Detecting non-Markovianity via uncertainty relations

Maity, Ananda G.; Bhattacharya, Samyadeb; Majumdar, A. S.

doi:10.1088/1751-8121/ab7135

Cited by 16 publications

(17 citation statements)

References 86 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where ρ Choi is the Choi state corresponding to the system, and LB s represents the lower bound of the sum form uncertainty relation ΔA 2 + ΔB 2 ≥ LB s . Here we should mention that the uncertainty relation is calculated on the Choi state ρ Choi , and the introduction of the Choi state is presented in Appendix F. According to the discussion above, we have that the dynmics is non-Markovian when Q(A,B,ρ Choi ) < 0 65 . The evolutions of γ(t) and Q(A,B,ρ Choi ) are presented in Fig.…”

Section: Application In Non-markovianity Witnessmentioning

confidence: 94%

“…In this section, taking the dephasing channel as the illustration, we show that the uncertainty relation with more auxiliary operators can be used to witness the non-Markovian dynamics more effectively. Reference 65 showed that dynamics of a system is non-Markovian when the uncertainty relation for the Choi state corresponding to this system is violated. The uncertainty relation with tighter lower bound is violated more easily than the regular uncertainty relation, because the tighter lower bound is "closer" to the left-hand side of the uncertainty relation.…”

Section: Application In Non-markovianity Witnessmentioning

confidence: 99%

“…λ and γ 0 are two positive constants related to the reservoir 66 . γ(t) is the time-dependent dephasing rate determined by the spectral density of the reservoir 67 , and the dynamics of the system is non-Markovian when γ(t) < 0 65 .…”

Section: Application In Non-markovianity Witnessmentioning

confidence: 99%

“…(12), one has: . In the following, we assume that the elements in the set    { , , 65 on the basic vectors of the matrix space 66 A B is 65 : . Then, Eq.…”

Section: Appendix A: the Equality Based On The Second-order Origin Momentioning

confidence: 99%

See 3 more Smart Citations

Unified and Exact Framework for Variance-Based Uncertainty Relations

Zheng

Fan

et al. 2020

Sci Rep

View full text Add to dashboard Cite

We provide a unified and exact framework for the variance-based uncertainty relations. This unified framework not only recovers some well-known previous uncertainty relations, but also fixes the deficiencies of them. Utilizing the unified framework, we can construct the new uncertainty relations in both product and sum form for two and more incompatible observables with any tightness we require. Moreover, one can even construct uncertainty equalities to exactly express the uncertainty relation by the unified framework, and the framework is therefore exact in describing the uncertainty relation. Some applications have been provided to illustrate the importance of this unified and exact framework. Also, we show that the contradiction between uncertainty relation and non-Hermitian operator, i.e., most of uncertainty relations will be violated when applied to non-Hermitian operators, can be fixed by this unified and exact framework. Quantum uncertainty relations 1-3 , expressing the impossibility of the joint sharp preparation of the incompatible observables 4,5 , are the most fundamental differences between quantum and classical mechanics 6-9. The uncertainty relation has been widely used in the quantum information science 10,11 , such as quantum non-cloning theorem 12,13 , quantum cryptography 14-17 , entanglement detection 18-22 , quantum spins squeezing 23-26 , quantum metrology 27-29 , quantum synchronization 30,31 and mixedness detection 32,33. In general, the improvement in uncertainty relations will greatly promote the development of quantum information science 18,28,34-36. The variance-based uncertainty relations for two incompatible observables A and B can be divided into two forms: the product form ΔA 2 ΔB 2 ≥ LB p 2,3,5,37,38 and the sum form ΔA 2 + ΔB 2 ≥ LB s 39-42 , where LB p and LB s represent the lower bounds of the two forms uncertainty relations, and ΔQ 2 is the variance of Q (To make sure that the quantity measuring the uncertainty will be a real number, the variance is taken as 〈(Q − 〈Q〉) † (Q − 〈Q〉) for non-Hermitian operators. Here the 〈Q〉 represents the expected value of Q). The product form uncertainty relation cannot fully capture the concept of the incompatible observables, because it can be trivial; i.e., the lower bound LB p can be null even for incompatible observables 39,40,43,44. This deficiency is referred to as the triviality problem of the product form uncertainty relation. In order to fix the triviality problem, Maccone and Pati deduced a sum form uncertainty relation with a non-zero lower bound for incompatible observables 44 , firstly showing that the triviality problem can be addressed by the sum form uncertainty relation. Thus, the sum form uncertainty relations were considered to be stronger than the product form uncertainty relations, and since then, lots of effort has been made to investigate the uncertainty relation in the sum form 18,39,45-48. However, most of the sum form uncertainty relations depend on the orthogonal state to the state of the system, and thus are diffic...

