Quantum Optics and Quantum Information Theory Group

2021

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• Time-traveling billiard-ball clocks: A quantum model, Lachlan Bishop, Fabio Costa, Timothy C. Ralph, Phys. Rev. A 103, 042223

• Hawking radiation particle spectrum from a Kerr-Newman black hole, Joshua Foo, Michael R.R. Good, Journal of Cosmology and Astroparticle Physics, JCAP01(2021)019
   

2020

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• Schrödinger's cat for de Sitter spacetime, Joshua Foo, Robert B. Mann, Magdalena Zych, Class. Quantum Grav. 38 115010

• Entanglement amplification between superposed detectors in flat and curved spacetimes, Joshua Foo, Robert B. Mann, Magdalena Zych, Phys. Rev. D 103, 065013

• Accelerating boundary analog of a Kerr black hole, Michael R.R. Good, Joshua Foo, Eric. V Linder, Class. Quantum Grav. 38 085011

• Generalized quantum scissors for noiseless linear amplification, Matthew S. Winnel, Nedasadat Hosseinidehaj, and Timothy C. Ralph, Phys. Rev. A, 102, 063715 (2020)

• Timothy C. Ralph, Chris Chang, Spinning up a time machine, Physical Review D 102, 124013 (2020)

• Quantum repeater for continuous-variable entanglement distribution, Josephine Dias, Matthew S. Winnel, Nedasadat Hosseinidehaj, T.C.Ralph, Phys. Rev. A, 102, 052425 (2020)

• Maximum entanglement of formation for a two-mode Gaussian state over passive operations, Spyros Tserkis, Jayne Thompson, Austin P. Lund, Timothy C. Ralph, Ping Koy Lam, Mile Gu and Syed M. Assad, Phys. Rev. A 102, 052418 (2020)

• Sho Onoe, Spyros Tserkis, Austin P. Lund, Timothy C. Ralph, Multipartite Gaussian Entanglement of Formation, Physical Review A 102, 042408

• Joshua Foo, Sho Onoe, Magdalena Zych, Unruh-deWitt detectors in quantum superpositions of trajectories, Physical Review D 102, 085013 (2020).

• Joshua J. Guanzon, Austin P. Lund, and Timothy C. Ralph, Controllable quantum interference from two-photon scattershot sources, Physical Review A 102, 032606 (2020).

• Madhav Krishnan Vijayan, Austin P. Lund, and Peter P. Rohde, A robust W-state encoding for linear quantum optics, Quantum 4, 303 (2020).

• Joshua Foo, Sho Onoe, Magdalena Zych, Timothy C. Ralph, Generating multi-partite entanglement from the quantum vacuum with a finite-lifetime mirror, New Journal of Physics 22, 083075 (2020).

• Nedasadat Hosseinidehaj, Andrew M. Lance, Thomas Symul, Nathan Walk, and Timothy C. Ralph, Finite-size effects in continuous-variable quantum key distribution with Gaussian postselection, Physical Review A 101, 052335 (2020).

• Joshua Foo, Timothy C. Ralph, Continuous-variable quantum teleportation with vacuum-entangled Rindler modes, Physical Review D 101, 085006 (2020).

• Teleportation-based collective attacks in Gaussian quantum key distribution, Spyros Tserkis, Nedasadat Hosseinidehaj, Nathan Walk, and Timothy C. Ralph, Phys. Rev. Research 2, 013208 (2020)

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​2019

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• Daiqin Su, Timothy C. Ralph, Decoherence of the radiation from an accelerated quantum source, Physical Review X 9, 011007 (2019)

• Ping Xu, Yiqiu Ma, Ji-Gang Ren, Hai-Lin Yong, Timothy C. Ralph, Sheng-Kai Liao, Juan Yin, Wei-Yue Liu, Wen-Qi  Cai, Xuan Han, Hui-Nan Wu, Wei-Yang Wang, Feng-Zhi Li, Meng Yang, Feng-Li Lin, Li Li, Nai-Le Liu, Yu-Ao Chen, Chao-Yang Lu, Yanbei Chen, Jingyun Fan, Cheng-Zhi Peng, Jian-Wei Pan, Satellite testing of a gravitationally induced quantum decoherence model, Science 366, 132-135 (2019).

• Riccardo Laurenza, Spyros Tserkis, Leonardo Banchi, Samuel L. Braunstein, Timothy C. Ralph, and Stefano Pirandola, Tight finite-resource bounds for private communication over Gaussian channels, Physical Review A 100, 042301 (2019).

