Pub Date : 2022-11-30DOI: 10.1142/s0219749923500156
Ce Wang
In this paper, we present an abstract model of continuous-time quantum walk (CTQW) based on Bernoulli functionals and show that the model has perfect state transfer (PST), among others. Let $mathfrak{h}$ be the space of square integrable complex-valued Bernoulli functionals, which is infinitely dimensional. First, we construct on a given subspace $mathfrak{h}_L subset mathfrak{h}$ a self-adjoint operator $Delta_L$ via the canonical unitary involutions on $mathfrak{h}$, and by analyzing its spectral structure we find out all its eigenvalues. Then, we introduce an abstract model of CTQW with $mathfrak{h}_L$ as its state space, which is governed by the Schr"{o}dinger equation with $Delta_L$ as the Hamiltonian. We define the time-average probability distribution of the model, obtain an explicit expression of the distribution, and, especially, we find the distribution admits a symmetry property. We also justify the model by offering a graph-theoretic interpretation to the operator $Delta_L$ as well as to the model itself. Finally, we prove that the model has PST at time $t=frac{pi}{2}$. Some other interesting results are also proven of the model.
{"title":"Abstract Model of Continuous-Time Quantum Walk Based on Bernoulli Functionals and Perfect State Transfer","authors":"Ce Wang","doi":"10.1142/s0219749923500156","DOIUrl":"https://doi.org/10.1142/s0219749923500156","url":null,"abstract":"In this paper, we present an abstract model of continuous-time quantum walk (CTQW) based on Bernoulli functionals and show that the model has perfect state transfer (PST), among others. Let $mathfrak{h}$ be the space of square integrable complex-valued Bernoulli functionals, which is infinitely dimensional. First, we construct on a given subspace $mathfrak{h}_L subset mathfrak{h}$ a self-adjoint operator $Delta_L$ via the canonical unitary involutions on $mathfrak{h}$, and by analyzing its spectral structure we find out all its eigenvalues. Then, we introduce an abstract model of CTQW with $mathfrak{h}_L$ as its state space, which is governed by the Schr\"{o}dinger equation with $Delta_L$ as the Hamiltonian. We define the time-average probability distribution of the model, obtain an explicit expression of the distribution, and, especially, we find the distribution admits a symmetry property. We also justify the model by offering a graph-theoretic interpretation to the operator $Delta_L$ as well as to the model itself. Finally, we prove that the model has PST at time $t=frac{pi}{2}$. Some other interesting results are also proven of the model.","PeriodicalId":51058,"journal":{"name":"International Journal of Quantum Information","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41290661","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-21DOI: 10.1142/S0219749923400026
Alessio Morea, Michele N. Notarnicola, S. Olivares
The task of preserving entanglement against noises is of crucial importance for both quantum communication and quantum information transfer. To this aim, quantum error correction (QEC) codes may be employed to compensate, at least partially, the detriments induced by environmental noise that can be modelled as a bit-flip or a phase-flip error channel. In this paper we investigate the effects of the simple three-qubit QEC codes to restore entanglement and nonlocality in a two-qubit system and consider two practical applications: superdense coding and quantum teleportation. Though the considered three-qubit QEC codes are known to perfectly work in the presence of very small noise, we show that they can avoid the sudden death of entanglement and improve the performance of the addressed protocols also for larger noise amplitudes.
{"title":"Entanglement recovery in noisy binary quantum information protocols via three-qubit quantum error correction codes","authors":"Alessio Morea, Michele N. Notarnicola, S. Olivares","doi":"10.1142/S0219749923400026","DOIUrl":"https://doi.org/10.1142/S0219749923400026","url":null,"abstract":"The task of preserving entanglement against noises is of crucial importance for both quantum communication and quantum information transfer. To this aim, quantum error correction (QEC) codes may be employed to compensate, at least partially, the detriments induced by environmental noise that can be modelled as a bit-flip or a phase-flip error channel. In this paper we investigate the effects of the simple three-qubit QEC codes to restore entanglement and nonlocality in a two-qubit system and consider two practical applications: superdense coding and quantum teleportation. Though the considered three-qubit QEC codes are known to perfectly work in the presence of very small noise, we show that they can avoid the sudden death of entanglement and improve the performance of the addressed protocols also for larger noise amplitudes.","PeriodicalId":51058,"journal":{"name":"International Journal of Quantum Information","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49250374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-15DOI: 10.1142/S0219749923500284
S. Hasibul, Hassan Chowdhury, Talal Ahmed Chowdhury, S. Nasri, Omar Ibna Nazim, S. Saad
Quantum simulation has become a promising avenue of research that allows one to simulate and gain insight into the models of High Energy Physics whose experimental realizations are either complicated or inaccessible with current technology. We demonstrate the quantum simulation of such a model, a quantum mechanical system with spatial noncommutativity, which is inspired by the works in Noncommutative Geometry and Noncommutative Field theory for a universal quantum computer. We use the novel group theoretical formalism to map the Hamiltonian of such a noncommutative quantum system into the ordinary quantum mechanical Hamiltonian and then carry out the quantum simulation using the Trotter-Suzuki product formula. Furthermore, we distinguish the impact of the noncommutativity parameter on the quantum simulation, especially on the Trotter error, and point out how its sizable value affects the simulation.
