Deterministic generation of hybrid entangled states using quantum walks
Abstract: In recent times, hybrid entanglement (HE) between a qubit and a coherent state has demonstrated superior performance in various quantum information processing tasks, particularly in quantum key distribution. Despite its theoretical advantages, efficient generation of such states in the laboratory has been a challenge. Here, we introduce a deterministic and efficient approach for generating HE states using quantum walks. Our method achieves a remarkable fidelity of $99.9\%$ with just $20$ time steps in a one-dimensional split-step quantum walk. This represents a significant improvement over prior approaches for probabilistic generation of HE states with fidelity as low as $80\%$. Our scheme not only provides a robust solution to the generation of HE states but also highlights a unique advantage of quantum walks, thereby contributing to the advancement of this burgeoning field. Moreover, our scheme is experimentally feasible with the current technology.
- M. Horodecki, P. Horodecki, and R. Horodecki, Separability of mixed states: necessary and sufficient conditions, Phys. Lett. A 223, 1 (1996).
- R. Simon, Peres-Horodecki separability criterion for continuous variable systems, Phys. Rev. Lett. 84, 2726 (2000).
- A. K. Ekert, Quantum cryptography based on Bell’s theorem, Phys. Rev. Lett. 67, 661 (1991).
- J. Singh, K. Bharti, and Arvind, Quantum key distribution protocol based on contextuality monogamy, Phys. Rev. A 95, 062333 (2017).
- J. Singh and S. Bose, Non-Gaussian operations in measurement-device-independent quantum key distribution, Phys. Rev. A 104, 052605 (2021).
- H. Jeong, Using weak nonlinearity under decoherence for macroscopic entanglement generation and quantum computation, Phys. Rev. A 72, 034305 (2005).
- S. Lloyd and S. L. Braunstein, Quantum computation over continuous variables, Phys. Rev. Lett. 82, 1784 (1999).
- S. D. Bartlett and B. C. Sanders, Universal continuous-variable quantum computation: Requirement of optical nonlinearity for photon counting, Phys. Rev. A 65, 042304 (2002).
- S. Bose, V. Vedral, and P. L. Knight, Multiparticle generalization of entanglement swapping, Phys. Rev. A 57, 822 (1998).
- J. Singh and A. Cabello, Loophole-free Bell tests with randomly chosen subsets of measurement settings, arXiv arXiv: 2309.00442 (2023).
- S. Yang and S. Zhang, Loophole-free Bell test with multi-photon-subtracted two-mode squeezed state, Optik 231, 166261 (2021).
- S. U. Shringarpure and J. D. Franson, Generating entangled Schrödinger cat states using a number state and a beam splitter, Phys. Rev. A 102, 023719 (2020).
- J. Singh, R. S. Bhati, and Arvind, Revealing quantum contextuality using a single measurement device, Phys. Rev. A 107, 012201 (2023a).
- Z.-B. Chen, G. Hou, and Y.-D. Zhang, Quantum nonlocality and applications in quantum-information processing of hybrid entangled states, Phys. Rev. A 65, 032317 (2002).
- K. Park, S.-W. Lee, and H. Jeong, Quantum teleportation between particlelike and fieldlike qubits using hybrid entanglement under decoherence effects, Phys. Rev. A 86, 062301 (2012).
- H. Kwon and H. Jeong, Violation of the Bell–Clauser-Horne-Shimony-Holt inequality using imperfect photodetectors with optical hybrid states, Phys. Rev. A 88, 052127 (2013).
- S.-W. Lee and H. Jeong, Near-deterministic quantum teleportation and resource-efficient quantum computation using linear optics and hybrid qubits, Phys. Rev. A 87, 022326 (2013).
- S. Omkar, Y. S. Teo, and H. Jeong, Resource-efficient topological fault-tolerant quantum computation with hybrid entanglement of light, Phys. Rev. Lett. 125, 060501 (2020).
- S. Bose and H. Jeong, Quantum teleportation of hybrid qubits and single-photon qubits using Gaussian resources, Phys. Rev. A 105, 032434 (2022).
