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- W2770639819 abstract "For both unitary and open qubit dynamics, we compare asymmetry monotone-based bounds on the minimal time required for an initial qubit state to evolve to a final qubit state from which it is probabilistically distinguishable with fixed minimal error probability (i.e., the minimal error distinguishability time). For the case of unitary dynamics generated by a time-independent Hamiltonian, we derive a necessary and sufficient condition on two asymmetry monotones that guarantees that an arbitrary state of a two-level quantum system or a separable state of <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>N</mml:mi></mml:math> two-level quantum systems will unitarily evolve to another state from which it can be distinguished with a fixed minimal error probability <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>δ</mml:mi><mml:mo>∈</mml:mo><mml:mo stretchy=false>[</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mrow class=MJX-TeXAtom-ORD><mml:mo>/</mml:mo></mml:mrow><mml:mn>2</mml:mn><mml:mo stretchy=false>]</mml:mo></mml:math>. This condition is used to order the set of qubit states based on their distinguishability time, and to derive an optimal release time for driven two-level systems such as those that occur, e.g., in the Landau-Zener problem. For the case of non-unitary dynamics, we compare three lower bounds to the distinguishability time, including a new type of lower bound which is formulated in terms of the asymmetry of the uniformly time-twirled initial system-plus-environment state with respect to the generator <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mi>H</mml:mi><mml:mrow class=MJX-TeXAtom-ORD><mml:mi>S</mml:mi><mml:mi>E</mml:mi></mml:mrow></mml:msub></mml:math> of the Stinespring isometry corresponding to the dynamics, specifically, in terms of <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mo fence=false stretchy=false>‖</mml:mo><mml:mo stretchy=false>[</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mrow class=MJX-TeXAtom-ORD><mml:mi>S</mml:mi><mml:mi>E</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>ρ</mml:mi><mml:mrow class=MJX-TeXAtom-ORD><mml:mtext>av</mml:mtext></mml:mrow></mml:msub><mml:mo stretchy=false>(</mml:mo><mml:mi>τ</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo stretchy=false>]</mml:mo><mml:msub><mml:mo fence=false stretchy=false>‖</mml:mo><mml:mrow class=MJX-TeXAtom-ORD><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math>, where <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mi>ρ</mml:mi><mml:mrow class=MJX-TeXAtom-ORD><mml:mtext>av</mml:mtext></mml:mrow></mml:msub><mml:mo stretchy=false>(</mml:mo><mml:mi>τ</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo>:=</mml:mo><mml:mrow class=MJX-TeXAtom-ORD><mml:mfrac><mml:mn>1</mml:mn><mml:mi>τ</mml:mi></mml:mfrac></mml:mrow><mml:msubsup><mml:mo>∫</mml:mo><mml:mrow class=MJX-TeXAtom-ORD><mml:mn>0</mml:mn></mml:mrow><mml:mrow class=MJX-TeXAtom-ORD><mml:mi>τ</mml:mi></mml:mrow></mml:msubsup><mml:mi>d</mml:mi><mml:mi>t</mml:mi><mml:mspace width=thinmathspace /><mml:msup><mml:mi>e</mml:mi><mml:mrow class=MJX-TeXAtom-ORD><mml:mo>−</mml:mo><mml:mi>i</mml:mi><mml:msub><mml:mi>H</mml:mi><mml:mrow class=MJX-TeXAtom-ORD><mml:mi>S</mml:mi><mml:mi>E</mml:mi></mml:mrow></mml:msub><mml:mi>t</mml:mi></mml:mrow></mml:msup><mml:mi>ρ</mml:mi><mml:mo>⊗</mml:mo><mml:mo fence=false stretchy=false>|</mml:mo><mml:mn>0</mml:mn><mml:msub><mml:mo fence=false stretchy=false>⟩</mml:mo><mml:mrow class=MJX-TeXAtom-ORD><mml:mi>E</mml:mi></mml:mrow></mml:msub><mml:mo fence=false stretchy=false>⟨</mml:mo><mml:mn>0</mml:mn><mml:msub><mml:mo fence=false stretchy=false>|</mml:mo><mml:mrow class=MJX-TeXAtom-ORD><mml:mi>E</mml:mi></mml:mrow></mml:msub><mml:msup><mml:mi>e</mml:mi><mml:mrow class=MJX-TeXAtom-ORD><mml:mi>i</mml:mi><mml:msub><mml:mi>H</mml:mi><mml:mrow class=MJX-TeXAtom-ORD><mml:mi>S</mml:mi><mml:mi>E</mml:mi></mml:mrow></mml:msub><mml:mi>t</mml:mi></mml:mrow></mml:msup></mml:math>." @default.
- W2770639819 created "2017-12-04" @default.
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- W2770639819 date "2018-10-01" @default.
- W2770639819 modified "2023-09-27" @default.
- W2770639819 title "Distinguishability times and asymmetry monotone-based quantum speed limits in the Bloch ball" @default.
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- W2770639819 doi "https://doi.org/10.22331/q-2018-10-01-96" @default.
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