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Gravitationally induced entanglement between two quantum walkers

Himanshu Badhani, C. M. Chandrashekar

Published Jul 16, 2019• 1 citation
OpenAlex

Abstract

Quantum walk is a synonym for multi-path interference and spread of particle in superposition of position space. We study the effects of a quantum mechanical interaction modeled to mimic quantum mechanical gravitational interaction between the two states of the walkers. The study has been carried out to investigate the entanglement generation between the two quantum walkers that do not otherwise interact. We see that the states do in fact get entangled more and more as the quantum walks unfold. We investigate the dependence of this entanglement generation on the coin parameter of the walks. With the introduction of noise into the dynamics, we also show the sensitivity of entanglement entropy between the two walkers on the noise introduced in one of the walks.

Related papers

Gravitationally induced entanglement dynamics between two quantum walkers

Himanshu Badhani, C. M. Chandrashekar

Abstract Quantum walk is a synonym for multi-path interference and faster spread of a particle in a superposition of position space. We study the effects of a quantum mechanical interaction modeled to mimic quantum mechanical gravitational interaction between the two states of the walkers. The study has been carried out to investigate the entanglement generation between the two quantum walkers that do not otherwise interact. We see that the states do in fact get entangled more and more as the quantum walks unfold, and there is an interesting dependence of entanglement generation on the mass of the two particles performing the walks. With the introduction of noise into the dynamics, we also show the sensitivity of entanglement between the two walkers on the noise introduced in one of the walks. The signature of quantum effects due to gravitational interactions highlights the potential role of quantum systems in probing the nature of gravity.

arXiv:1907.06953•The European Physical Journal C•May 1, 2021•3 citations

Quantum Walk-based Generation of Entanglement Between Two Walkers

Salvador Elías Venegas-Andraca, Sougato Bose

Quantum walks can be used either as tools for quantum algorithm development or as entanglement generators, potentially useful to test quantum hardware. We present a novel algorithm based on a discrete Hadamard quantum walk on a line with one coin and two walkers whose purpose is to generate entanglement between walkers. We provide several classical computer simulations of our quantum algorithm in which we show that, although the asymptotical amount of entanglement generated between walkers does not reach the highest degree of entanglement possible at each step for either coin measurement outcome, the entanglement ratio (entanglement generated/highest value of entanglement possible, for each step) tends to converge, and the actual convergence value depends on the coin initial state and on the coin measurement outcome. Furthermore, our numerical simulations show that, for the quantum walks used in our algorithm, the value towards which entanglement ratio converges also depends on the position probability distribution symmetry of a quantum walk computed with one single walker and the same coin initial state employed in the corresponding quantum walk with two walkers.

arXiv:0901.3946•Jan 26, 2009•12 citations

Diverse tunable dynamics of two quantum random walkers

Shrabanti Dhar, Khaleque, Abdul, Tushar Kanti Bose

Quantum walk research has mainly focused on evolutions due to repeated applications of time-independent unitary coin operators. However, the idea of controlling the single particle evolution using time-dependent unitary coins has still been a subject of multiple studies as it not only hosts interesting possibilities for quantum information processing but also opens a much richer array of phenomena including static and dynamic localizations. So far, such studies have been performed only for single quantum walkers. In case of multi-walker systems, time-dependent coins may generate measurable phenomena not described by the single-particle model, due to entanglement and interaction among the walkers. In this context, we present here a thorough numerical study of an one dimensional system of two quantum walkers exhibiting rich collective dynamics controlled by simple time-dependent unitary coins proposed in [Phys. Rev. A \textbf{80}, 042332(2009)] and [Phys. Rev. A \textbf{73},062304(2006)]. We study how the interplay of coin time-dependence, simple interaction schemes, entanglement and the relative phase between the coin states of the particles influences the evolution of the quantum walk. The results show that the system offers a rich variety of collective dynamical behavior while being controlled by time dependent coins. In particular, we find and characterize fascinating two-body localization phenomena with tunable quasiperiodic dynamics of correlations and entanglements which are quantities of quantum origin.

arXiv:1909.08527•Sep 17, 2019•3 citations

Long-time entanglement in the Quantum Walk

Gonzalo Abal, R. Donangelo, Hugo Fort

Abstract. The coin-position entanglement generated by the evolution operator of a discrete–time quantum walk is quantified, using the von Neumann entropy of the reduced density operator (entropy of entanglement). In the case of a single walker, the entropy of entanglement converges, in the long time limit, to a well defined value which depends on the initial state. Exact expressions are obtained for local and non-local initial conditions. We also discuss the asymptotic bi-partite entanglement generated by non-separable coin operations for two coherent quantum walkers. In this case, the entropy of entanglement is observed to increase logarithmically with time. 1.

•Nov 21, 2012•2 citations

Quantum Walks with Entangled Coins and Walkers in Superposition

Salvador Elías Venegas-Andraca

We introduce a generalization of quantum walks with entangled coins consisting of a model of discrete quantum walks with coin pairs under various degrees of entanglement and walkers in quantum superposition as initial states. We introduce novel position probability distributions that may be used for algorithm development based on quantum-mechanical phenomena. Also, we numerically show that the skewness of position probability distribution produced by using coin initial state with various degrees of entanglement cannot be easily inferred.

