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arXiv:2506.24066 · Annalen der Physik

Quantum State Transfer and Periodicity in Discrete‐Time Quantum Walks Under Non‐Markovian Dephasing Noise

Monika Rani, Supriyo Dutta, Subhashish Banerjee

Published Nov 21, 2025• 0 citations
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Abstract

ABSTRACT In quantum communication, quantum state transfer from one location to another in a quantum network plays a prominent role, where the impact of noise could be crucial. The idea of state transfer can be fruitfully associated with quantum walk on graphs. We investigate the consequences of non‐Markovian quantum noises on periodicity and state transfer induced by a discrete‐time quantum walk on graphs, governed by the Grover coin operator. Different bipartite graphs, such as the path graph, cycle graph, star graph, and complete bipartite graph, present periodicity and state transfer in a discrete‐time quantum walk depending on the topology of the graph. We investigate the effect of quantum non‐Markovian dephasing noises, particularly quantum non‐Markovian Random Telegraph Noise (RTN) and modified non‐Markovian Ornstein‐Uhlenbeck Noise (OUN) on state transfer and periodicity. We demonstrate how the RTN and OUN noises allow state transfer and periodicity for a finite number of steps in a quantum walk. Our investigation brings out the feasibility of state transfer in a noisy environment.

DOI
10.1002/andp.202500310

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ABSTRACT In quantum communication, quantum state transfer from one location to another in a quantum network plays a prominent role, where the impact of noise could be crucial. The idea of state transfer can be fruitfully associated with quantum walk on graphs. We investigate the consequences of non‐Markovian quantum noises on periodicity and state transfer induced by a discrete‐time quantum walk on graphs, governed by the Grover coin operator. Different bipartite graphs, such as the path graph, cycle graph, star graph, and complete bipartite graph, present periodicity and state transfer in a discrete‐time quantum walk depending on the topology of the graph. We investigate the effect of quantum non‐Markovian dephasing noises, particularly quantum non‐Markovian Random Telegraph Noise (RTN) and modified non‐Markovian Ornstein‐Uhlenbeck Noise (OUN) on state transfer and periodicity. We demonstrate how the RTN and OUN noises allow state transfer and periodicity for a finite number of steps in a quantum walk. Our investigation brings out the feasibility of state transfer in a noisy environment.
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In the case of the discrete time coined quantum walk the reduced dynamics of the coin shows non-Markovian recurrence features due to information back-flow from the position degree of freedom. Here we study how this non-Markovian behavior is modified in the presence of open system dynamics. In the process, we obtain useful insights into the nature of non-Markovian physics. In particular, we show that in the case of (non-Markovian) random telegraph noise (RTN), a further discernbile recurrence feature is present in the dynamics. Moreover, this feature is correlated with the localization of the walker. On the other hand, no additional recurruence feature appears for other non-Markovian types of noise (Ornstein-Uhlenbeck and Power Law noise). We propose a power spectral method for comparing the relative strengths of the non-Markovian component due to the external noise and that due to the internal position degree of freedom.
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Abstract. We systematically investigated perfect state transfer between antipodal nodes of discrete time quantum walks on variants of the cycles C4, C6 and C8 for three choices of coin operator. Perfect state transfer was found, in general, to be very rare, only being preserved for a very small number of ways of modifying the cycles. We observed that some of our useful modifications of C4 could be generalised to an arbitrary num-ber of nodes, and present three families of graphs which admit quantum walks with interesting dynamics either in the continuous time walk, or in the discrete time walk for appropriate selections of coin and initial conditions. These dynamics are either periodicity, perfect state trans-fer, or very high fidelity state transfer. These families are modifications of families known not to exhibit periodicity or perfect state transfer in general. The robustness of the dynamics is tested by varying the initial state, interpolating between structures and by adding decoherence. 1