• Sebastian P. Kish, Timothy C. Ralph, Quantum metrology in the Kerr metric, Physical Review D 99, 124015 (2019).

• Sho Onoe, Timothy. C. Ralph, Universal Transformation of Displacement Operators and its Application to Homodyne Tomography In Differing Relativistic Reference Frames, Physical Review D 99, 116001 (2019).

• Farid Shahandeh, Austin P. Lund, Timothy C. Ralph, Quantum Correlations and Global Coherence in Distributed Quantum Computing, Physical Review A 99, 052303 (2019).

• Nedasadat Hosseinidehaj, Nathan Walk, and Timothy C. Ralph, Optimal realistic attacks in continuous-variable quantum key distribution, Physical Review A 99, 052336 (2019).

• Spyros Tserkis, Sho Onoe, Timothy. C. Ralph, Quantifying entanglement of formation for two-mode Gaussian states: Analytical expressions for upper and lower bounds and numerical estimation of its exact value, Physical Review A 99, 052337 (2019).

• ​Hao Jeng, Spyros Tserkis, Jing Yan Haw, Helen M. Chrzanowski, Jiri Janousek, Timothy C. Ralph, Ping Koy Lam, Syed M. Assad, Entanglement properties of a measurement-based entanglement distillation experiment, Physical Review A 99, 042304 (2019).

• Shuying Y. Chen and Timothy C. Ralph, Estimation of gravitational acceleration with quantum optical interferometers, Physical Review A 99, 023803 (2019).

​2018

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• ​Spyros Tserkis, Josephine Dias, and Timothy C. Ralph, Simulation of Gaussian channels via teleportation and error correction of Gaussian states, Physical Review A 98, 052355 (2018).

• Xiaogang Qiang, Xiaoqi Zhou, Jianwei Wang, Callum M. Wilkes, Thomas Loke, Sean O'Gara, Laurent Kling, Graham D. Marshall, Raffaele Santagati, Timothy C. Ralph, Jingbo B. Wang, Jeremy L. O'Brien, Mark G. Thompson, and Jonathan C. F. Matthews, Large-scale silicon quantum photonics implementing arbitrary two-qubit processing, Nature Photonics 12, 534 (2018).

• Joshi, Siddarth; Pienaar, Jacques; Ralph, Timothy; Cacciapuoti, Luigi; McCutcheon, Will; Rarity, John; Giggenbach, Dirk; Lim, Jin Gyu; Makarov, Vadim; Fuentes, Ivette; Scheidl, Thomas; Beckert, Erik; Bourennane, Mohamed; Bruschi, David Edward; Cabello, Adan; Capmany, Jose; Carrasco-Casado,  Alberto; Diamanti, Eleni; Dusek, Miloslav; Elser, Dominique; Gulinatti, Angelo; Hadfield, Robert; Jennewein, Thomas; Kaltenbaek, Rainer; Krainak, Michael ; Lo, Hoi-Kwong; Marquardt, Christoph ; Milburn, Gerard; Peev, Momtchil; Poppe, Andreas; Pruneri, Valerio; Renner, Renato ; Salomon, Christophe; Skaar, Johannes; Solomos, Nikolaos ; Stipˇcevi´c, Mario ; Torres, Juan; Toyoshima, Morio; Villoresi, Paolo ; Walmsley, Ian; Weihs, Gregor; Weinfurter, Harald; Zeilinger, Anton; Zukowski, Marek; Ursin, Rupert, Space QUEST mission proposal: Experimentally testing decoherence due to gravity, New Journal of Physics 20, 063016 (2018).

• Sho Onoe, Daiqin Su, Timothy Ralph, Particle production and apparent decoherence due to an accelerated time-delay, Physical Review D, 98, 036011 (2018).

• Josephine Dias and T. C. Ralph, Quantum error correction of continuous-variable states with realistic resources, Physical Review A, 97, 032335 (2018).

• Ryan J. Marshman, Austin P. Lund, Peter P. Rohde, and Timothy C. Ralph, Passive quantum error correction of linear optics networks through error averaging, Physical Review A 97, 022324 (2018).

• Oliver Thearle, Jiri Janousek, Seiji Armstrong, Sara Hosseini, Melanie Schünemann (Mraz), Syed Assad, Thomas Symul, Matthew R. James, Elanor Huntington, Timothy C. Ralph, and Ping Koy Lam, Violation of Bell’s Inequality Using Continuous Variable Measurements, Physical Review Letters 120, 040406 (2018).

