Quantum limits on probabilistic amplifiers

An ideal phase-preserving linear amplifier is a deterministic device that adds to an input signal the minimal amount of noise consistent with the constraints imposed by quantum mechanics. A noiseless linear amplifier takes an input coherent state to an amplified coherent state, but only works part of the time. Such a device is actually better than noiseless, since the output has less noise than the amplified noise of the input coherent state; for this reason we refer to such devices as immaculate. Here we bound the working probabilities of probabilistic and approximate immaculate amplifiers and construct theoretical models that achieve some of these bounds. Our chief conclusions are the following: (i) The working probability of any phase-insensitive immaculate amplifier is very small in the phase-plane region where the device works with high fidelity; (ii) phase-sensitive immaculate amplifiers that work only on coherent states sparsely distributed on a phase-plane circle centered at the origin can have a reasonably high working probability.

[1]  Samuel L. Braunstein,et al.  Quantum-information distributors: Quantum network for symmetric and asymmetric cloning in arbitrary dimension and continuous limit , 2001 .

[2]  Nathan Walk,et al.  Security of continuous-variable quantum cryptography with Gaussian postselection , 2013 .

[3]  Anthony Chefles,et al.  Unambiguous discrimination between linearly independent quantum states , 1998, quant-ph/9807022.

[4]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[5]  Carl W. Helstrom,et al.  Cutoff rate for the M-ary PSK modulation channel with optimal quantum detection , 1989, IEEE Trans. Inf. Theory.

[6]  Extremal equation for optimal completely positive maps , 2001, quant-ph/0105124.

[7]  E. Knill,et al.  A scheme for efficient quantum computation with linear optics , 2001, Nature.

[8]  Julius Goldhar,et al.  Experimental demonstration of a receiver beating the standard quantum limit for multiple nonorthogonal state discrimination , 2013, Nature Photonics.

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

[10]  C. Helstrom Quantum detection and estimation theory , 1969 .

[11]  C. Caves Quantum limits on noise in linear amplifiers , 1982 .

[12]  John Jeffers,et al.  Nondeterministic amplifier for two-photon superpositions , 2010, 1012.3008.

[13]  R. Filip,et al.  Probabilistic Cloning of Coherent States without a Phase Reference , 2011, 1108.4241.

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

[15]  Jaromir Fiurasek,et al.  Engineering quantum operations on traveling light beams by multiple photon addition and subtraction , 2009, 0910.4104.

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

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

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

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

[20]  Horace P. Yuen,et al.  Amplification of quantum states and noiseless photon amplifiers , 1986 .

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

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

[23]  Stephen M. Barnett,et al.  Strategies and networks for state-dependent quantum cloning , 1999 .

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

[25]  Erika Andersson,et al.  Truly noiseless probabilistic amplification , 2012 .

[26]  Göran Lindblad,et al.  Cloning the quantum oscillator , 2000 .

[27]  H. Haus,et al.  QUANTUM NOISE IN LINEAR AMPLIFIERS , 1962 .

[28]  J. L. Kelly,et al.  B.S.T.J. briefs: On the simultaneous measurement of a pair of conjugate observables , 1965 .

[29]  Radim Filip,et al.  Coherent-state phase concentration by quantum probabilistic amplification , 2009, 0907.2402.

[30]  S. Braunstein,et al.  Quantum Information with Continuous Variables , 2004, quant-ph/0410100.

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

[32]  Nicolas J. Cerf,et al.  Optical Quantum Cloning - a Review , 2005 .

[33]  A. Dolinska,et al.  Optimal cloning for finite distributions of coherent states (6 pages) , 2004 .

[34]  N. Cerf,et al.  Gaussian postselection and virtual noiseless amplification in continuous-variable quantum key distribution , 2012 .

[35]  Saikat Guha,et al.  SymmetricM-ary phase discrimination using quantum-optical probe states , 2012, 1206.0673.

[36]  S. Barnett,et al.  Optimum unambiguous discrimination between linearly independent symmetric states , 1998, quant-ph/9807023.