77 55 143 55q42 0 69 -24.5t27 -59.5zM313 350
q0 26 -14.5 40.5t-37.5 14.5q-32 0 -44 -7q-82 -46 -104 -175q200 49 200 127z" id="x1D452"></path></g><g transform="matrix(.017,-0,0,-.017,190.793,16.25)"><path d="M307 267l-192 -430h-62l193 433l-193 433h62l192 -430v-6z" id="x27E9"></path></g>
<g transform="matrix(.012,-0,0,-.012,197.825,20.338)"><path d="M716 28l-8 -28h-254l8 28q55 5 66 17.5t5 47.5l-30 145h-232l-74 -138q-21 -43 -11 -54.5t72 -17.5l-6 -28h-235l8 28q53 7 73.5 21t53.5 70l319 540l33 8q6 -43 33 -176l80 -381q10 -49 26.5 -63t72.5 -19zM495 281l-49 264h-2l-149 -264h200z" id="x1D434"></path></g>
<g transform="matrix(.017,-0,0,-.017,207.175,16.25)"><path d="M162 -163h-61v866h61v-866z" id="x7C"></path></g><g transform="matrix(.017,-0,0,-.017,211.646,16.25)"><path d="M546 430q-14 -33 -37.5 -140t-38.5 -209q-29 -195 -156 -289q-29 -21 -70 -37t-78 -16q-62 0 -102.5 37t-40.5 69q0 27 26 48q19 15 25 -3q13 -43 46.5 -69t87.5 -26q55 0 83 21q29 22 50 65t43 140q14 64 29 163h-2q-55 -81 -149 -152q-59 -44 -102 -44q-23 0 -43.5 30
t-20.5 85q0 74 32.5 145.5t84.5 117.5q40 35 100 58.5t117 23.5q21 0 65 -8q30 -6 44 -6zM456 386q-40 16 -81 16q-29 0 -64 -13q-42 -17 -85 -97q-19 -36 -31.5 -86t-12.5 -86q0 -64 30 -64q20 0 52.5 21t60.5 52q74 81 95 123q26 62 36 134z" id="x1D454"></path></g><g transform="matrix(.017,-0,0,-.017,221.318,16.25)"><path d="M307 267l-192 -430h-62l193 433l-193 433h62l192 -430v-6z" id="x27E9"></path></g>
<g transform="matrix(.012,-0,0,-.012,228.338,20.338)"><path d="M594 511q0 -122 -171 -157l1 -2q158 -33 158 -159q0 -52 -34.5 -95t-90.5 -65q-76 -33 -217 -33h-223l8 28q63 5 79.5 19t26.5 72l83 426q9 48 -2.5 60t-77.5 17l6 28h259q195 0 195 -139zM499 509q0 59 -37 83t-91 24q-36 0 -51 -9q-17 -9 -22 -44l-35 -195h62
q82 0 128 37t46 104zM481 199q0 71 -48 102.5t-121 31.5h-56l-37 -201q-11 -58 7.5 -77t80.5 -19q76 0 125 44.5t49 118.5z" id="x1D435"></path></g>
<g transform="matrix(.017,-0,0,-.017,236.3,16.25)"><path d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" id="x29"></path></g>
</svg>.</table>

International Scholarly Research Notices

Universal Dynamical Control of Open Quantum Systems

Figure 8