Entanglement concentration of microwave photons based on the Kerr effect in circuit QED

In recent years, superconducting qubits show great potential in quantum computation. Hence, microwave photons become very interesting qubits for quantum information processing assisted by superconducting quantum computation. Here, we present the first protocol for the entanglement concentration on microwave photons, resorting to the cross-Kerr effect in circuit quantum electrodynamics (QED). Two superconducting transmission line resonators (TLRs) coupled to superconducting molecule with the N-type level structure induce the effective cross-Kerr effect for realizing the quantum nondemolition (QND) measurement on microwave photons. With this device, we present a two-qubit polarization parity QND detector on the photon states of the superconducting TLRs, which can be used to concentrate efficiently the nonlocal non-maximally entangled states of microwave photons assisted by several linear microwave elements. This protocol has a high efficiency and it may be useful for solid-state quantum information processing assisted by microwave photons.

[1]  Frederick W Strauch,et al.  All-resonant control of superconducting resonators. , 2012, Physical review letters.

[2]  G. Long,et al.  General scheme for superdense coding between multiparties , 2001, quant-ph/0110112.

[3]  Luigi Frunzio,et al.  Realization of three-qubit quantum error correction with superconducting circuits , 2011, Nature.

[4]  S. Girvin,et al.  Charge-insensitive qubit design derived from the Cooper pair box , 2007, cond-mat/0703002.

[5]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[6]  Erik Lucero,et al.  Deterministic entanglement of photons in two superconducting microwave resonators. , 2010, Physical review letters.

[7]  Alexandre Blais,et al.  Quantum information processing with circuit quantum electrodynamics , 2007 .

[8]  Bao-Cang Ren,et al.  General hyperentanglement concentration for photon systems assisted by quantum-dot spins inside optical microcavities. , 2014, Optics express.

[9]  F. Nori,et al.  Superconducting Circuits and Quantum Information , 2005, quant-ph/0601121.

[10]  Marcus P. da Silva,et al.  Implementation of a Toffoli gate with superconducting circuits , 2011, Nature.

[11]  Fuguo Deng,et al.  Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block , 2003, quant-ph/0308173.

[12]  David P. DiVincenzo,et al.  Exploiting Kerr cross nonlinearity in circuit quantum electrodynamics for nondemolition measurements , 2009, 0906.2979.

[13]  S. Girvin,et al.  Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation , 2004, cond-mat/0402216.

[14]  V. Buzek,et al.  Quantum secret sharing , 1998, quant-ph/9806063.

[15]  Shi Chen,et al.  Cross-Kerr-effect induced by coupled Josephson qubits in circuit quantum electrodynamics , 2010, 1012.5404.

[16]  Fuguo Deng,et al.  One-step resonant controlled-phase gate on distant transmon qutrits in different 1D superconducting resonators , 2015, Scientific Reports.

[17]  Chongjun Jin,et al.  Incident-angle-insensitive and Polarization Independent Polarization Rotator References and Links , 2022 .

[18]  Charles H. Bennett,et al.  Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. , 1992, Physical review letters.

[19]  Analysis and design of a two-octave polarization rotator for microwave frequency , 1993 .

[20]  Shohini Ghose,et al.  Hyperconcentration for multipartite entanglement via linear optics , 2014, 1601.03755.

[21]  M Mirrahimi,et al.  Single-Photon-Resolved Cross-Kerr Interaction for Autonomous Stabilization of Photon-Number States. , 2015, Physical review letters.

[22]  Fuguo Deng,et al.  Faithful qubit transmission against collective noise without ancillary qubits , 2007, 0708.0068.

[23]  Jian-Wei Pan,et al.  Practical scheme for entanglement concentration , 2001, quant-ph/0104039.

[24]  Fu-Guo Deng,et al.  Fast universal quantum gates on microwave photons with all-resonance operations in circuit QED , 2014, Scientific Reports.

[25]  S. Girvin,et al.  Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics , 2004, Nature.

[26]  Lin Tian,et al.  Deterministic generation of entangled photons in superconducting resonator arrays. , 2010, Physical review letters.

[27]  Jason Twamley,et al.  Giant Kerr nonlinearities in circuit quantum electrodynamics. , 2009, Physical review letters.

[28]  S. Bose,et al.  PURIFICATION VIA ENTANGLEMENT SWAPPING AND CONSERVED ENTANGLEMENT , 1998, quant-ph/9812013.

[29]  Bao-Cang Ren,et al.  Highly efficient hyperentanglement concentration with two steps assisted by quantum swap gates , 2015, Scientific Reports.

[30]  S. Girvin,et al.  Observation of quantum state collapse and revival due to the single-photon Kerr effect , 2012, Nature.

