Quantum coherence of two-qubit over quantum channels with memory

Using the axiomatic definition of the quantum coherence measure, such as the $$l_{1}$$l1 norm and the relative entropy, we study the phenomena of two-qubit system quantum coherence through quantum channels where successive uses of the channels are memory. Different types of noisy channels with memory, such as amplitude damping, phase damping, and depolarizing channels effect on quantum coherence have been discussed in detail. The results show that quantum channels with memory can efficiently protect coherence from noisy channels. Particularly, as channels with perfect memory, quantum coherence is unaffected by the phase damping as well as depolarizing channels. Besides, we also investigate the cohering and decohering power of quantum channels with memory.

[1]  Gerardo Adesso,et al.  Frozen quantum coherence. , 2014, Physical review letters.

[2]  C. Macchiavello,et al.  Entanglement-enhanced information transmission over a quantum channel with correlated noise , 2001, quant-ph/0107052.

[3]  Eric Chitambar,et al.  Critical Examination of Incoherent Operations and a Physically Consistent Resource Theory of Quantum Coherence. , 2016, Physical review letters.

[4]  Vahid Karimipour,et al.  Cohering and decohering power of quantum channels , 2015, 1506.02304.

[5]  Florian Mintert,et al.  A quantitative theory of coherent delocalization , 2013, 1310.6962.

[6]  Xiaobao Liu,et al.  Protecting quantum coherence of two-level atoms from vacuum fluctuations of electromagnetic field , 2015, 1509.06832.

[7]  Gerardo Adesso,et al.  Robustness of Coherence: An Operational and Observable Measure of Quantum Coherence. , 2016, Physical review letters.

[8]  Giuliano Benenti,et al.  Quantum capacity of dephasing channels with memory , 2007 .

[9]  Davide Girolami,et al.  Observable measure of quantum coherence in finite dimensional systems. , 2014, Physical review letters.

[10]  Gerardo Adesso,et al.  Measuring Quantum Coherence with Entanglement. , 2015, Physical review letters.

[11]  Jianwei Xu,et al.  Quantifying coherence of Gaussian states , 2015, 1510.02916.

[12]  Hamidreza Mohammadi,et al.  Progress on Quantum Discord of Two-Qubit States: Optimization and Upper Bound , 2013, 1304.3914.

[13]  Arun Kumar Pati,et al.  Duality of quantum coherence and path distinguishability , 2015, 1503.02990.

[14]  Horodecki.  Information-theoretic aspects of inseparability of mixed states. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[15]  Xiaofei Qi,et al.  Coherence measures and optimal conversion for coherent states , 2015, Quantum Inf. Comput..

[16]  G. Karpat,et al.  Quantum coherence and uncertainty in the anisotropic XY chain , 2014, 1404.6427.

[17]  M. Plenio,et al.  Quantifying coherence. , 2013, Physical review letters.

[18]  Artur Ekert,et al.  Witnessing quantum coherence in the presence of noise , 2013, 1312.5724.

[19]  Heng Fan,et al.  Fidelity and trace-norm distances for quantifying coherence , 2014, 1410.8327.

[20]  C. Macchiavello,et al.  Transition behavior in the channel capacity of two-quibit channels with memory , 2004 .

[21]  A. Winter,et al.  Operational Resource Theory of Coherence. , 2015, Physical review letters.

[22]  Xueyuan Hu.  Channels that do not generate coherence , 2016 .

[23]  H. Fan,et al.  Maximally coherent states and coherence-preserving operations , 2015, 1511.02576.

[24]  Kaifeng Bu,et al.  Coherence-breaking channels and coherence sudden death , 2016 .

[25]  Chi-Kwong Li,et al.  Quantifying the coherence of pure quantum states , 2016, 1601.06269.

[26]  Andrew Skeen,et al.  Time-correlated quantum amplitude-damping channel , 2003 .

[27]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[28]  Maira Amezcua,et al.  Quantum Optics , 2012 .

[29]  Alexander N. Korotkov,et al.  Decoherence suppression by quantum measurement reversal , 2010 .

[30]  Maciej Lewenstein,et al.  Trace distance measure of coherence , 2015, ArXiv.

[31]  Haozhen Situ,et al.  Dynamics of relative entropy of coherence under Markovian channels , 2016, Quantum Inf. Process..

[32]  Xiongfeng Ma,et al.  Intrinsic randomness as a measure of quantum coherence , 2015, 1505.04032.

[33]  G. Gour,et al.  Comparison of incoherent operations and measures of coherence , 2016 .

[34]  J. Åberg.  Quantifying Superposition , 2006, quant-ph/0612146.

[35]  Sk Sazim,et al.  Quantum coherence sets the quantum speed limit for mixed states , 2015, 1506.03199.