Abstract
We propose a unified scheme to implement the optimal 1 → 3 economical phase-covariant quantum cloning and optimal 1 → 3 economical real state cloning with superconducting quantum interference devices (SQUIDs) in a cavity. During this process, no transfer of quantum information between the SQUIDs and cavity is required. The cavity field is only virtually excited. The scheme is insensitive to cavity decay. Therefore, the scheme can be experimentally realized in the range of current cavity QED techniques.
Similar content being viewed by others
References
Wang Y H, Song H S. Preparation of multi-atom specially entangled W-class state and splitting quantum information. Chin Sci Bull, 2009, 54(15): 2599–2605; Zhang Y J, **a Y J, Man Z X, et al. Simulation of the Ising model, memory for Bell states and generation of four-atom entangled states in cavity QED. Sci China Ser G-Phys Mech Astron, 2009, 52(5): 700–707
Wootters W K, Zurek W H. A single quantum cannot be cloned. Nature, 1882, 299: 802–803
Bruß D, DiVincenzo D P, Ekert A, et al. Optimal universal and state-dependent quantum cloning. Phys Rev A, 1998, 57: 2368–2378
Bruss D, Ekert A, Macchiavello C. Optimal universal quantum cloning and state estimation. Phys Rev Lett, 1998, 81: 2598–2601
Werner R F. Optimal cloning of pure states. Phys Rev A, 1998, 58: 1827–1832
Duan L M, Guo G C. Probabilistic cloning and identification of linearly independent quantum states. Phys Rev Lett, 1998, 80: 4999–5002
Duan L M, Guo G C. A probabilistic cloning machine for replicating two non-orthogonal states. Phys Lett A, 1998, 243: 261–264
Bužek V, Hillery M. Quantum copying: Beyond the no-cloning theorem. Phys Rev A, 1996, 54: 1844–1852
Bužek V, Hillery M, Werner R F. Optimal manipulations with qubits: Universal-NOT gate. Phys Rev A, 1999, 60: R2626–R2629
Han Y J, Zhang Y S, Guo G C. Bounds for state-dependent quantum cloning. Phys Rev A, 2002, 66: 052301-1–6
Durt T, Du J F. Characterization of low-cost one-to-two qubit cloning. Phys Rev A, 2004, 69: 062316-1–10
Zhang W H, Wu T, Ye L, et al. Optimal real state cloning in d dimensions. Phys Rev A, 2007, 75: 044303-1–4; Zhang W H, Ye L. Optimal asymmetric phase-covariant and real state cloning in d dimensions. New J Phys, 2007, 9: 318–328
Gisin N, Ribordy G, Tittel W, et al. Quantum cryptography. Rev Mod Phys, 2002, 74: 145–195
Zou X B, Dong Y L, Guo G C. Scheme for realizing ancilla-free 1 → M economic phase-covariant quantum cloning of qubits and qutrits. Phys Lett A, 2006, 360: 44–48
Zheng S B, Guo G C. Entangling and cloning machine with increasing robustness against decoherence as the number of qubits increases. Phys Rev A, 2005, 72: 064303-1–4
Zhang W H, Ye L. Scheme to implement general economical phase-covariant telecloning. Phys Lett A, 2006, 353: 130–137
Zhao Z, Zhang A N, Zhou X Q, et al. Experimental realization of optimal asymmetric cloning and telecloning via partial teleportation. Phys Rev Lett, 2005, 95: 030502-1–4
Chen H W, Zhou X Y, Suter D, et al. Experimental realization of 1 → 2 asymmetric phase-covariant quantum cloning. Phys Rev A, 2007, 75: 012317-1–5
Sabuncu M, Andersen U L, Leuchs G, et al. Experimental demonstration of continuous variable cloning with phase-conjugate inputs. Phys Rev Lett, 2007, 98: 170503-1–4
Sabuncu M, Leuchs G, Anderson U L, et al. Experimental continuous-variable cloning of partial quantum information. Phys Rev A, 2008, 78: 052312-1–5
Shao X Q, Wang H F, Chen L, et al. One-step implementation of the 1 → 3 orbital state quantum cloning machine via quantum Zeno dynamics. Phys Rev A, 2009, 80: 062323-1–7; Wang X W, Yang G J. Probabilistic ancilla-free phase-covariant telecloning of qudits with the optimal fidelity. Phys Rev A, 2009, 79: 064306-1–4; Hu J Z, Yu Z W, Wang X B. Quantum cloning machine of a state in a belt of Bloch sphere. Eur Phys J D, 2009, 51: 381–385
Makhlin Y, Schoen G, Shnirman A. Josephson-junction qubits with controlled couplings. Nature, 1999, 398: 305–306
