The uncertainty and quantum correlation of measurement in double quantum-dot systems

doi:10.1007/s11467-022-1178-x

Front. Phys.

2022, Vol. 17

Issue (6) : 61504 https://doi.org/10.1007/s11467-022-1178-x

RESEARCH ARTICLE

The uncertainty and quantum correlation of measurement in double quantum-dot systems

Long-Yu Cheng¹, Fei Ming¹, Fa Zhao¹, Liu Ye¹, Dong Wang^1,²(

)

¹. School of Physics and Optoelectronic Engineering, Anhui University, Hefei 230601, China
². CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China

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Abstract

In this work, we study the entropic uncertainty and quantum discord in two double-quantum-dot (DQD) system coupled via a transmission line resonator (TLR). Explicitly, the dynamics of the systemic quantum correlation and measured uncertainty are analysed with respect to a general X-type state as the initial state. Interestingly, it is found that the different parameters, including the eigenvalue α of the coherent state, detuning amount δ, frequency ω and the coupling constant g, have subtle effects on the dynamics of the entropic uncertainty, such as the oscillation period of the uncertainty. It is clear to reveal that the quantum discord and the lower bound of the entropic uncertainty are anti-correlated when the initial state of the system is the Werner-type state, while quantum discord and the lower bound of the entropic uncertainty are not anti-correlated when the initial state of the system is the Bell-diagonal state. Thereby, we claim that the current investigation would provide an insight into the entropic uncertainty and quantum correlation in DQDs system, and are basically of importance to quantum precision measurement in practical quantum information processing.

Keywords uncertainty relations quantum correlation quantum dot

Corresponding Author(s): Dong Wang

Issue Date: 02 August 2022

Cite this article:

Long-Yu Cheng,Fei Ming,Fa Zhao, et al. The uncertainty and quantum correlation of measurement in double quantum-dot systems[J]. Front. Phys. , 2022, 17(6): 61504.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-022-1178-x
https://academic.hep.com.cn/fop/EN/Y2022/V17/I6/61504

Fig.1 Schematic of a system consisting of two DQDs and TLR.

L

denotes the length of the TLR. The two DQDs are labeled as 1 and 2, which positions are located at

L / 4

and

3 L / 4

of the TLR respectively, with the external potentials

Δ 0 j

. The distance between the two quantum dots is

r

, which is same as that from one of quantum dots to the nearest TLR.

Fig.2 The entropic uncertainty

U

with respect to time

t

in the case of the different eigenvalues

α

of the coherent state, detuning

δ

, frequency

ω

and the coupling constant

g

. (a)

α = 1

(red solid line),

α = 2

(black solid line),

α = 3

(green solid line), with

ω = 1

δ = 1

and

g = 1

. (b)

δ = 0.5

(red solid line),

δ = 1

(black solid line),

δ = 1.5

(green solid line), with

ω = 1

α = 1

g = 1

. (c)

ω = 0

(red solid line),

ω = 2

(black solid line),

ω = 5

(green solid line), with

δ = 1

α = 1

g = 1

. (d)

g = 0.7

(red solid line),

g = 1

(black solid line),

g = 1.3

(green solid line) with

ω = 1

δ = 1

α = 1

. And

p = 0.5

is set for all plotted.

Fig.3 The lower bound (

U R

) of the entropic uncertainty and quantum discord (QD) as a function of time

t

. The solid lines represent

U R

, and the dashed lines represent QD. (a)

U R

and QD vs. time

t

for

ω = 1

δ = 1

and

g = 1

. (b)

U R

and QD vs. time

t

for

ω = 1

α = 1

and

g = 1

. (c)

U R

and QD vs. time

t

for

δ = 1

α = 1

and

g = 1

. (d)

U R

and QD vs. time

t

for

ω = 1

δ = 1

and

α = 1

. All results are plotted with

p = 0.5

Fig.4 The entropic uncertainty

U

with respect to time

t

in the case of the different eigenvalues

α

of the coherent state, detuning

δ

, frequency

ω

and the coupling constant

g

. (a)

α = 1

(red solid line),

α = 2

(black solid line),

α = 3

(green solid line), with

ω = 1

δ = 1

and

g = 1

. (b)

δ = 0.5

(red solid line),

δ = 1

(black solid line),

δ = 1.5

(green solid line), with

ω = 1

α = 1

g = 1

. (c)

ω = 0

(red solid line),

ω = 2

(black solid line),

ω = 5

(green solid line), with

δ = 1

α = 1

g = 1

. (d)

g = 0.7

(red solid line),

g = 1

(black solid line),

g = 1.3

(green solid line), with

ω = 1

δ = 1

α = 1

p = 0.5

is set for all plotted.

Fig.5 The lower bound (

U R

) of the entropic uncertainty and quantum discord (QD) as a function of time

t

. The solid lines represent

U R

, and the dashed lines represent QD. (a)

U R

and QD vs. time

t

for

ω = 1

δ = 1

and

g = 1

. (b)

U R

and QD vs. time

t

for

ω = 1

α = 1

and

g = 1

. (c)

U R

and QD vs. time

t

for

δ = 1

α = 1

and

g = 1

. (d)

U R

and QD vs. time

t

for

ω = 1

δ = 1

and

α = 1

. All results are plotted with

p = 0.5

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