Shared quantum control via sharing operation on remote single qutrit

Two qubit-operation-sharing schemes (Zhang and Cheung in J. Phys. B 44:165508, 2011) are generalized to the qutrit ones. Operations to be shared are classified into three different classes in terms of different probabilities (i.e, 1/3, 2/3 and 1). For the latter two classes, ten and three restricted sets of operations are found out, respectively. Moreover, the two generalized schemes are amply compared from four aspects, namely, quantum and classical resource consumption, necessary-operation complexity, success probability and efficiency. It is found that the second scheme is overall more optimal than the first one as far as three restricted sets of operations are concerned. Moreover, the experimental feasibility of our schemes is confirmed with respect to the nowaday technique.

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

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

[3]  H. Weinfurter,et al.  Experimental quantum teleportation , 1997, Nature.

[4]  R. Cleve,et al.  HOW TO SHARE A QUANTUM SECRET , 1999, quant-ph/9901025.

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

[6]  H. Lo.  Classical-communication cost in distributed quantum-information processing: A generalization of quantum-communication complexity , 1999, quant-ph/9912009.

[7]  H. Briegel,et al.  Persistent entanglement in arrays of interacting particles. , 2000, Physical review letters.

[8]  London,et al.  Quantum Remote Control: Teleportation of Unitary Operations , 2000, quant-ph/0005061.

[9]  Jindong Zhou,et al.  Teleportation scheme of S-level quantum pure states by two-level Einstein-Podolsky-Rosen states , 2000, quant-ph/0004095.

[10]  S. Huelga,et al.  Remote control of restricted sets of operations: Teleportation of Angles , 2001, quant-ph/0107110.

[11]  M. Chekhova,et al.  Operationalistic orthogonality condition for single-mode biphotons (qutrits) , 2002, quant-ph/0305113.

[12]  B. Zeng,et al.  Remote-state preparation in higher dimension and the parallelizable manifold Sn-1 , 2001, quant-ph/0105088.

[13]  L. A. Krivitskii,et al.  Biphotons as three-level systems: Transformation and measurement , 2003 .

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

[15]  L. A. Krivitskii,et al.  Measurement of qutrits , 2002, quant-ph/0207096.

[16]  Fuguo Deng,et al.  Reply to ``Comment on `Secure direct communication with a quantum one-time-pad' '' , 2004, quant-ph/0405177.

[17]  M. Nielsen.  Optical quantum computation using cluster States. , 2004, Physical review letters.

[18]  W. Bowen,et al.  Tripartite quantum state sharing. , 2003, Physical review letters.

[19]  Z. Man,et al.  Secure direct bidirectional communication protocol using the Einstein-Podolsky-Rosen pair block , 2004, quant-ph/0403215.

[20]  Fuguo Deng,et al.  Quantum secure direct communication with high-dimension quantum superdense coding , 2005 .

[21]  Zhan-jun Zhang,et al.  Multiparty quantum secret sharing , 2004, quant-ph/0412203.

[22]  Yong-Sheng Zhang,et al.  Experimental demonstration of a simple method to engineer a single qutrit state with biphotons , 2005 .

[23]  Fuguo Deng,et al.  Improving the security of multiparty quantum secret sharing against Trojan horse attack , 2005, quant-ph/0506194.

[24]  Z. Man,et al.  Multiparty quantum secret sharing of classical messages based on entanglement swapping , 2004, quant-ph/0406103.

[25]  Shou Zhang,et al.  Secure direct communication based on secret transmitting order of particles , 2006, quant-ph/0601119.

[26]  M. Dušek,et al.  Optical implementation of the encoding of two qubits to a single qutrit , 2006, quant-ph/0603174.

[27]  He-Shan Song,et al.  Remote preparation of a qudit using maximally entangled states of qubits , 2006, quant-ph/0603036.

[28]  Deng Fu-Guo,et al.  Erratum: Improving the security of multiparty quantum secret sharing against Trojan horse attack [Phys. Rev. A 72, 044302 (2005)] , 2006 .

[29]  Yan Xia,et al.  Controlled quantum secure direct communication using a non-symmetric quantum channel with quantum superdense coding , 2007 .

[30]  Zhan-jun Zhang.  Comment on : Quantum direct communication with authentication , 2006, quant-ph/0604125.

[31]  S. Giampaolo,et al.  Characterization of separability and entanglement in (2×D) - and (3×D) -dimensional systems by single-qubit and single-qutrit unitary transformations , 2007, 0706.1561.

[32]  Yi-Min Liu,et al.  Multiparty Quantum Secret Sharing Scheme Of Classical Messages By Swapping Qudit-State Entanglement , 2007 .

[33]  H. Weinfurter,et al.  Experimental demonstration of four-party quantum secret sharing. , 2006, Physical review letters.

[34]  P. Panigrahi,et al.  Perfect teleportation, quantum-state sharing, and superdense coding through a genuinely entangled five-qubit state , 2007, 0708.3785.

[35]  M. Bourennane,et al.  Experimental quantum secret sharing using telecommunication fiber , 2008 .

[36]  P. Panigrahi,et al.  Quantum-information splitting using multipartite cluster states , 2008, 0802.0781.

[37]  Zhan-jun Zhang,et al.  Criterion for faithful teleportation with an arbitrary multiparticle channel , 2009, 0901.2784.

[38]  Prasanta K. Panigrahi,et al.  Splitting of quantum information using N-qubit linear cluster states , 2009, 0904.0563.

[39]  P. Panigrahi,et al.  Quantum teleportation and state sharing using a genuinely entangled six-qubit state , 2008, 0811.2576.

[40]  Armando Pérez.  Information encoding of a qubit into a multilevel environment , 2010 .

[41]  A. Zeilinger,et al.  Experimental non-classicality of an indivisible quantum system , 2011, Nature.

[42]  Zhan-jun Zhang,et al.  Shared quantum remote control: quantum operation sharing , 2011 .

[43]  Jie Song,et al.  Probabilistic joint remote preparation of a two-particle high-dimensional equatorial state , 2011 .

[44]  Chui-Ping Yang,et al.  Generation of Greenberger-Horne-Zeilinger entangled states of photons in multiple cavities via a superconducting qutrit or an atom through resonant interaction , 2012, 1202.2084.

[45]  Lin Chen,et al.  Qubit-qudit states with positive partial transpose , 2012, 1210.0111.

[46]  Prasanta K. Panigrahi,et al.  N-qubit quantum teleportation, information splitting and superdense coding through the composite GHZ–Bell channel , 2011, Quantum Inf. Process..

[47]  Yoon-Ho Kim,et al.  Experimental realization of an approximate transpose operation for qutrit systems using a structural physical approximation , 2012 .

[48]  Yimin Liu,et al.  Quantum operation sharing with symmetric and asymmetric W states , 2013, Quantum Inf. Process..

[49]  Liu Yimin,et al.  Remotely Sharing a Single-Qubit Operation with a Five-Qubit Genuine State , 2013 .

[50]  Yimin Liu,et al.  Deterministic single-qubit operation sharing with five-qubit cluster state , 2013, Quantum Inf. Process..

[51]  X. Yin,et al.  GENERALIZED THREE-PARTY QUBIT OPERATION SHARING , 2013 .

[52]  Fu-Guo Deng,et al.  Geometric measure of quantum discord for a two-parameter class of states in a qubit–qutrit system under various dissipative channels , 2012, Quantum Inf. Process..

[53]  Chui-Ping Yang,et al.  Generating entanglement between microwave photons and qubits in multiple cavities coupled by a superconducting qutrit , 2011, 1106.3237.