Manipulating the measured uncertainty under Lee−Yang dephasing channels through local <inline-formula><math xmlns:mml=

doi:10.1007/s11467-023-1280-8

Front. Phys.

2023, Vol. 18

Issue (5) : 51302 https://doi.org/10.1007/s11467-023-1280-8

RESEARCH ARTICLE

Manipulating the measured uncertainty under Lee−Yang dephasing channels through local

P T

-symmetric operations

Ling-Yu Yao, Li-Juan Li, Xue-Ke Song, Liu Ye, Dong Wang(

)

School of Physics and Optoelectronic Engineering, Anhui University, Hefei 230601, China

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Abstract

Uncertainty relation lies at the heart of quantum physics, which is one of the fundamental characteristics of quantum mechanics. With the advent of quantum information theory, entropic uncertainty relation was proposed, which plays an important and irreplaceable role in quantum information science. In this work, we attempt to observe dynamics of entropic uncertainty in the presence of quantum memory under two different types of Lee−Yang dephasing channels. It is interesting to find that the dephasing channels have a negative effect on decreasing the uncertainty and the analogous partition function is anti-correlated with the uncertainty. In addition, we here propose an effective strategy to manipulate the uncertainty of interest of the subsystem by performing a parity-time symmetric ( $P T$ -symmetric) operation. It is worth noting that the uncertainty of measurement will be reduced to a certain extent by properly modulating the $P T$ -symmetric operations under the considered channels. In this sense, we argue that our explorations offer insight into dynamics of entropic uncertainty in typical Lee−Yang dephasing channels, and might be beneficial to quantum measurement estimation in practical quantum systems.

Keywords entropic uncertainty relation quantum correlation ${\color{[RGB]{12,108,100}}{{\cal {PT}}}} $-symmetric operation

Corresponding Author(s): Dong Wang

Issue Date: 17 April 2023

Cite this article:

Ling-Yu Yao,Li-Juan Li,Xue-Ke Song, et al. Manipulating the measured uncertainty under Lee−Yang dephasing channels through local

P T

-symmetric operations[J]. Front. Phys. , 2023, 18(5): 51302.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-023-1280-8
https://academic.hep.com.cn/fop/EN/Y2023/V18/I5/51302

Fig.1 Two different dephasing channels under a probe(s)-bath system. (a) N dephasing channels where probes are only respectively coupled to their own bath. (b) The dephasing channel where N probes are coupled to one bath together. The red circles mark probes and the blue circles mark bath spins.

Fig.2 QMA entropic uncertainty, the lower bounds and quantum discord (QD) as a function of the dephasing strength in the case of qubit

A

passing through the dephasing channel where probes are coupled to their own baths, and keep

B

as a quantum memory.

N

= 3 and

θ = π / 2

. Here, LHS denotes the left-hand side of Eq. (3), RHS denotes the right-hand side of the inequality, QD represents quantum discord of

A

and

B

Fig.3 The relationship between the Lee−Yang zeros, the entropic uncertainty and the lower bounds of the probes coupled to their own baths, LHS for the red line, RHS for the black line and the analogous partition function

P 2

for the blue line.

Fig.4 Entropic uncertainty with the change of

t

under the infinite temperature

(β = 0)

in the case of qubit

A

passing through the dephasing channel where probes are coupled to their own baths. (a) The number of the probes

N

= 3 and the twist angle

θ = π / 2

for the red line,

θ = π / 4

for the black line. (b)

N

= 3 for the red line,

N

= 5 for the blue line,

N

= 10 for the black line under

θ = π / 2

. The probes-bath coupling constant is

η = 0.01

Fig.5 Entropic uncertainty, the lower bounds and QD as a function of the dephasing strength in the case of qubit

A

passing through the dephasing channel where

N

probes are coupled to one bath together, and keep

B

as a quantum memory.