IEEE Globecom Workshops (GC Wkshps)•Dec 1, 2018•2 citations

Quantum walks with entangled coins

S E Venegas-Andraca, J L Ball, K Burnett +1 more

We present a mathematical formalism for the description of un- restricted quantum walks with entangled coins and one walker. The numerical behaviour of such walks is examined when using a Bell state as the initial coin state, with two different coin operators, two different shift operators, and one walker. We compare and contrast the performance of these quantum walks with that of a classical random walk consisting of one walker and two maximally correlated coins as well as quantum walks with coins sharing different degrees of entanglement. We illustrate that the behaviour of our walk with entangled coins can be very different in comparison to the usual quantum walk with a single coin. We also demonstrate that simply by changing the shift operator, we can generate widely different distributions. We also compare the behaviour of quantum walks with maximally entangled coins with that of quantum walks with non-entangled coins. Finally, we show that the use of different shift operators on two and three qubit coins leads to different position probability distributions in one- and two-dimensional graphs.

arXiv:quant-ph/0411151•New Journal of Physics•Oct 17, 2005•60 citations
Quantum walk is a synonym for multi-path interference and spread of particle in superposition of position space. We study the effects of a quantum mechanical interaction modeled to mimic quantum mechanical gravitational interaction between the two states of the walkers. The study has been carried out to investigate the entanglement generation between the two quantum walkers that do not otherwise interact. We see that the states do in fact get entangled more and more as the quantum walks unfold. We investigate the dependence of this entanglement generation on the coin parameter of the walks. With the introduction of noise into the dynamics, we also show the sensitivity of entanglement entropy between the two walkers on the noise introduced in one of the walks.
Abstract Quantum walk is a synonym for multi-path interference and faster spread of a particle in a superposition of position space. We study the effects of a quantum mechanical interaction modeled to mimic quantum mechanical gravitational interaction between the two states of the walkers. The study has been carried out to investigate the entanglement generation between the two quantum walkers that do not otherwise interact. We see that the states do in fact get entangled more and more as the quantum walks unfold, and there is an interesting dependence of entanglement generation on the mass of the two particles performing the walks. With the introduction of noise into the dynamics, we also show the sensitivity of entanglement between the two walkers on the noise introduced in one of the walks. The signature of quantum effects due to gravitational interactions highlights the potential role of quantum systems in probing the nature of gravity.
Quantum walks can be used either as tools for quantum algorithm development or as entanglement generators, potentially useful to test quantum hardware. We present a novel algorithm based on a discrete Hadamard quantum walk on a line with one coin and two walkers whose purpose is to generate entanglement between walkers. We provide several classical computer simulations of our quantum algorithm in which we show that, although the asymptotical amount of entanglement generated between walkers does not reach the highest degree of entanglement possible at each step for either coin measurement outcome, the entanglement ratio (entanglement generated/highest value of entanglement possible, for each step) tends to converge, and the actual convergence value depends on the coin initial state and on the coin measurement outcome. Furthermore, our numerical simulations show that, for the quantum walks used in our algorithm, the value towards which entanglement ratio converges also depends on the position probability distribution symmetry of a quantum walk computed with one single walker and the same coin initial state employed in the corresponding quantum walk with two walkers.
Quantum walk research has mainly focused on evolutions due to repeated applications of time-independent unitary coin operators. However, the idea of controlling the single particle evolution using time-dependent unitary coins has still been a subject of multiple studies as it not only hosts interesting possibilities for quantum information processing but also opens a much richer array of phenomena including static and dynamic localizations. So far, such studies have been performed only for single quantum walkers. In case of multi-walker systems, time-dependent coins may generate measurable phenomena not described by the single-particle model, due to entanglement and interaction among the walkers. In this context, we present here a thorough numerical study of an one dimensional system of two quantum walkers exhibiting rich collective dynamics controlled by simple time-dependent unitary coins proposed in [Phys. Rev. A \textbf{80}, 042332(2009)] and [Phys. Rev. A \textbf{73},062304(2006)]. We study how the interplay of coin time-dependence, simple interaction schemes, entanglement and the relative phase between the coin states of the particles influences the evolution of the quantum walk. The results show that the system offers a rich variety of collective dynamical behavior while being controlled by time dependent coins. In particular, we find and characterize fascinating two-body localization phenomena with tunable quasiperiodic dynamics of correlations and entanglements which are quantities of quantum origin.
Abstract. The coin-position entanglement generated by the evolution operator of a discrete–time quantum walk is quantified, using the von Neumann entropy of the reduced density operator (entropy of entanglement). In the case of a single walker, the entropy of entanglement converges, in the long time limit, to a well defined value which depends on the initial state. Exact expressions are obtained for local and non-local initial conditions. We also discuss the asymptotic bi-partite entanglement generated by non-separable coin operations for two coherent quantum walkers. In this case, the entropy of entanglement is observed to increase logarithmically with time. 1.
We introduce a generalization of quantum walks with entangled coins consisting of a model of discrete quantum walks with coin pairs under various degrees of entanglement and walkers in quantum superposition as initial states. We introduce novel position probability distributions that may be used for algorithm development based on quantum-mechanical phenomena. Also, we numerically show that the skewness of position probability distribution produced by using coin initial state with various degrees of entanglement cannot be easily inferred.
We present a mathematical formalism for the description of un- restricted quantum walks with entangled coins and one walker. The numerical behaviour of such walks is examined when using a Bell state as the initial coin state, with two different coin operators, two different shift operators, and one walker. We compare and contrast the performance of these quantum walks with that of a classical random walk consisting of one walker and two maximally correlated coins as well as quantum walks with coins sharing different degrees of entanglement. We illustrate that the behaviour of our walk with entangled coins can be very different in comparison to the usual quantum walk with a single coin. We also demonstrate that simply by changing the shift operator, we can generate widely different distributions. We also compare the behaviour of quantum walks with maximally entangled coins with that of quantum walks with non-entangled coins. Finally, we show that the use of different shift operators on two and three qubit coins leads to different position probability distributions in one- and two-dimensional graphs.