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Attainable and usable coherence in X states over Markovian and non-Markovian channels

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Abstract

The relations between the resource theoretic measures of quantum coherence are rigorously investigated for various Markovian and non-Markovian channels for the two-qubit X states with specific attention to the maximum and minimum attainable coherence and usefulness of these states in performing quantum teleportation in noisy environment. The investigation has revealed that under both dephasing and dissipative type noises the maximally entangled mixed states and Werner states lose their form and usefulness. However, maximally non-local mixed states (MNMSs) lose their identity in dissipative noise only. Thus, MNMSs are established to be useful in teleporting a qubit with fidelity greater than the classical limit in the presence of dephasing noise. MNMSs also remain useful for device independent quantum key distribution in this case as they still violate Bell’s inequality. In the presence of noise, coherence measured by relative entropy of coherence is found to fall faster than the same measured using \(l_1\) norm of coherence. Further, information back-flow from the environment to the system is observed over non-Markovian channels which leads to revival in coherence. Additionally, sequential interaction of two qubits with the same environment is found to result in correlated noise on both qubits, and coherence is observed to be frozen in this case under dephasing channel. Under the effect of Markovian and non-Markovian dephasing channels studied here, we observed that MNMSs have maximum relative coherence, i.e. they have the maximum amount of \(l_1\) norm of coherence among the states with the same amount of relative entropy of coherence. However, this feature is not visible in any X state evolving over dissipative channels.

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Data Availability Statement

Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

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Acknowledgements

AP and SM acknowledge the support from the QUEST scheme of Interdisciplinary Cyber Physical Systems (ICPS) program of the Department of Science and Technology (DST), India (Grant No.: DST/ICPS/QuST/Theme-1/2019/14). KT acknowledges GA ČR (Project No. 18-22102S) and support from ERDF/ESF project ‘Nanotechnologies for Future’ (CZ.02.1.01/0.0/0.0/16_019/0000754).

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  1. Jaypee Institute of Information Technology, A-10, Sector-62, Noida, Uttar Pradesh, 201309, India

    Sandeep Mishra & Anirban Pathak

  2. Joint Laboratory of Optics of Palacký University and Institute of Physics of CAS, Faculty of Science, Palacký University, 17. listopadu 12, 771 46, Olomouc, Czech Republic

    Kishore Thapliyal

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Mishra, S., Thapliyal, K. & Pathak, A. Attainable and usable coherence in X states over Markovian and non-Markovian channels. Quantum Inf Process 21, 70 (2022). https://doi.org/10.1007/s11128-021-03408-2

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