arXiv subjects

Mostafa Annabestani

Publications and source records attributed to Mostafa Annabestani.

10 recordsLinked to original sources

arXiv2026

Self-Sifting quantum key distribution

In this paper, we introduce a novel two-way quantum key distribution (QKD) protocol in which the sender (Alice) and receiver (Bob) employ one qubit of a maximally entangled Bell state as the quantum channel for key exchange. The protocol incorporates a new security mechanism based on a scrambling operator. Unlike conventional two-way QKD protocols, all sifting operations and eavesdropper detection procedures are postponed until the completion of the quantum communication stage and are performed exclusively by Bob. Since the control mode is never publicly announced, attacks that rely on mode-dependent adaptations or attempt to remain hidden within the control mode are inherently prevented. Furthermore, the traveling qubit does not directly encode key information, substantially limiting the information that can be extracted from attacks targeting the quantum channel alone. An additional distinctive feature of the protocol is that rounds that would ordinarily be discarded can instead be utilized to detect the presence of an eavesdropper. We analyze a broad class of ancilla-based attacks, in which an eavesdropper couples an ancillary system to the transmitted qubit in an attempt to gain information about the key, and show that such attacks are detectable in their most general form.

quant-ph↗

arXiv2025

Improving quantum walk metrology with split-step quantum walk

A new estimation scheme based on the split-step quantum walk (SSQW) revealed that by just setting a single parameter, SSQW can potentially achieve quantum Crame\'r-Rao bound in multiparameter estimation. This parameter even does not involve the parameterization but the initial state and unlike ordinary Quantum walk (OQW) there is no necessity for an entangled initial states or even a parameter dependent initial state. The rigorous analytic equations derived in this study revealed that SSQW surpasses OQW in achievable precision of multiparameter estimation in almost all possible scenarios. Furthermore, in single parameter estimation, the extra parameter can be used to tune the dynamics of the walk in such a way to enhance the precision of the estimation through maximizing the elements of quantum Fisher information matrix. The results of this study indicate that SSQW can remarkably improve the estimation schemes through its rich topological properties.

quant-ph↗

arXiv2021

Multi-parameter quantum metrology with discrete-time quantum walks

We address multi-parameter quantum estimation for one-dimensional discrete-time quantum walks and its applications to quantum metrology. We use the quantum walker as a probe for unknown parameters encoded on its coin degrees of freedom. We find an analytic expression of the quantum Fisher information matrix for the most general coin operator, and show that only two out of the three coin parameters can be accessed. We also prove that the resulting two-parameter coin model is asymptotically classical i.e. the Uhlmann curvature vanishes. Finally, we apply our findings to relevant case studies, including the simultaneous estimation of charge and mass in the discretized Dirac model.

quant-ph↗

arXiv2019

Asymptotic Behavior and Limiting Distribution of Quantum Walk on Cycles with General U(2) Coin by Reduced Characteristic Matrix Method

We calculated reduced density characteristic matrix (RDCM) for quantum walk on cycles (QWC) to study asymptotic properties of the most general form of quantum walk on cycles with general $U(2)$ coin operator. As an example, entanglement temperature for general initial state has been calculated and compared to previous results. Also, we have modified RDCM to derive analytical expression for general form of limiting distribution (LD).

quant-ph↗

arXiv2019

Asymptotic reduced density matrix of discrete-time quantum walks

In this article we show that for any quantum walker with \textit{m}-dimensional coin subspace, we have $m^2\times m^2$ specific constant matrix $\mathcal{C}$ where it completely determines the asymptotic reduced density matrix of the walker. We show that for any initial state with $P_0$ projector, reduced density matrix, can be obtained by $Tr_1\left(P_0\otimes I\;\mathcal{C}\right)$ or equivalently $Tr_2\left(I\otimes P_0\;\mathcal{C}\right)$. It is worth to mention that characteristic matrix $\mathcal{C}$ is independent of the initial state and just depends on coin operator, so by finding this matrix for specific type of QW the long-time behavior of it, such as local state of the coin after a long time walking and asymptotic entanglement between coin and position will be completely known for any initial state. We have found the characteristic matrix $\mathcal{C}$ for general coin operator, $U\left(2\right)$, as well as exact form of this matrix for local initial state.

