Improving QKD for Entangled States with Low Squeezing via Non-Gaussian Operations

In this work we focus on evaluating the effectiveness of two non-Gaussian operations, photon subtraction (PS) and quantum scissors (QS) in terms of Continuous Variable (CV)-Quantum Key Distribution (QKD) over lossy channels. Each operation is analysed in two scenarios, one with the operation applied transmitter-side to a Two- Mode Squeezed Vacuum (TMSV) state and a second with the operation applied to the TMSV state receiver-side. We numerically evaluate the entanglement and calculate the QKD key rates produced in all four possible scenarios. Our results show that for a fixed value of initial squeezing in the TMSV state, the states produced by the non-Gaussian operations are more robust to loss, being capable of generating higher key rates for a given loss. More specifically, we find that for values of initial TMSV squeezing below 1.5dB the highest key rates are obtained by means of transmitter-QS. On the other hand, for squeezing above 1.5dB we find that receiver-PS produces higher key rates. Our results will be important for future CV-QKD implementations over free-space channels, such as the Earth-satellite channel.

[1]  Masahide Sasaki,et al.  Entanglement evaluation of non-Gaussian states generated by photon subtraction from squeezed states , 2005, quant-ph/0512069.

[2]  Jonathan Green,et al.  Photonic Engineering for CV-QKD Over Earth-Satellite Channels , 2019, ICC 2019 - 2019 IEEE International Conference on Communications (ICC).

[3]  M. Plenio.  Logarithmic negativity: a full entanglement monotone that is not convex. , 2005, Physical review letters.

[4]  Sheng-li Ma,et al.  Two-mode squeezed states of two separated nitrogen-vacancy-center ensembles coupled via dissipative photons of superconducting resonators , 2019, Physical Review A.

[5]  Saikat Guha,et al.  Continuous-variable entanglement distillation over a pure loss channel with multiple quantum scissors , 2018, Physical Review A.

[6]  R. Brouri,et al.  Non-gaussian statistics from individual pulses of squeezed light , 2004, InternationalQuantum Electronics Conference, 2004. (IQEC)..

[7]  S. Braunstein,et al.  Quantum computation over continuous variables , 1998 .

[8]  Christian Weedbrook,et al.  Continuous-variable quantum key distribution with entanglement in the middle , 2012, 1205.1497.

[9]  Zeyang Liao,et al.  Improvement of entanglement via quantum scissors , 2018 .

[10]  H. Briegel,et al.  Entanglement purification and quantum error correction , 2007, 0705.4165.

[11]  Alexander S. Holevo,et al.  One-mode quantum Gaussian channels: Structure and quantum capacity , 2007, Probl. Inf. Transm..

[12]  Seth Lloyd,et al.  Gaussian quantum information , 2011, 1110.3234.

[13]  Martin B. Plenio,et al.  An introduction to entanglement measures , 2005, Quantum Inf. Comput..

[14]  P. Grangier,et al.  Continuous variable quantum cryptography using coherent states. , 2001, Physical review letters.

[15]  Timothy C. Ralph,et al.  Quantum information with continuous variables , 2000, Conference Digest. 2000 International Quantum Electronics Conference (Cat. No.00TH8504).

[16]  Klaus Molmer.  Non-Gaussian states from continuous-wave Gaussian light sources , 2006 .

[17]  Masoud Ghalaii,et al.  Discrete-Modulation Continuous-Variable Quantum Key Distribution Enhanced by Quantum Scissors , 2019, IEEE Journal on Selected Areas in Communications.

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

[19]  Charles H. Bennett,et al.  Concentrating partial entanglement by local operations. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[20]  J Eisert,et al.  Distilling Gaussian states with Gaussian operations is impossible. , 2002, Physical review letters.

[21]  Karsten Danzmann,et al.  Detection of 15 dB Squeezed States of Light and their Application for the Absolute Calibration of Photoelectric Quantum Efficiency. , 2016, Physical review letters.

[22]  Masahide Sasaki,et al.  Entanglement distillation from Gaussian input states , 2010 .

[23]  S. Lloyd,et al.  Quantum illumination with Gaussian states. , 2008, Physical review letters.

[24]  Jonathan Green,et al.  Quantum Communications via Satellite with Photon Subtraction , 2018, 2018 IEEE Globecom Workshops (GC Wkshps).

[25]  Masato Koashi,et al.  Quantum-scissors device for optical state truncation: A proposal for practical realization , 2001 .

[26]  N. Cerf,et al.  Unconditional optimality of Gaussian attacks against continuous-variable quantum key distribution. , 2006, Physical Review Letters.

[27]  Reynaud,et al.  Observation of quantum noise reduction on twin laser beams. , 1987, Physical review letters.

[28]  Peter van Loock,et al.  Distillation of mixed-state continuous-variable entanglement by photon subtraction , 2010, 1009.4888.

[29]  J. Cirac,et al.  Extremality of Gaussian quantum states. , 2005, Physical review letters.

[30]  Masoud Ghalaii,et al.  Long-Distance Continuous-Variable Quantum Key Distribution With Quantum Scissors , 2018, IEEE Journal of Selected Topics in Quantum Electronics.