Quantum replication at the Heisenberg limit

No process in nature can perfectly clone an arbitrary quantum state. But is it possible to engineer processes that replicate quantum information with vanishingly small error? Here we demonstrate the possibility of probabilistic super-replication phenomena where N equally prepared quantum clocks are transformed into a much larger number of M nearly perfect replicas, with an error that rapidly vanishes whenever M is small compared with N(2). The quadratic replication rate is the ultimate limit imposed by quantum mechanics to the proliferation of information and is fundamentally linked with the Heisenberg limit of quantum metrology.

[1]  Buzek,et al.  Quantum copying: Beyond the no-cloning theorem. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[2]  L. Davidovich,et al.  General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology , 2011, 1201.1693.

[3]  Jinyu Xie,et al.  Optimal design and quantum benchmarks for coherent state amplifiers. , 2013, Physical review letters.

[4]  Moore,et al.  Spin squeezing and reduced quantum noise in spectroscopy. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[5]  Joonwoo Bae,et al.  Asymptotic quantum cloning is state estimation. , 2006, Physical review letters.

[6]  J. Cirac,et al.  Improvement of frequency standards with quantum entanglement , 1997, quant-ph/9707014.

[7]  G. D’Ariano,et al.  Quantum information becomes classical when distributed to many users. , 2006, Physical review letters.

[8]  H. Yuen.  Quantum detection and estimation theory , 1978, Proceedings of the IEEE.

[9]  L. Ballentine,et al.  Probabilistic and Statistical Aspects of Quantum Theory , 1982 .

[10]  Vladimir B. Braginsky,et al.  Quantum Measurement , 1992 .

[11]  J. Fiurášek.  Optimal probabilistic estimation of quantum states , 2006, quant-ph/0606156.

[12]  John T. Lewis,et al.  An operational approach to quantum probability , 1970 .

[13]  K. Kraus.  General state changes in quantum theory , 1971 .

[14]  R. Filip,et al.  Noise-powered probabilistic concentration of phase information , 2010, 1005.3706.

[15]  William K. Wootters,et al.  Limited Holism and Real-Vector-Space Quantum Theory , 2010, 1005.4870.

[16]  I. Chuang,et al.  Quantum Computation and Quantum Information: Introduction to the Tenth Anniversary Edition , 2010 .

[17]  S. Lloyd,et al.  Quantum metrology. , 2005, Physical review letters.

[18]  Nicolas Cerf,et al.  Optical quantum cloning , 2006 .

[19]  Jacob F. Sherson,et al.  Quantum teleportation between light and matter , 2006, Nature.

[20]  M. Ozawa.  Quantum measuring processes of continuous observables , 1984 .

[21]  H. Everett.  "Relative State" Formulation of Quantum Mechanics , 1957 .

[22]  Zeilinger,et al.  Optimal quantum cloning via stimulated emission , 2000, Physical review letters.

[23]  V. Scarani,et al.  Quantum cloning , 2005, quant-ph/0511088.

[24]  S. Braunstein,et al.  Statistical distance and the geometry of quantum states. , 1994, Physical review letters.

[25]  N. Walk,et al.  Heralded noiseless linear amplification and distillation of entanglement , 2009, 0907.3638.

[26]  Ipe,et al.  Cloning of continuous quantum variables , 1999, Physical review letters.

[27]  Guang-Can Guo,et al.  A probabilistic cloning machine for replicating two non-orthogonal states , 1998 .

[28]  Peter W. Milonni,et al.  PHOTONS CANNOT ALWAYS BE REPLICATED , 1982 .

[29]  S. Lloyd,et al.  Advances in quantum metrology , 2011, 1102.2318.

[30]  Holland,et al.  Interferometric detection of optical phase shifts at the Heisenberg limit. , 1993, Physical review letters.

[31]  E Bagan,et al.  Quantum metrology assisted by abstention. , 2012, Physical review letters.

[32]  Geoff J. Pryde,et al.  Heralded noiseless amplification of a photon polarization qubit , 2012, Nature Physics.

[33]  S. Massar,et al.  Optimal Quantum Cloning Machines , 1997, quant-ph/9705046.

[34]  Cloning of spin-coherent states , 2003, quant-ph/0307061.

[35]  J. Fiurášek,et al.  A high-fidelity noiseless amplifier for quantum light states , 2010, 1004.3399.

[36]  Masahito Hayashi,et al.  Comparison Between the Cramer-Rao and the Mini-max Approaches in Quantum Channel Estimation , 2010, 1003.4575.

[37]  Hiroshi Nagaoka,et al.  Quantum Fisher metric and estimation for pure state models , 1995 .

[38]  Jaromir Fiurasek.  Optimal probabilistic cloning and purification of quantum states , 2004 .

[39]  R. Gill,et al.  State estimation for large ensembles , 1999, quant-ph/9902063.

[40]  W. Hoeffding.  Probability Inequalities for sums of Bounded Random Variables , 1963 .

[41]  M. Barbieri,et al.  Implementation of a non-deterministic optical noiseless amplifier , 2010, CLEO/QELS: 2010 Laser Science to Photonic Applications.

[42]  G. Guo,et al.  Probabilistic Cloning and Identification of Linearly Independent Quantum States , 1998, quant-ph/9804064.

[43]  A. C. Berry.  The accuracy of the Gaussian approximation to the sum of independent variates , 1941 .

[44]  D. Dieks.  Communication by EPR devices , 1982 .

[45]  W. Wootters,et al.  A single quantum cannot be cloned , 1982, Nature.

[46]  G. M. D'Ariano,et al.  Extremal quantum cloning machines , 2005, quant-ph/0507130.

[47]  Albert Einstein,et al.  Strahlungs-Emission und ­Absorption nach der Quantentheorie , 1916 .

[48]  Nick Herbert.  FLASH—A superluminal communicator based upon a new kind of quantum measurement , 1982 .

[49]  S. Lloyd,et al.  Quantum-Enhanced Measurements: Beating the Standard Quantum Limit , 2004, Science.

[50]  G. M. D'Ariano,et al.  Optimal phase covariant cloning for qubits and qutrits , 2003, quant-ph/0301175.

[51]  T. Ralph,et al.  Nondeterministic Noiseless Linear Amplification of Quantum Systems , 2009 .

[52]  D. Bruß,et al.  Optimal Universal Quantum Cloning and State Estimation , 1997, quant-ph/9712019.

[53]  R. Werner.  OPTIMAL CLONING OF PURE STATES , 1998, quant-ph/9804001.

[54]  Marian Grabowski,et al.  Operational Quantum Physics , 2001 .

[55]  Giulio Chiribella,et al.  On Quantum Estimation, Quantum Cloning and Finite Quantum de Finetti Theorems , 2010, TQC.

[56]  G. D’Ariano,et al.  Optimal nonuniversally covariant cloning , 2001, quant-ph/0101100.