{"title":"Quantum simulation of quantum mechanical system with spatial noncommutativity","authors":"S. Hasibul, Hassan Chowdhury, Talal Ahmed Chowdhury, S. Nasri, Omar Ibna Nazim, S. Saad","doi":"10.1142/S0219749923500284","DOIUrl":"https://doi.org/10.1142/S0219749923500284","url":null,"abstract":"Quantum simulation has become a promising avenue of research that allows one to simulate and gain insight into the models of High Energy Physics whose experimental realizations are either complicated or inaccessible with current technology. We demonstrate the quantum simulation of such a model, a quantum mechanical system with spatial noncommutativity, which is inspired by the works in Noncommutative Geometry and Noncommutative Field theory for a universal quantum computer. We use the novel group theoretical formalism to map the Hamiltonian of such a noncommutative quantum system into the ordinary quantum mechanical Hamiltonian and then carry out the quantum simulation using the Trotter-Suzuki product formula. Furthermore, we distinguish the impact of the noncommutativity parameter on the quantum simulation, especially on the Trotter error, and point out how its sizable value affects the simulation.","PeriodicalId":51058,"journal":{"name":"International Journal of Quantum Information","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46382222","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-04DOI: 10.1142/s0219749922500265
A. N. Khedr, M. Tammam, M. Abdel-Aty
We introduce a new framework for quantum two-spin correlations based on a quantum skew information quantity and long-negativity. The quantum correlations for an anisotropic two-qubit Heisenberg [Formula: see text] model are affected by physical parameters such as intrinsic decoherence, Werner states and time-dependent magnetic fields. In particular, the joint effects of Werner states, magnetic fields and anisotropic parameters on quantum correlation robustness are investigated in the presence of intrinsic decoherence. For an initially uncorrelated state, robust entanglement is generated while skew information between the two quantum bits no longer exists. It is shown that the magnetic field makes the system strongly correlated with incredibly significant steady-state values in uncorrelated states. The phenomenon of sudden death and sudden birth appear during the evolution process of initial conditions. Finally, if the system starts from a mixed state or a Werner state, the magnetic field does not play a significant role in the monotonically decreasing correlations. By leveraging our framework, one can create a kind of stability between the uncertainty-induced quantum nonlocality and the local quantum uncertainty correlations.
{"title":"Correlations dynamics of two-spin XYZ Heisenberg model via negativity and skew information","authors":"A. N. Khedr, M. Tammam, M. Abdel-Aty","doi":"10.1142/s0219749922500265","DOIUrl":"https://doi.org/10.1142/s0219749922500265","url":null,"abstract":"We introduce a new framework for quantum two-spin correlations based on a quantum skew information quantity and long-negativity. The quantum correlations for an anisotropic two-qubit Heisenberg [Formula: see text] model are affected by physical parameters such as intrinsic decoherence, Werner states and time-dependent magnetic fields. In particular, the joint effects of Werner states, magnetic fields and anisotropic parameters on quantum correlation robustness are investigated in the presence of intrinsic decoherence. For an initially uncorrelated state, robust entanglement is generated while skew information between the two quantum bits no longer exists. It is shown that the magnetic field makes the system strongly correlated with incredibly significant steady-state values in uncorrelated states. The phenomenon of sudden death and sudden birth appear during the evolution process of initial conditions. Finally, if the system starts from a mixed state or a Werner state, the magnetic field does not play a significant role in the monotonically decreasing correlations. By leveraging our framework, one can create a kind of stability between the uncertainty-induced quantum nonlocality and the local quantum uncertainty correlations.","PeriodicalId":51058,"journal":{"name":"International Journal of Quantum Information","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46438668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-03DOI: 10.1142/S0219749923400038
M. Genovese
Quantum non locality, as described by EPR paradox, represents one of the mysteries at the very foundations of quantum mechanics. Here we suggest to investigate if it can be understood by considering extra dimensions.