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2017

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• Spyros Tserkis and Timothy C. Ralph, Quantifying entanglement in two-mode Gaussian states, Physical Review A 96, 062338 (2017).

• Jie Zhao, Josephine Dias, Jing Yan Haw, Thomas Symul, Mark Bradshaw, Rémi Blandino, Timothy Ralph, Syed M. Assad, and Ping Koy Lam, Quantum enhancement of signal-to-noise ratio with a heralded linear amplifier, Optica, 4, 1421-1428 (2017).

• Sebastian P. Kish and Timothy C. Ralph, Quantum-limited measurement of space-time curvature with scaling beyond the conventional Heisenberg limit, Physical Review A 96, 041801(R) (2017).

• Daiqin Su, C. T. Marco Ho, Robert B. Mann, and Timothy C. Ralph, Black hole squeezers, Physical Review D 96, 065017 (2017).

• Farid Shahandeh, Austin P. Lund, and Timothy C. Ralph, Quantum Correlations in Nonlocal Boson Sampling, Physical Review Letters 119, 120502 (2017).

• Austin P. Lund, Saleh Rahimi-Keshari, and Timothy C. Ralph, Exact boson sampling using Gaussian continuous-variable measurements, Physical Review A 96, 022301 (2017).

• Daiqin Su, C. T. Marco Ho, Robert B. Mann, and Timothy C. Ralph, Quantum circuit model for non-inertial objects: a uniformly accelerated mirror, New Journal of Physics, 19 (2017).

• Matthias Fink, Ana Rodriguez-Aramendia, Johannes Handsteiner, Abdul Ziarkash, Fabian Steinlechner, Thomas Scheidl, Ivette Fuentes, Jacques Pienaar, Timothy C. Ralph, and Rupert Ursin, Experimental test of photonic entanglement in accelerated reference frames, Nature Communications 8, 15304 (2017).

• Farid Shahandeh, Michael J. W. Hall, and Timothy C. Ralph, Measurement-Device-Independent Approach to Entanglement Measures, Physical Review Letters 118, 150505 (2017).

• Austin P. Lund, Michael J. Bremner, and Timothy C. Ralph, Quantum sampling problems, BosonSampling and quantum supremacy, npj Quantum Information 3, 15 (2017).

• Farid Shahandeh, Martin Ringbauer, Juan C. Loredo, and Timothy C. Ralph, Ultrafine Entanglement Witnessing, Physical Review Letters 118, 110502 (2017).

• Josephine Dias and Timothy C. Ralph, Quantum repeaters using continuous-variable teleportation, Physical Review A 95, 022312 (2017).

• Sarah J. Johnson, Andrew M Lance, Lawrence Ong, Mahyar Shirvanimoghaddam, Timothy C. Ralph, and Thomas Symul, On the problem of non-zero word error rates for fixed-rate error correction codes in continuous variable quantum key distribution, New Journal of Physics 19, (2017).

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2016

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• Jing Yan Haw, Jie Zhao, Josephine Dias, Syed M. Assad, Mark Bradshaw, Rémi Blandino, Thomas Symul, Timothy C. Ralph, and Ping Koy Lam, Surpassing the no-cloning limit with a heralded hybrid linear amplifier for coherent states, Nature Communications, 7, 13222 (2016).

• C. T. Marco Ho, Daiqin Su, Robert B. Mann, and Timothy C. Ralph, Black hole field theory with a firewall in two spacetime dimensions, Physical Review D 94, 081502(R) (2016).

• Farid Shahandeh, Austin P. Lund, Timothy C. Ralph, and Michael R. Vanner, Arbitrary multi-qubit generation, New Journal of Physics, 18, (2016).

• Kai Liu, Austin P. Lund, Yong-Jian Gu, and Timothy C. Ralph, A certification scheme for the boson sampler, Journal of the Optical Society of America B, 33, 1835-1841 (2016).

• Nathan Walk, Sara Hosseini, Jiao Geng, Oliver Thearle, Jing Yan Haw, Seiji Armstrong, Syed M. Assad, Jiri Janousek, Timothy C. Ralph, Thomas Symul, Howard M. Wiseman, and Ping Koy Lam, Experimental demonstration of Gaussian protocols for one-sided device-independent quantum key distribution, Optica 3, 634-642 (2016).

• Saleh Rahimi-Keshari, Timothy C. Ralph, and Carlton M. Caves, Sufficient Conditions for Efficient Classical Simulation of Quantum Optics, Physical Review X 6, 021039 (2016).

• Sebastian P. Kish and Timothy  C. Ralph, Estimating spacetime parameters with a quantum probe in a lossy environment, Physical Review D 93, 105013 (2016).