[31]  Ru Zhang,et al.  One-step hyperentanglement purification and hyperdistillation with linear optics. , 2015, Optics express.

[32]  R. J. Schoelkopf,et al.  Resolving photon number states in a superconducting circuit , 2007, Nature.

[33]  Gui-Lu Long,et al.  Quantum secure direct communication , 2011 .

[34]  L Frunzio,et al.  Generating single microwave photons in a circuit. , 2007, Nature.

[35]  Chuan Wang,et al.  Nonlocal hyperconcentration on entangled photons using photonic module system , 2016 .

[36]  Holger Schmidt,et al.  Strongly Interacting Photons in a Nonlinear Cavity , 1997 .

[37]  Zhang Yong Entanglement purification and concentration of electron-spin entangled states using quantum-dot spins in optical microcavities , 2011 .

[38]  Fu-Guo Deng,et al.  Two-step hyperentanglement purification with the quantum-state-joining method , 2014, 1408.0048.

[39]  Fuguo Deng Optimal nonlocal multipartite entanglement concentration based on projection measurements , 2011, 1112.1355.

[40]  Xi-Han Li,et al.  Efficient quantum key distribution over a collective noise channel (6 pages) , 2008, 0808.0042.

[41]  Ekert,et al.  Quantum cryptography based on Bell's theorem. , 1991, Physical review letters.

[42]  Fuguo Deng,et al.  One-step deterministic polarization-entanglement purification using spatial entanglement , 2010, 1008.3509.

[43]  S. Girvin,et al.  Quantum non-demolition detection of single microwave photons in a circuit , 2010, 1003.2734.

[44]  L. DiCarlo,et al.  Demonstration of two-qubit algorithms with a superconducting quantum processor , 2009, Nature.

[45]  B. Zheng,et al.  Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs , 2012, 1202.2190.

[46]  G. Long,et al.  Theoretically efficient high-capacity quantum-key-distribution scheme , 2000, quant-ph/0012056.

[47]  Jens Siewert,et al.  Aspects of Qubit Dynamics in the Presence of Leakage , 2000 .

[48]  Qing Ai,et al.  Theory of degenerate three-wave mixing using circuit QED in solid-state circuits , 2011 .

[49]  Jens Koch,et al.  Coupling superconducting qubits via a cavity bus , 2007, Nature.

[50]  Fuguo Deng,et al.  Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics , 2008, 0806.0115.

[51]  D. Pozar Microwave Engineering , 1990 .

[52]  A. Wallraff,et al.  Fabrication and characterization of superconducting circuit QED devices for quantum computation , 2005, IEEE Transactions on Applied Superconductivity.

[53]  Charles H. Bennett,et al.  Purification of noisy entanglement and faithful teleportation via noisy channels. , 1995, Physical review letters.

[54]  R. Y. Chiao,et al.  Photonic crystal polarizers and polarizing beam splitters , 2003 .

[55]  Charles H. Bennett,et al.  Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. , 1993, Physical review letters.

[56]  T. Jiang,et al.  Manipulating electromagnetic wave polarizations by anisotropic metamaterials. , 2007, Physical review letters.

[57]  R. Laflamme,et al.  Robust quantum communication using a polarization-entangled photon pair. , 2004, Physical review letters.

[58]  Xihan Li Deterministic polarization-entanglement purification using spatial entanglement , 2010, 1010.5301.

[59]  M. Teich,et al.  Decoherence-free subspaces in quantum key distribution. , 2003, Physical review letters.

[60]  ChuanLiang Wang Efficient entanglement concentration for partially entangled electrons using a quantum-dot and microcavity coupled system , 2012 .

[61]  Fu-Guo Deng,et al.  Practical hyperentanglement concentration for two-photon four-qubit systems with linear optics , 2013, 1306.0050.

[62]  R. Laflamme,et al.  Robust polarization-based quantum key distribution over a collective-noise channel. , 2003, Physical review letters.

[63]  Fuguo Deng,et al.  Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement , 2010 .

[64]  Charles H. Bennett,et al.  Quantum cryptography without Bell's theorem. , 1992, Physical review letters.

[65]  Xi-Han Li,et al.  Efficient hyperconcentration of nonlocal multipartite entanglement via the cross-Kerr nonlinearity. , 2015, Optics express.

[66]  Io-Chun Hoi,et al.  Giant cross-Kerr effect for propagating microwaves induced by an artificial atom. , 2012, Physical review letters.

[67]  Shohini Ghose,et al.  Hyperentanglement concentration for time-bin and polarization hyperentangled photons , 2015, 1502.02891.

[68]  M. Koashi,et al.  Concentration and purification scheme for two partially entangled photon pairs , 2001, quant-ph/0101042.