Turbocharging Quantum Tomography

Quantum tomography is used to characterize quantum operations implemented in quantum information processing (QIP) hardware. Traditionally, state tomography has been used to characterize the quantum state prepared in an initialization procedure, while quantum process tomography is used to characterize dynamical operations on a QIP system. As such, tomography is critical to the development of QIP hardware (since it is necessary both for debugging and validating as-built devices, and its results are used to influence the next generation of devices). But tomography su %7C ers from several critical drawbacks. In this report, we present new research that resolves several of these flaws. We describe a new form of tomography called gate set tomography (GST), which unifies state and process tomography, avoids prior methods critical reliance on precalibrated operations that are not generally available, and can achieve unprecedented accuracies. We report on theory and experimental development of adaptive tomography protocols that achieve far higher fidelity in state reconstruction than non-adaptive methods. Finally, we present a new theoretical and experimental analysis of process tomography on multispin systems, and demonstrate how to more e %7C ectively detect and characterize quantum noise using carefully tailored ensembles of input states.

[1]  Identification of decoherence-free subspaces without quantum process tomography , 2012, 1206.4510.

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

[3]  J. Fiurášek Conditional generation of N -photon entangled states of light , 2001, quant-ph/0110138.

[4]  Jian-Wei Pan,et al.  De Broglie wavelength of a non-local four-photon state , 2003, Nature.

[5]  Massar,et al.  Optimal extraction of information from finite quantum ensembles. , 1995, Physical review letters.

[6]  M W Mitchell,et al.  Multiparticle state tomography: hidden differences. , 2007, Physical review letters.

[7]  K. Audenaert,et al.  Discriminating States: the quantum Chernoff bound. , 2006, Physical review letters.

[8]  N. Houlsby,et al.  Adaptive Bayesian quantum tomography , 2011, 1107.0895.

[9]  R. Blume-Kohout Robust error bars for quantum tomography , 2012, 1202.5270.

[10]  Aephraim M. Steinberg,et al.  Improving quantum state estimation with mutually unbiased bases. , 2008, Physical review letters.

[11]  John A Smolin,et al.  Efficient method for computing the maximum-likelihood quantum state from measurements with additive Gaussian noise. , 2012, Physical review letters.

[12]  Abrams,et al.  Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit , 1999, Physical review letters.

[13]  Aephraim M. Steinberg,et al.  Experimental characterization of qutrits using symmetric informationally complete positive operator-valued measurements , 2011 .

[14]  Aephraim M. Steinberg,et al.  Diagnosis, prescription, and prognosis of a bell-state filter by quantum process tomography. , 2003, Physical review letters.

[15]  Joseph M. Renes,et al.  Symmetric informationally complete quantum measurements , 2003, quant-ph/0310075.

[16]  R. Blume-Kohout Hedged maximum likelihood quantum state estimation. , 2010, Physical review letters.

[17]  Barry C Sanders,et al.  Complete Characterization of Quantum-Optical Processes , 2008, Science.

[18]  R. Blume-Kohout Optimal, reliable estimation of quantum states , 2006, quant-ph/0611080.

[19]  Yaron Silberberg,et al.  Sub-Rayleigh lithography using high flux loss-resistant entangled states of light. , 2012, Physical review letters.

[20]  T. Ralph,et al.  Quantum process tomography of a controlled-NOT gate. , 2004, Physical review letters.

[21]  M. Hübner Explicit computation of the Bures distance for density matrices , 1992 .

[22]  Matthias Christandl,et al.  Reliable quantum state tomography. , 2011, Physical review letters.

[23]  P. Turner,et al.  The Curious Nonexistence of Gaussian 2-Designs , 2011, 1110.1042.

[24]  Cheng-Zhi Peng,et al.  Observation of eight-photon entanglement , 2011, Nature Photonics.

[25]  H. Sommers,et al.  Average fidelity between random quantum states , 2003, quant-ph/0311117.

[26]  Andrew G. White,et al.  Measurement of qubits , 2001, quant-ph/0103121.

[27]  Keiji Sasaki,et al.  Beating the standard quantum limit: phase super-sensitivity of N-photon interferometers , 2008, 0804.0087.

[28]  Separable measurement estimation of density matrices and its fidelity gap with collective protocols. , 2006, Physical review letters.

[29]  G. Agarwal Relation between atomic coherent-state representation, state multipoles, and generalized phase-space distributions , 1981 .