• Joshua Combes, Nathan Walk, Aaustin P. Lund, Timothy C. Ralph, and Carlton M. Caves, Models of reduced-noise, probabilistic linear amplifiers, Physical Review A 93, 052310 (2016).

• Raj B. Patel, Joseph Ho, Franck Ferreyrol, Timothy C. Ralph and Geoff J. Pryde, A quantum Fredkin gate, Science Advances, 2, e1501531 (2016).

• Daiqin Su and Timothy C. Ralph, Spacetime diamonds, Physical Review D 93, 044023 (2016).

• Rémi Blandino, Nathan Walk, Austin P. Lund, and Timothy C. Ralph, Channel purification via continuous-variable quantum teleportation with Gaussian postselection, Physical Review A 93, 012326 (2016).

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2015

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• Xiao Yuan, Syed M Assad, Jayne Thompson, Jing Yan Haw, Vlatko Vedral, Timothy C Ralph, Ping Koy Lam, Christian Weedbrook, and Mile Gu, Replicating the benefits of Deutschian closed timelike curves without breaking causality, npj Quantum Information 1, 15007 (2015).

• Austin P. Lund, Classes of two-photon states defined by linear interactions and destructive two-photon quantum interference in a single mode, Physical Review A 92, 053844 (2015).

• Seung-Woo Lee, Kimin Park, Timothy C. Ralph, and Hyunseok Jeong, Nearly deterministic Bell measurement with multiphoton entanglement for efficient quantum-information processing, Physical Review A 92, 052324 (2015).

• Alexander E. Ulanov, Ilya A. Fedorov, Anastasia A. Pushkina, Yury V. Kurochkin, Timothy C. Ralph, and A. I. Lvovsky, Undoing the effect of loss on quantum entanglement, Nature Photonics 9, 764-768 (2015).

• L. S. Costanzo, A. Zavatta, S. Grandi, M. Bellini, H. Jeong, M. Kang, S.-W. Lee, and Timothy C. Ralph, Physica Scripta 90, (2015).

• Saleh Rahimi-Keshari, Timothy C. Ralph, and Carlton M. Caves, Operational discord measure for Gaussian states with Gaussian measurements, New Journal of Physics 17, (2015).

• Timothy C. Ralph, and Nathan Walk, Quantum key distribution without sending a quantum signal, New Journal of Physics 17, (2015).

• Timothy C. Ralph, I. Söllner, S. Mahmoodian, Andrew G. White, and P. Lodahl, Photon Sorting, Efficient Bell Measurements, and a Deterministic Controlled-Z Gate Using a Passive Two-Level Nonlinearity, Physical Review Letters 114, 173603 (2015).

• Seung-Woo Lee, Kimin Park, Timothy C. Ralph, and Hyunseok Jeong, Nearly Deterministic Bell Measurement for Multiphoton Qubits and its Application to Quantum Information Processing, Physical Review Letters 114, 113603 (2015).

• Saleh Rahimi-Keshari, Austin P. Lund, and Timothy C. Ralph, What Can Quantum Optics Say about Computational Complexity Theory?, Physical Review Letters 114, 060501 (2015).

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2014

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• Hyunseok Jeong, Changsuk Noh, Seunglee Bae, Dimitris G. Angelakis, and Timothy C. Ralph, Detecting the degree of macroscopic quantumness using an overlap measurement, Journal of the Optical Society of America B 31, 3057-3066 (2014).

• David Edward Bruschi, Animesh Datta, Rupert Ursin, Timothy C. Ralph, and Ivette Fuentes, Quantum estimation of the Schwarzschild spacetime parameters of the Earth, Physical Review D 90, 124001 (2014).

• J. Bernu, S. Armstrong, T. Symul, T. C. Ralph, and P. K. Lam, Theoretical analysis of an ideal noiseless linear amplifier for Einstein–Podolsky–Rosen entanglement distillation, Journal of Physics B: Atomic, Molecular and Optical Physics, 47, (2014).

• Luca S. Costanzo, Alessandro Zavatta, Samuele Grandi, Marco Bellini, Hyunseok Jeong, Minsu Kang, Seung-Woo Lee, and Timothy C. Ralph, Experimental hybrid entanglement between quantum and classical states of light, International Journal of Quantum Information 12, 1560015 (2014).

• Daiqin Su and Timothy  C. Ralph, Quantum communication in the presence of a horizon, Physical Review D 90, 084022 (2014).