N

= 3 and

θ = π / 2

. Here, LHS denotes the left-hand side of Eq. (3), while RHS denotes the right-hand side of the inequality. QD represents quantum discord of

A

and

B

Fig.6 The relationship between the Lee−Yang zeros, entropic uncertainty and the lower bounds of the probes coupled to own bath together, LHS for the red line, RHS for the black line and the analogous partition function

P ′

for the blue line.

Fig.7 Entropic uncertainty with the change of

t

under the infinite temperature

(β = 0)

in the case of qubit

A

passing through the dephasing channel where probes are coupled to one bath together. (a)

N

= 3 and

θ = π / 2

for the red line,

θ = π / 4

for the black line. (b)

N

= 3 for the red line,

N

= 5 for the blue line,

N

= 10 for the black line under

θ = π / 2

. The probes-bath coupling constant is

η = 0.01

Fig.8 QMA entropic uncertainty under the local

P T

-symmetric operation with the change of

t

where probes are coupled to their own baths,

N

= 3 for the red line,

N

= 5 for the blue line,

N

= 10 for the black line. All plotted with

α = π 4

and

θ = π / 2

Fig.9 QMA entropic uncertainty under the local

P T

-symmetric operation with the change of

t

where probes are coupled to one bath together,

N

= 3 for the red line,

N

= 5 for the blue line,

N

= 10 for the black line. All plotted with

α = π 4

and

θ = π / 2

1	Heisenberg W.. Über den anschaulichen Inhalt der quantentheoretischen kinematik und mechanik. Eur. Phys. J. A, 1927, 43(3−4): 172 https://doi.org/10.1007/BF01397280
2	H. Kennard E.. Zur quantenmechanik einfacher bewegungstypen. Eur. Phys. J. A, 1927, 44(4−5): 326 https://doi.org/10.1007/BF01391200
3	P. Robertson H.. The uncertainty principle. Phys. Rev., 1929, 34(1): 163 https://doi.org/10.1103/PhysRev.34.163
4	Maassen H., B. M. Uffink J.. Generalized entropic uncertainty relations. Phys. Rev. Lett., 1988, 60(12): 1103 https://doi.org/10.1103/PhysRevLett.60.1103
5	Białynicki-Birula I., Mycielski J.. Uncertainty relations for information entropy in wave mechanics. Commun. Math. Phys., 1975, 44(2): 129 https://doi.org/10.1007/BF01608825
6	Deutsch D.. Uncertainty in quantum measurements. Phys. Rev. Lett., 1983, 50(9): 631 https://doi.org/10.1103/PhysRevLett.50.631
7	Kraus K.. Complementary observables and uncertainty relations. Phys. Rev. D, 1987, 35(10): 3070 https://doi.org/10.1103/PhysRevD.35.3070
8	M. Renes J., C. Boileau J.. Conjectured strong complementary information tradeoff. Phys. Rev. Lett., 2009, 103(2): 020402 https://doi.org/10.1103/PhysRevLett.103.020402
9	Berta M., Christandl M., Colbeck R., M. Renes J., Renner R.. The uncertainty principle in the presence of quantum memory. Nat. Phys., 2010, 6(9): 659 https://doi.org/10.1038/nphys1734
10	F. Li C., S. Xu J., Y. Xu X., Li K., C. Guo G.. Experimental investigation of the entanglement-assisted entropic uncertainty principle. Nat. Phys., 2011, 7(10): 752 https://doi.org/10.1038/nphys2047
11	J. Li L., Ming F., K. Song X., Ye L., Wang D.. Review on entropic uncertainty relations. Acta Physica Sinica, 2022, 71(7): 070302 https://doi.org/10.7498/aps.71.20212197