Nakamura Y, Pashkin Y, Tsai J S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature, 1999, 398: 786–787
Rouse R, Han S, Lukens J E. Observation of resonant tunneling between macroscopically distinct quantum levels. Phys Rev Lett, 1995, 75: 1614–1617
van der Wal C H, ter Haar A C J, et al. Quantum superposition of macroscopic persistent-current states. Science, 2000, 290: 773–777
Han S, Rouse R, Lukens J E. Generation of a population inversion between quantum states of a macroscopic variable. Phys Rev Lett, 1996, 76: 3404–3407
Friedman J R, Patel V, Chen W, et al. Quantum superposition of distinct macroscopic states. Nature, 2000, 406: 43–45
Zhu S L, Wang Z D, Zanardi P. Geometric quantum computation and multiqubit entanglement with superconducting qubits inside a cavity. Phys Rev Lett, 2005, 94: 100502-1–4
Zhou Z, Chu S I, Han S. A three-level SQUID qubit Quantum computing with superconducting devices. Phys Rev B, 2002, 66: 054527-1–6
Kis Z, Paspalakis E. Arbitrary rotation and entanglement of flux SQUID qubits. Phys Rev B, 2004, 69: 024510-1–6
Yang C P, Chu S I, Han S. Possible realization of entanglement, logical gates, and quantum-information transfer with superconducting-quantum-interference-device qubits in cavity QED. Phys Rev A, 2003, 67: 042311-1–8
Yang C P, Han S. Arbitrary single-qubit operations without energy relaxation in a three-level SQUID qubit. Phys Lett A, 2004, 321: 273–279
Amin M H S, Smirnov A Y, van den Brink A M, et al. Josephson-phase qubit without tunneling. Phys Rev B, 2003, 67: 100508 (R)-1–4
Song K H, Zhou Z W, Guo G C. Quantum logic gate operation and entanglement with superconducting quantum interference devices in a cavity via a Raman transition. Phys Rev A, 2005, 71: 052310-1–4
Yu L B, Zhang W H, Ye L. Implementing an ancilla-free 1 → M economical phase-covariant quantum cloning machine with superconducting quantum-interference devices in cavity QED. Phys Rev A, 2007, 76: 034303-1–4
Fan H, Matsumoto K, Wang X B, et al. Quantum cloning machines for equatorial qubits. Phys Rev A, 2001, 65: 012304-1–7
Feng M. Quantum computing with trapped ions in an optical cavity via Raman transition. Phys Rev A, 2001, 66: 054303-1–4
Yang C P, Han S. n-qubit-controlled phase gate with superconducting quantum-interference devices coupled to a resonator. Phys Rev A, 2005, 72: 032311-1–8
Yang C P, Han S. Realization of an n-qubit controlled-U gate with superconducting quantum interference devices or atoms in cavity QED. Phys Rev A, 2006, 73: 032317-1–11
Song K H, **ang S H, Liu Q, et al. Quantum computation and W-state generation using superconducting flux qubits coupled to a cavity without geometric and dynamical manipulation. Phys Rev A, 2007, 75: 032347-1–5; Zhang P, Wang Z D, Sun J D, et al. Holonomic quantum computation using rf superconducting quantum interference devices coupled through a microwave cavity. Phys Rev A, 2005, 71: 042301-1–5
Yu Y, Han S, Chu X, et al. Coherent temporal oscillations of macroscopic quantum states in a Josephson junction. Science, 2002, 296: 889–892
Chiorescu I, Nakamura Y, Harmans C J P M, et al. Coherent quantum dynamics of a superconducting flux qubit. Science, 2003, 299: 1869–1871
Yu Y, Nakada D, Lee J C, et al. Energy relaxation time between macroscopic quantum levels in a superconducting persistent-current qubit. Phys Rev Lett, 2004, 92: 117904-1–4
Yang C P, Han S. Rotation gate for a three-level superconducting quantum interference device qubit with resonant interaction. Phys Rev A, 2006, 74: 044302-1–4
Liu Y X, Wei L F, Nori F, et al. Quantum tomography for solid-state qubits. Europhys Lett, 2004, 67: 874–880
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ye, L., Hu, G. & Li, A. Implementing two optimal economical quantum cloning with superconducting quantum interference devices in a cavity. Sci. China Phys. Mech. Astron. 54, 115–120 (2011). https://doi.org/10.1007/s11433-010-4116-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11433-010-4116-9