Proper error bars for self-calibrating quantum tomography

Self-calibrating quantum state tomography aims at reconstructing the unknown quantum state and certain properties of the measurement devices from the same data. Since the estimates of the state and device parameters come from the same data, one should employ a joint estimation scheme, including the construction and reporting of joint state-device error regions to quantify uncertainty. We explain how to do this naturally within the framework of optimal error regions. As an illustrative example, we apply our procedure to the double-crosshair measurement of the BB84 scenario in quantum cryptography and so reconstruct the state and estimate the detection efficiencies simultaneously and reliably. We also discuss the practical situation of a satellite-based quantum key distribution scheme, for which self-calibration and proper treatment of the data are necessities.

[1]  Yang Guo,et al.  Measuring and Controlling Bias for Some Bayesian Inferences and the Relation to Frequentist Criteria , 2019, Entropy.

[2]  C. Oh,et al.  Efficient Bayesian credible-region certification for quantum-state tomography , 2019, Physical Review A.

[3]  Michael Evans.  The Measurement of Statistical Evidence as the Basis for Statistical Reasoning , 2019 .

[4]  Jian-Wei Pan,et al.  Satellite-to-Ground Entanglement-Based Quantum Key Distribution. , 2017, Physical review letters.

[5]  Testing of quantum phase in matter-wave optics , 1999, quant-ph/9904047.

[6]  Rauch,et al.  Quantum phase in interferometry. , 1996, Physical review letters.

[7]  Paolo Villoresi,et al.  Space-quest, experiments with quantum entanglement in space , 2008, 0806.0945.

[8]  Pavel Lougovski,et al.  Quantum state estimation when qubits are lost: a no-data-left-behind approach , 2016, 1610.03714.

[9]  Gorjan Alagic,et al.  #p , 2019, Quantum information & computation.

[10]  Jiangwei Shang,et al.  Optimal error intervals for properties of the quantum state , 2016, 1602.05780.

[11]  Jaroslav Rehacek,et al.  Relative tomography of an unknown quantum state , 2009 .

[12]  B. Englert,et al.  Very strong evidence in favor of quantum mechanics and against local hidden variables from a Bayesian analysis , 2018, Physical Review A.

[13]  D. Klyshko,et al.  Use of two-photon light for absolute calibration of photoelectric detectors , 1980 .

[14]  D. Mogilevtsev.  Calibration of single-photon detectors using quantum statistics , 2010 .

[15]  Alexander Ling,et al.  Progress in satellite quantum key distribution , 2017, 1707.03613.

[16]  Jian-Wei Pan,et al.  Satellite-Relayed Intercontinental Quantum Network. , 2018, Physical review letters.

[17]  Michael Evans,et al.  Measuring statistical evidence using relative belief , 2015, Computational and structural biotechnology journal.

[18]  H. Weinfurter,et al.  Entanglement-based quantum communication over 144km , 2007 .

[19]  P R Tapster,et al.  Absolute measurement of detector quantum efficiency using parametric downconversion. , 1987, Applied optics.

[20]  Yongmei Huang,et al.  Satellite-to-ground quantum key distribution , 2017, Nature.

[21]  이현주.  Q. , 2005 .

[22]  Paolo Villoresi,et al.  CubeSat quantum communications mission , 2017, EPJ Quantum Technology.

[23]  Gilles Brassard,et al.  Quantum cryptography: Public key distribution and coin tossing , 2014, Theor. Comput. Sci..

[24]  D. Nott,et al.  Monte Carlo sampling from the quantum state space. II , 2014, 1407.7805.

[25]  H. Weinfurter,et al.  Free-Space distribution of entanglement and single photons over 144 km , 2006, quant-ph/0607182.

[26]  Lee A. Rozema,et al.  Self-calibrating quantum state tomography , 2011, Frontiers in Optics 2011/Laser Science XXVII.

[27]  H. Ng,et al.  Optimal error regions for quantum state estimation , 2013, 1302.4081.

[28]  Monte Carlo sampling from the quantum state space. I , 2014, 1407.7805.

[29]  Tim B. Swartz,et al.  Optimally and computations for relative surprise inferences , 2006 .