12	Tomamichel M., Renner R.. Uncertainty relation for smooth entropies. Phys. Rev. Lett., 2011, 106(11): 110506 https://doi.org/10.1103/PhysRevLett.106.110506
13	J. Coles P., Colbeck R., Yu L., Zwolak M.. Uncertainty relations from simple entropic properties. Phys. Rev. Lett., 2012, 108(21): 210405 https://doi.org/10.1103/PhysRevLett.108.210405
14	Zhang J., Zhang Y., S. Yu C.. Rényi entropy uncertainty relation for successive projective measurements. Quantum Inform. Process., 2015, 14(6): 2239 https://doi.org/10.1007/s11128-015-0950-z
15	Schneeloch J., J. Broadbent C., P. Walborn S., G. Cavalcanti E., C. Howell J.. Einstein−Podolsky−Rosen steering inequalities from entropic uncertainty relations. Phys. Rev. A, 2013, 87(6): 062103 https://doi.org/10.1103/PhysRevA.87.062103
16	L. Hu M., Fan H.. Quantum-memory-assisted entropic uncertainty principle, teleportation, and entanglement witness in structured reservoirs. Phys. Rev. A, 2012, 86(3): 032338 https://doi.org/10.1103/PhysRevA.86.032338
17	L. Hu M., Fan H.. Competition between quantum correlations in the quantum-memory-assisted entropic uncertainty relation. Phys. Rev. A, 2013, 87(2): 022314 https://doi.org/10.1103/PhysRevA.87.022314
18	L. Hu M., Fan H.. Upper bound and shareability of quantum discord based on entropic uncertainty relations. Phys. Rev. A, 2013, 88(1): 014105 https://doi.org/10.1103/PhysRevA.88.014105
19	K. Pati A., M. Wilde M., R. U. Devi A., K. Rajagopal A.. Quantum discord and classical correlation can tighten the uncertainty principle in the presence of quantum memory. Phys. Rev. A, 2012, 86(4): 042105 https://doi.org/10.1103/PhysRevA.86.042105
20	Zhang J., Zhang Y., S. Yu C.. Entropic uncertainty relation and information exclusion relation for multiple measurements in the presence of quantum memory. Sci. Rep., 2015, 5(1): 11701 https://doi.org/10.1038/srep11701
21	Liu S., Z. Mu L., Fan H.. Entropic uncertainty relations for multiple measurements. Phys. Rev. A, 2015, 91(4): 042133 https://doi.org/10.1103/PhysRevA.91.042133
22	Adabi F., Salimi S., Haseli S.. Tightening the entropic uncertainty bound in the presence of quantum memory. Phys. Rev. A, 2016, 93(6): 062123 https://doi.org/10.1103/PhysRevA.93.062123
23	Adabi F., Haseli S., Salimi S.. Reducing the entropic uncertainty lower bound in the presence of quantum memory via LOCC. Europhys. Lett., 2016, 115(6): 60004 https://doi.org/10.1209/0295-5075/115/60004
24	E. Rastegin A., Zyczkowski K.. Majorization entropic uncertainty relations for quantum operations. J. Phys. A Math. Theor., 2016, 49(35): 355301 https://doi.org/10.1088/1751-8113/49/35/355301
25	Wang D., J. Huang A., D. Hoehn R., Ming F., Y. Sun W., D. Shi J., Ye L., Kais S.. Entropic uncertainty relations for Markovian and non-Markovian processes under a structured bosonic reservoir. Sci. Rep., 2017, 7(1): 1066 https://doi.org/10.1038/s41598-017-01094-8
26	Baek K., Son W.. Unsharpness of generalized measurement and its effects in entropic uncertainty relations. Sci. Rep., 2016, 6(1): 30228 https://doi.org/10.1038/srep30228
27	Berta M., Wehner S., M. Wilde M.. Entropic uncertainty and measurement reversibility. New J. Phys., 2016, 18(7): 073004 https://doi.org/10.1088/1367-2630/18/7/073004