{"title":"Can quantum non-locality be connected to extra-dimensions?","authors":"M. Genovese","doi":"10.1142/S0219749923400038","DOIUrl":"https://doi.org/10.1142/S0219749923400038","url":null,"abstract":"Quantum non locality, as described by EPR paradox, represents one of the mysteries at the very foundations of quantum mechanics. Here we suggest to investigate if it can be understood by considering extra dimensions.","PeriodicalId":51058,"journal":{"name":"International Journal of Quantum Information","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48517407","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-02DOI: 10.1142/S0219749923500119
S. Mousavi
Some aspects of quantum damped harmonic oscillator (DHO) obeying a Markovian master equation are considered in the absence of thermal noise. The continuity equation is derived and Bohmian trajectories are constructed. As a solution of the master equation, we take a single coherent state and compute analytically the relative entropy of coherence, $C_r$, in the energy, position and momentum bases. Although $C_r$ is constant in both the position and the momentum bases, it is a decreasing function of time in the energy basis becoming zero at long times, revealing its role as the preferred basis. Then, quantum coherence is computed for a superposition of two coherent states, a cat state, and also a superposition of two cat states in the energy basis as a function of separation, in the complex plane, between the two superposed states. It is seen that the quantum coherence increases with this separation. Furthermore, quantum coherence of superposition is compared to that of decomposed states in the superposition. Finally, considering a system of two non-interacting DHOs, the effect of quantum statistics is studied on the coherence of reduced single-particle states, the joint detection probability and the mean square separation of particles. Our computations show that the single-particle coherence for antisymmetric states is always less than that of symmetric ones. Furthermore, boson anti-bunching and fermion bunching is seen in this open system. This behavior of bosons is the matter-wave analogue of photon anti-bunching seen in a modified Hanbury Brown-Twiss (HBT) interferometer.
{"title":"Identical damped harmonic oscillators described by coherent states","authors":"S. Mousavi","doi":"10.1142/S0219749923500119","DOIUrl":"https://doi.org/10.1142/S0219749923500119","url":null,"abstract":"Some aspects of quantum damped harmonic oscillator (DHO) obeying a Markovian master equation are considered in the absence of thermal noise. The continuity equation is derived and Bohmian trajectories are constructed. As a solution of the master equation, we take a single coherent state and compute analytically the relative entropy of coherence, $C_r$, in the energy, position and momentum bases. Although $C_r$ is constant in both the position and the momentum bases, it is a decreasing function of time in the energy basis becoming zero at long times, revealing its role as the preferred basis. Then, quantum coherence is computed for a superposition of two coherent states, a cat state, and also a superposition of two cat states in the energy basis as a function of separation, in the complex plane, between the two superposed states. It is seen that the quantum coherence increases with this separation. Furthermore, quantum coherence of superposition is compared to that of decomposed states in the superposition. Finally, considering a system of two non-interacting DHOs, the effect of quantum statistics is studied on the coherence of reduced single-particle states, the joint detection probability and the mean square separation of particles. Our computations show that the single-particle coherence for antisymmetric states is always less than that of symmetric ones. Furthermore, boson anti-bunching and fermion bunching is seen in this open system. This behavior of bosons is the matter-wave analogue of photon anti-bunching seen in a modified Hanbury Brown-Twiss (HBT) interferometer.","PeriodicalId":51058,"journal":{"name":"International Journal of Quantum Information","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42061126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-19DOI: 10.1142/s0219749922500241
Cheng-Han Pan, Jiaoyang Zhang, S. Cong, Sajede Harraz
{"title":"Quantum state tomography of multi-qubit systems—a comparative study","authors":"Cheng-Han Pan, Jiaoyang Zhang, S. Cong, Sajede Harraz","doi":"10.1142/s0219749922500241","DOIUrl":"https://doi.org/10.1142/s0219749922500241","url":null,"abstract":"","PeriodicalId":51058,"journal":{"name":"International Journal of Quantum Information","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48692697","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-15DOI: 10.1142/s0219749922500228
Xiao-Jing Lu, Zhikang Feng, Zheng-Yin Zhao, Ming Li, Zi-Liang Cai
{"title":"Generation of entangled states between two transmon qubits via invariant-based shortcuts with constant drivings","authors":"Xiao-Jing Lu, Zhikang Feng, Zheng-Yin Zhao, Ming Li, Zi-Liang Cai","doi":"10.1142/s0219749922500228","DOIUrl":"https://doi.org/10.1142/s0219749922500228","url":null,"abstract":"","PeriodicalId":51058,"journal":{"name":"International Journal of Quantum Information","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43773417","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-13DOI: 10.1142/s0219749922500204
Jaideep Mulherkar, Rishikant Rajdeepak, V. Sunitha
{"title":"Implementation of Quantum Hitting Times of Cubelike Graphs on IBM'S Qiskit Platform","authors":"Jaideep Mulherkar, Rishikant Rajdeepak, V. Sunitha","doi":"10.1142/s0219749922500204","DOIUrl":"https://doi.org/10.1142/s0219749922500204","url":null,"abstract":"","PeriodicalId":51058,"journal":{"name":"International Journal of Quantum Information","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41680125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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