[30]  P. Humphreys,et al.  Quantum enhanced multiple phase estimation. , 2013, Physical review letters.

[31]  S P Kulik,et al.  Qutrit state engineering with biphotons. , 2004, Physical review letters.

[32]  Holger F. Hofmann,et al.  High-photon-number path entanglement in the interference of spontaneously down-converted photon pairs with coherent laser light , 2007, 0705.0047.

[33]  Hugo Cable,et al.  Quantum-enhanced tomography of unitary processes , 2014, 1402.2897.

[34]  Experimental demonstration of adaptive quantum state estimation , 2013 .

[35]  Ruediger Schack,et al.  Unknown Quantum States and Operations, a Bayesian View , 2004, quant-ph/0404156.

[36]  Lloyd,et al.  Dynamical generation of noiseless quantum subsystems , 2000, Physical review letters.

[37]  Holger F. Hofmann Generation of highly nonclassical n-photon polarization states by superbunching at a photon bottleneck , 2004 .

[38]  Stephen Becker,et al.  Quantum state tomography via compressed sensing. , 2009, Physical review letters.

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

[40]  Aephraim M. Steinberg,et al.  Scalable spatial super-resolution using entangled photons , 2013, 2014 Conference on Lasers and Electro-Optics (CLEO) - Laser Science to Photonic Applications.

[41]  SU(2)-invariant depolarization of quantum states of light , 2013 .

[42]  Aephraim M. Steinberg,et al.  Squeezing and over-squeezing of triphotons , 2009, Nature.

[43]  Johan Löfberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004 .

[44]  S. Schiller,et al.  Measurement of the quantum states of squeezed light , 1997, Nature.

[45]  A. J. Scott Optimizing quantum process tomography with unitary 2-designs , 2007, 0711.1017.

[46]  M. Murao,et al.  Effect of non-negativity on estimation errors in one-qubit state tomography with finite data , 2012, 1205.2976.

[47]  Alexei Gilchrist,et al.  Choice of measurement sets in qubit tomography , 2007, 0706.3756.

[48]  R. Glauber Coherent and incoherent states of the radiation field , 1963 .

[49]  F. Arecchi,et al.  Atomic coherent states in quantum optics , 1972 .

[50]  R. Gill,et al.  Optimal full estimation of qubit mixed states , 2005, quant-ph/0510158.

[51]  W. Wootters,et al.  Optimal state-determination by mutually unbiased measurements , 1989 .

[52]  E. Bagan,et al.  Quantum Chernoff bound as a measure of distinguishability between density matrices: Application to qubit and Gaussian states , 2007, 0708.2343.

[53]  Y. Silberberg,et al.  High-NOON States by Mixing Quantum and Classical Light , 2010, Science.

[54]  C. Saavedra,et al.  Quantum process reconstruction based on mutually unbiased basis , 2011, 1104.2888.

[55]  Yaron Silberberg,et al.  Experimental tomography of NOON states with large photon numbers , 2011, 1112.4371.

[56]  Jay M. Gambetta,et al.  Self-Consistent Quantum Process Tomography , 2012, 1211.0322.

[57]  A. J. Scott Tight informationally complete quantum measurements , 2006, quant-ph/0604049.

[58]  W. Wootters Statistical distance and Hilbert space , 1981 .

[59]  C. Fuchs Distinguishability and Accessible Information in Quantum Theory , 1996, quant-ph/9601020.

[60]  Marco Barbieri,et al.  Multiparameter quantum metrology , 2012 .

[61]  M. W. Mitchell,et al.  Super-resolving phase measurements with a multiphoton entangled state , 2004, Nature.

[62]  D. Kaszlikowski,et al.  Minimal qubit tomography , 2004, quant-ph/0405084.

[63]  R Laflamme,et al.  Experimental Realization of Noiseless Subsystems for Quantum Information Processing , 2001, Science.

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

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

[66]  D. Petz,et al.  Geometries of quantum states , 1996 .

[67]  M. W. Mitchell,et al.  Detecting Hidden Differences via Permutation Symmetries , 2007 .

[68]  Jeroen van de Graaf,et al.  Cryptographic Distinguishability Measures for Quantum-Mechanical States , 1997, IEEE Trans. Inf. Theory.

[69]  N. Langford,et al.  Distance measures to compare real and ideal quantum processes (14 pages) , 2004, quant-ph/0408063.

[70]  Robin Blume-Kohout,et al.  When quantum tomography goes wrong: drift of quantum sources and other errors , 2013 .