show abstract

Section: Application In Non-markovianity Witnessmentioning

confidence: 94%

Section: Application In Non-markovianity Witnessmentioning

confidence: 99%

Section: Application In Non-markovianity Witnessmentioning

confidence: 99%

“…(12), one has: . In the following, we assume that the elements in the set    { , , 65 on the basic vectors of the matrix space 66 A B is 65 : . Then, Eq.…”

Section: Appendix A: the Equality Based On The Second-order Origin Momentioning

confidence: 99%

See 2 more Smart Citations

Unified and Exact Framework for Variance-Based Uncertainty Relations

Zheng

Fan

et al. 2020

Sci Rep

View full text Add to dashboard Cite

show abstract

“…Both the qualitative and quantitative analysis of quantum non-Markovianity is of fundamental importance in the theory of open quantum dynamics. Over the past decade, there has been numerous proposals for quantifing non-Markovianity based on CP divisibility [36,44] and non-Markovianity witness [10,36,39,40,[44][45][46][47][48][49][50][51][52][53][54][55][56]. One of the prominent non-Markovianity measures based on the composition of the dynamical map was introduced in [36], the so called RHP measure.…”

Section: Dynamics Of Non-markovianitymentioning

confidence: 99%

Revisiting the Quantum Open System Dynamics of Central Spin Model

Bhattacharya

Banerjee

2021

Quanta

Self Cite

View full text Add to dashboard Cite

In this work, we revisit the theory of open quantum systems from the perspective of fermionic baths. Specifically, we concentrate on the dynamics of a central spin half particle interacting with a spin bath. We have calculated the exact reduced dynamics of the central spin and constructed the Kraus operators in relation to that. Further, the exact Lindblad type canonical master equation corresponding to the reduced dynamics is constructed. We have also briefly touched upon the aspect of non-Markovianity from the backdrop of the reduced dynamics of the central spin.Quanta 2021; 10: 55–64.

show abstract

Detecting entanglement harnessing Lindblad structure

Chimalgi,

Bhattacharya,

Goswami

et al. 2023

Phys. Scr.

Self Cite

View full text Add to dashboard Cite

The problem of entanglement detection is a long standing problem in quantum information theory. One of the primary procedures of detecting entanglement is to ﬁnd the suitable positive but noncompletely positive maps. Here we try to give a generic prescription to construct a positive map that can be useful for such scenarios. We study a class of positive maps arising from Lindblad structures. We show that two famous positive maps viz. transposition and Choi map can be obtained as a special case of a class of positive maps having Lindblad structure. Generalizing the transposition map to a one parameter family we have used it to detect genuine multipartite entanglement. Finally being motivated by the negativity of entanglement, we have deﬁned a similar measure for genuine multipartite entanglement.

show abstract

Detecting non-Markovianity via uncertainty relations

Cited by 16 publications

References 86 publications

Unified and Exact Framework for Variance-Based Uncertainty Relations

Unified and Exact Framework for Variance-Based Uncertainty Relations

Revisiting the Quantum Open System Dynamics of Central Spin Model

Detecting entanglement harnessing Lindblad structure

Contact Info

Product

Resources

About