28	Y. Yang Y., Y. Sun W., N. Shi W., Ming F., Wang D., Ye L.. Dynamical characteristic of measurement uncertainty under Heisenberg spin models with Dzyaloshinskii–Moriya interactions. Front. Phys., 2019, 14(3): 31601 https://doi.org/10.1007/s11467-018-0880-1
29	Wang D., Ming F., L. Hu M., Ye L.. Quantum-memory-assisted entropic uncertainty relations. Ann. Phys., 2019, 531(10): 1900124 https://doi.org/10.1002/andp.201900124
30	Ming F., Wang D., G. Fan X., N. Shi W., Ye L., L. Chen J.. Improved tripartite uncertainty relation with quantum memory. Phys. Rev. A, 2020, 102(1): 012206 https://doi.org/10.1103/PhysRevA.102.012206
31	F. Xie B., Wang D., Ye L., L. Chen J.. Optimized entropic uncertainty relations for multiple measurements. Phys. Rev. A, 2021, 104(6): 062204 https://doi.org/10.1103/PhysRevA.104.062204
32	Wu L., Ye L., Wang D.. Tighter generalized entropic uncertainty relations in multipartite systems. Phys. Rev. A, 2022, 106(6): 062219 https://doi.org/10.1103/PhysRevA.106.062219
33	A. Wang Z.F. Xie B.Ming F.T. Wang Y.Wang D. Meng Y.H. Liu Z.S. Tang J.Ye L.F. Li C. C. Guo G.Kais S., Generalized multipartite entropic uncertainty relations: Theory and experiment, arXiv: 2207.12693 (2022)
34	Y. Cheng L., Ming F., Zhao F., Ye L., Wang D.. The uncertainty and quantum correlation of measurement in double quantum-dot systems. Front. Phys., 2022, 17(6): 61504 https://doi.org/10.1007/s11467-022-1178-x
35	J. Li L., Ming F., K. Song X., Ye L., Wang D.. Quantumness and entropic uncertainty in curved space-time. Eur. Phys. J. C, 2022, 82(8): 726 https://doi.org/10.1140/epjc/s10052-022-10687-1
36	L. Song M., J. Li L., K. Song X., Ye L., Wang D.. Environment-mediated entropic uncertainty in charging quantum batteries. Phys. Rev. E, 2022, 106(5): 054107 https://doi.org/10.1103/PhysRevE.106.054107
37	R. Pourkarimi M., Haddadi S.. Quantum-memory-assisted entropic uncertainty, teleportation, and quantum discord under decohering environments. Laser Phys. Lett., 2020, 17(2): 025206 https://doi.org/10.1088/1612-202X/ab6a15
38	Benabdallah F., U. Rahman A., Haddadi S., Daoud M.. Long-time protection of thermal correlations in a hybrid-spin system under random telegraph noise. Phys. Rev. E, 2022, 106(3): 034122 https://doi.org/10.1103/PhysRevE.106.034122
39	R. Pourkarimi M., Haseli S., Haddadi S., Hadipour M.. Scrutinizing entropic uncertainty and quantum discord in an open system under quantum critical environment. Laser Phys. Lett., 2022, 19(6): 065201 https://doi.org/10.1088/1612-202X/ac6c2f
40	Haddadi S., L. Hu M., Khedif Y., Dolatkhah H., R. Pourkarimi M., Daoud M.. Measurement uncertainty and dense coding in a two-qubit system: Combined effects of bosonic reservoir and dipole–dipole interaction. Results Phys., 2022, 32: 105041 https://doi.org/10.1016/j.rinp.2021.105041
41	Vallone G., G. Marangon D., Tomasin M., Villoresi P.. Quantum randomness certified by the uncertainty principle. Phys. Rev. A, 2014, 90(5): 052327 https://doi.org/10.1103/PhysRevA.90.052327
