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High Resolution non-Markovianity in NMR

View Article: PubMed Central - PubMed

ABSTRACT

Memoryless time evolutions are ubiquitous in nature but often correspond to a resolution-induced approximation, i.e. there are correlations in time whose effects are undetectable. Recent advances in the dynamical control of small quantum systems provide the ideal scenario to probe some of these effects. Here we experimentally demonstrate the precise induction of memory effects on the evolution of a quantum coin (qubit) by correlations engineered in its environment. In particular, we design a collisional model in Nuclear Magnetic Resonance (NMR) and precisely control the strength of the effects by changing the degree of correlation in the environment and its time of interaction with the qubit. We also show how these effects can be hidden by the limited resolution of the measurements performed on the qubit. The experiment reinforces NMR as a test bed for the study of open quantum systems and the simulation of their classical counterparts.

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Related in: MedlinePlus

The trace distance, , was employed to witness non-Markovianity.The increase of D(ρ1(t), ρ2(t)) with time is a trace of non-Markovianity. (a) The plots show the dependence of ΔD with the strength of each collision η for different values of the correlation parameter q (0 for the solid blue line, 0.15 for the dashed orange line and 0.25 for the dash-dotted green line). q = 0 means that the two collisions were totally anti-correlated. (b) Detail of the ΔD curve for η < 0.01 and q = 0. In both plots the error bars were estimated taking into account every possible error source, as discussed in ref. 38. This led to the error determining the Bloch vector of the quantum state of δr = 5 × 10−4, independent of the direction. By propagating this error, the error in D(ρ1(t), ρ2(t)) is given by .
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f2: The trace distance, , was employed to witness non-Markovianity.The increase of D(ρ1(t), ρ2(t)) with time is a trace of non-Markovianity. (a) The plots show the dependence of ΔD with the strength of each collision η for different values of the correlation parameter q (0 for the solid blue line, 0.15 for the dashed orange line and 0.25 for the dash-dotted green line). q = 0 means that the two collisions were totally anti-correlated. (b) Detail of the ΔD curve for η < 0.01 and q = 0. In both plots the error bars were estimated taking into account every possible error source, as discussed in ref. 38. This led to the error determining the Bloch vector of the quantum state of δr = 5 × 10−4, independent of the direction. By propagating this error, the error in D(ρ1(t), ρ2(t)) is given by .

Mentions: Figure 2 shows the change in distance between the two initial states of the system after one and two collisions ΔD = D(ρ1(2), ρ2(2)) − D(ρ1(1), ρ2(1)), as a function of the strength of each collision η and for different degrees of correlation q of the environmental state. For large enough interactions (larger η) and anti-correlation in the environment (smaller q), the collisions clearly generate a non-Markovian dynamics in the system (ΔD > 0). The phenomenon, witnessed by the increase in ΔD also reflects a backflow of information from the environment to the system as time progresses.


High Resolution non-Markovianity in NMR
The trace distance, , was employed to witness non-Markovianity.The increase of D(ρ1(t), ρ2(t)) with time is a trace of non-Markovianity. (a) The plots show the dependence of ΔD with the strength of each collision η for different values of the correlation parameter q (0 for the solid blue line, 0.15 for the dashed orange line and 0.25 for the dash-dotted green line). q = 0 means that the two collisions were totally anti-correlated. (b) Detail of the ΔD curve for η < 0.01 and q = 0. In both plots the error bars were estimated taking into account every possible error source, as discussed in ref. 38. This led to the error determining the Bloch vector of the quantum state of δr = 5 × 10−4, independent of the direction. By propagating this error, the error in D(ρ1(t), ρ2(t)) is given by .
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5037399&req=5

f2: The trace distance, , was employed to witness non-Markovianity.The increase of D(ρ1(t), ρ2(t)) with time is a trace of non-Markovianity. (a) The plots show the dependence of ΔD with the strength of each collision η for different values of the correlation parameter q (0 for the solid blue line, 0.15 for the dashed orange line and 0.25 for the dash-dotted green line). q = 0 means that the two collisions were totally anti-correlated. (b) Detail of the ΔD curve for η < 0.01 and q = 0. In both plots the error bars were estimated taking into account every possible error source, as discussed in ref. 38. This led to the error determining the Bloch vector of the quantum state of δr = 5 × 10−4, independent of the direction. By propagating this error, the error in D(ρ1(t), ρ2(t)) is given by .
Mentions: Figure 2 shows the change in distance between the two initial states of the system after one and two collisions ΔD = D(ρ1(2), ρ2(2)) − D(ρ1(1), ρ2(1)), as a function of the strength of each collision η and for different degrees of correlation q of the environmental state. For large enough interactions (larger η) and anti-correlation in the environment (smaller q), the collisions clearly generate a non-Markovian dynamics in the system (ΔD > 0). The phenomenon, witnessed by the increase in ΔD also reflects a backflow of information from the environment to the system as time progresses.

View Article: PubMed Central - PubMed

ABSTRACT

Memoryless time evolutions are ubiquitous in nature but often correspond to a resolution-induced approximation, i.e. there are correlations in time whose effects are undetectable. Recent advances in the dynamical control of small quantum systems provide the ideal scenario to probe some of these effects. Here we experimentally demonstrate the precise induction of memory effects on the evolution of a quantum coin (qubit) by correlations engineered in its environment. In particular, we design a collisional model in Nuclear Magnetic Resonance (NMR) and precisely control the strength of the effects by changing the degree of correlation in the environment and its time of interaction with the qubit. We also show how these effects can be hidden by the limited resolution of the measurements performed on the qubit. The experiment reinforces NMR as a test bed for the study of open quantum systems and the simulation of their classical counterparts.

No MeSH data available.


Related in: MedlinePlus