- M. He and R. Malaney, Teleportation of hybrid entangled states with continuous-variable entanglement, Sci. Rep. 12, 17169 (2022).
- Y.-B. Sheng, L. Zhou, and G.-L. Long, Hybrid entanglement purification for quantum repeaters, Phys. Rev. A 88, 022302 (2013).
- P. van Loock, Optical hybrid approaches to quantum information, Laser Photonics Rev. 5, 167 (2011).
- K. Nemoto and W. J. Munro, Nearly deterministic linear optical controlled-not gate, Phys. Rev. Lett. 93, 250502 (2004).
- W. J. Munro, K. Nemoto, and T. P. Spiller, Weak nonlinearities: a new route to optical quantum computation, New J. Phys. 7, 137 (2005).
- Y. Aharonov, L. Davidovich, and N. Zagury, Quantum random walks, Phys. Rev. A 48, 1687 (1993).
- J. Kempe, Quantum random walks: An introductory overview, Contemp. Phys. 44, 307 (2003).
- B. C. Travaglione and G. J. Milburn, Implementing the quantum random walk, Phys. Rev. A 65, 032310 (2002).
- A. Alberti and S. Wimberger, Quantum walk of a Bose-Einstein condensate in the Brillouin zone, Phys. Rev. A 96, 023620 (2017).
- R. Vieira, E. P. M. Amorim, and G. Rigolin, Dynamically disordered quantum walk as a maximal entanglement generator, Phys. Rev. Lett. 111, 180503 (2013).
- P. A. A. Yasir and C. M. Chandrashekar, Generation of hyperentangled states and two-dimensional quantum walks using j𝑗jitalic_j or q𝑞qitalic_q plates and polarization beam splitters, Phys. Rev. A 105, 012417 (2022).
- M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, 1997).
- S. E. Venegas-Andraca, Quantum walks: a comprehensive review, Quantum Inf. Process. 11, 1015 (2012).
- A. Ambainis, Quantum walks and their algorithmic applications, Int. J. Quantum Inf. 01, 507 (2003).
- A. M. Childs and J. Goldstone, Spatial search by quantum walk, Phys. Rev. A 70, 022314 (2004).
- N. Shenvi, J. Kempe, and K. B. Whaley, Quantum random-walk search algorithm, Phys. Rev. A 67, 052307 (2003).
- E. Agliari, A. Blumen, and O. Mülken, Quantum-walk approach to searching on fractal structures, Phys. Rev. A 82, 012305 (2010).
- A. M. Childs, Universal computation by quantum walk, Phys. Rev. Lett. 102, 180501 (2009).
- A. M. Childs, D. Gosset, and Z. Webb, Universal computation by multiparticle quantum walk, Science 339, 791 (2013).
- P. Kurzyński and A. Wójcik, Quantum walk as a generalized measuring device, Phys. Rev. Lett. 110, 200404 (2013).
- V. Kendon, Decoherence in quantum walks – a review, Math. Struct. Comput. Sci. 17, 1169–1220 (2007).
- E. Farhi and S. Gutmann, Quantum computation and decision trees, Phys. Rev. A 58, 915 (1998).
- A. Ambainis, J. Kempe, and A. Rivosh, Coins make quantum walks faster, in Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA ’05 (Society for Industrial and Applied Mathematics, USA, 2005) p. 1099–1108.
- M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge University Press, 2010).
- R. Jozsa, Fidelity for mixed quantum states, J. Mod. Opt. 41, 2315 (1994).
- R. Blatt, J. I. Cirac, and P. Zoller, Trapping states of motion with cold ions, Phys. Rev. A 52, 518 (1995).
- P. Carruthers and M. M. Nieto, Coherent states and the forced quantum oscillator, Am. J. Phys. 33, 537 (1965).
- D. W. Moore, A. A. Rakhubovsky, and R. Filip, Estimation of squeezing in a nonlinear quadrature of a mechanical oscillator, New J. Phys. 21, 113050 (2019).
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