42	N. Yang C., D. Lee T.. Statistical theory of equations of state and phase transitions. I. Theory of condensation. Phys. Rev., 1952, 87(3): 404 https://doi.org/10.1103/PhysRev.87.404
43	D. Lee T., N. Yang C.. Statistical theory of equations of state and phase transitions. II. Lattice gas and Ising model. Phys. Rev., 1952, 87(3): 410 https://doi.org/10.1103/PhysRev.87.410
44	E. Fisher M.. Yang−Lee edge singularity and ϕ3 field theory. Phys. Rev. Lett., 1978, 40(25): 1610 https://doi.org/10.1103/PhysRevLett.40.1610
45	J. Kortman P., B. Griffiths R.. Density of zeros on the Lee−Yang circle for two Ising ferromagnets. Phys. Rev. Lett., 1971, 27(21): 1439 https://doi.org/10.1103/PhysRevLett.27.1439
46	B. Wei B., B. Liu R.. Lee−Yang zeros and critical times in decoherence of a probe spin coupled to a bath. Phys. Rev. Lett., 2012, 109(18): 185701 https://doi.org/10.1103/PhysRevLett.109.185701
47	Schlosshauer M.. Decoherence, the measurement problem, and interpretations of quantum mechanics. Rev. Mod. Phys., 2005, 76(4): 1267 https://doi.org/10.1103/RevModPhys.76.1267
48	B. Liu R., Yao W., J. Sham L.. Control of electron spin decoherence caused by electron–nuclear spin dynamics in a quantum dot. New J. Phys., 2007, 9(7): 226 https://doi.org/10.1088/1367-2630/9/7/226
49	Białynicki-Birula I.. Rényi entropy and the uncertainty relations. AIP Conf. Proc., 2007, 889: 52 https://doi.org/10.1063/1.2713446
50	G. Su Y., B. Liang H., G. Wang X.. Spin squeezing and concurrence under Lee−Yang dephasing channels. Phys. Rev. A, 2020, 102(5): 052423 https://doi.org/10.1103/PhysRevA.102.052423
51	Yin X., Ma J., Wang X., Nori F.. Spin squeezing under non-Markovian channels by the hierarchy equation method. Phys. Rev. A, 2012, 86(1): 012308 https://doi.org/10.1103/PhysRevA.86.012308
52	Wang X., C. Sanders B.. Spin squeezing and pairwise entanglement for symmetric multiqubit states. Phys. Rev. A, 2003, 68(1): 012101 https://doi.org/10.1103/PhysRevA.68.012101
53	L. Chen J., L. Ren C., B. Chen C., J. Ye X., K. Pati A.. Bell’s nonlocality can be detected by the violation of Einstein−Podolsky−Rosen steering inequality. Sci. Rep., 2016, 6(1): 39063 https://doi.org/10.1038/srep39063
54	Sun K., J. Ye X., S. Xu J., Y. Xu X., S. Tang J., C. Wu Y., L. Chen J., F. Li C., C. Guo G.. Experimental quantification of asymmetric Einstein−Podolsky−Rosen steering. Phys. Rev. Lett., 2016, 116(16): 160404 https://doi.org/10.1103/PhysRevLett.116.160404
55	R. Pourkarimi M., Haddadi S., Haseli S.. Exploration of entropic uncertainty bound in a symmetric multi-qubit system under noisy channels. Phys. Scr., 2020, 96(1): 015101 https://doi.org/10.1088/1402-4896/abc505
56	M. Bender C., Boettcher S.. Real spectra in non-Hermitian Hamiltonians having PT symmetry. Phys. Rev. Lett., 1998, 80(24): 5243 https://doi.org/10.1103/PhysRevLett.80.5243
57	M. Bender C., C. Brody D., F. Jones H.. Complex extension of quantum mechanics. Phys. Rev. Lett., 2002, 89(27): 270401 https://doi.org/10.1103/PhysRevLett.89.270401
58	Günther U., F. Samsonov B.. Naimark-dilated PT-symmetric brachistochrone. Phys. Rev. Lett., 2008, 101(23): 230404 https://doi.org/10.1103/PhysRevLett.101.230404

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