quant-ph↗

arXiv2017

Möbius Quantum Walk

By adding an extra Hilbert space to Hadamard Quantum Walk on Cycles (QWC), we presented a new type of QWCs called Möbius Quantum Walk (MQW). The new space configuration enables the particle to rotate around the axis of movement. We defined factor $α$ as the Möbius factor which is number of rotations per cycle. So by $α=0$ we have normal QWC, while $α\neq 0$ defines new type of QWC (namely Möbius Quantum Walk). Specially $α= \frac{1}{2}$ defines a structure similar to Möbius strip. We analytically investigated this new type of QW and found that by tuning the parameter $α$ we can reach uniform distribution for any number of nodes, while it is impossible for QWC. The effects of $α$ on limiting distribution have been investigated and an explicit formula for non-uniform cases has been derived as well.

quant-ph↗

arXiv2017

Analytical expression for variance of homogeneous-position quantum walk with decoherent position

We have derived an analytical expression for variance of homogeneous-position decoherent quantum walk (HPDQW) with general form of noise on its position, and have shown that, while the quadratic ($t^2$) term of variance never changes by position decoherency, the linear term ($t$) does and always increases the variance. We study the walker with ability to tunnel out to $d$ nearest neighbors as an example and compare our result with former studies. We also show that, although our expression have been derived for asymptotic case, the rapid decay of time-dependent terms cause the expressions to be correct with a good accuracy even after dozens of steps.

quant-ph↗

arXiv2010

Tunneling effects in a one-dimensional quantum walk

In this article we investigate the effects of shifting position decoherence, arisen from the tunneling effect in the experimental realization of the quantum walk, on the one-dimensional discreet time quantum walk. We show that in the regime of this type of noise the quantum behavior of the walker does not fade, in contrary to the coin decoherence for which the walker undergos the quantum-to-classical transition even for weak noise. Particularly, we show that the quadratic dependency of the variance on the time and also the coin-position entanglement, i.e. two important quantum aspects of the coherent quantum walk, are preserved in the presence of tunneling decoherence. Furthermore, we present an explicit expression for the probability distribution of decoherent one-dimensional quantum walk in terms of the corresponding coherent probabilities, and show that this type of decoherence smooths the probability distribution.

quant-ph↗

arXiv2009

Decoherence in one-dimensional Quantum Walk

In this paper we study decoherence in the quantum walk on the line. We generalize the method of decoherent coin quantum walk, introduced by Brun et al [Phys. Rev. A {\bf 67}, 32304 (2003)]. Our analytical expressions are applicable for all kinds of decoherence. As an example of the coin-position decoherence, we study the broken line quantum walk and compare our results with the numerical one. We also show that our analytical results reduce to the Brun formalism when only the coin is subjected to decoherence.

quant-ph↗

arXiv2009

Asymptotic entanglement in a two-dimensional quantum walk

The evolution operator of a discrete-time quantum walk involves a conditional shift in position space which entangles the coin and position degrees of freedom of the walker. After several steps, the coin-position entanglement (CPE) converges to a well defined value which depends on the initial state. In this work we provide an analytical method which allows for the exact calculation of the asymptotic reduced density operator and the corresponding CPE for a discrete-time quantum walk on a two-dimensional lattice. We use the von Neumann entropy of the reduced density operator as an entanglement measure. The method is applied to the case of a Hadamard walk for which the dependence of the resulting CPE on initial conditions is obtained. Initial states leading to maximum or minimum CPE are identified and the relation between the coin or position entanglement present in the initial state of the walker and the final level of CPE is discussed. The CPE obtained from separable initial states satisfies an additivity property in terms of CPE of the corresponding one-dimensional cases. Non-local initial conditions are also considered and we find that the extreme case of an initial uniform position distribution leads to the largest CPE variation.

quant-ph↗