• A. P. Lund, A. Laing, S. Rahimi-Keshari, T. Rudolph, J. L. O’Brien, and T. C. Ralph, Boson Sampling from a Gaussian State, Physical Review Letters 113, 100502 (2014).

• G. T. Campbell, O. Pinel, M. Hosseini, T. C. Ralph, B. C. Buchler, and P. K. Lam, Configurable Unitary Transformations and Linear Logic Gates Using Quantum Memories, Physical Review Letters 113, 063601 (2014).

• David Edward Bruschi, Timothy C. Ralph, Ivette Fuentes, Thomas Jennewein, and Mohsen Razavi, Spacetime effects on satellite-based quantum communications, Physical Review D 90, 045041 (2014).

• Martin Ringbauer, Matthew A. Broome, Casey R. Myers, Andrew G. White, and Timothy C. Ralph, Experimental simulation of closed timelike curves, Nature Communications volume 5, 4145 (2014).

• M. P. Almeida, Mile Gu, Alessandro Fedrizzi, Matthew A. Broome, Timothy C. Ralph, and Andrew G. White, Entanglement-free certification of entangling gates, Physical Review A 89, 042323 (2014).

• Helen M. Chrzanowski, Nathan Walk, Syed M. Assad, Jiri Janousek, Sara Hosseini, Timothy C. Ralph, Thomas Symul, and Ping Koy Lam, Measurement-based noiseless linear amplification for quantum communication, Nature Photonics 8, 333–338 (2014).

• N. A. McMahon, A. P. Lund, and T. C. Ralph, Optimal architecture for a nondeterministic noiseless linear amplifier, Physical Review A 89, 023846 (2014).

• S. Hosseini, S. Rahimi-Keshari, J. Y. Haw, S. M. Assad, H. M. Chrzanowski, J. Janousek., T. Symul, T. C. Ralph, and P. K. Lam, Experimental verification of quantum discord in continuous-variable states, Journal of Physics B: Atomic, Molecular and Optical Physics 47, (2014).

• T. C. Ralph and J. Pienaar, Entanglement decoherence in a gravitational well according to the event formalism, New Journal of Physics, 16, (2014).

• Hyunseok Jeong, Alessandro Zavatta, Minsu Kang, Seung-Woo Lee, Luca S. Costanzo, Samuele Grandi, Timothy C. Ralph & Marco Bellini, Generation of hybrid entanglement of light, Nature Photonics 8, 564–569 (2014).

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2013

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• A. P. Lund, T. C. Ralph, and H. Jeong, Generation of distributed entangled coherent states over a lossy environment with inefficient detectors, Physical Review A 88, 052335 (2013).

• Timothy C. Ralph, Quantum communication: Reliable teleportation, Nature 500, 282–283 (2013).

• Ulrik L. Andersen and Timothy C. Ralph, High-Fidelity Teleportation of Continuous-Variable Quantum States Using Delocalized Single Photons, Physical Review Letters 111, 050504 (2013).

• D. Ahn, C. R. Myers, T. C. Ralph, and R. B. Mann, Quantum-state cloning in the presence of a closed timelike curve, Physical Review A 88, 022332 (2013).

• Nathan Walk, Austin P. Lund, and Timothy C. Ralph, Nondeterministic noiseless amplification via non-symplectic phase space transformations, New Journal of Physics 15, (2013).

• Timothy C. Ralph, Quantum computation: Boson sampling on a chip, Nature Photonics 7, 514–515 (2013).

• Saleh Rahimi-Keshari, Matthew A. Broome, Robert Fickler, Alessandro Fedrizzi, Timothy C. Ralph, and Andrew G. White, Direct characterization of linear-optical networks, Optics Express 21, 13450-13458 (2013).

• H. M. Chrzanowski, S. M. Assad, J. Bernu, B. Hage, A. P. Lund, T. C. Ralph, P. K. Lam, and T. Symul, Reconstruction of photon number conditioned states using phase randomized homodyne measurements, Journal of Physics B: Atomic, Molecular and Optical Physics 46, (2013).

• P. K. Lam and T. C. Ralph, Quantum cryptography: Continuous improvement, Nature Photonics 7, 350–352 (2013).

• Xiao-Qi Zhou, Pruet Kalasuwan, Timothy C. Ralph, and Jeremy L. O'Brien, Calculating unknown eigenvalues with a quantum algorithm, Nature Photonics 7, 223–228 (2013).

• Nathan Walk, Timothy C. Ralph, Thomas Symul, and Ping Koy Lam, Security of continuous-variable quantum cryptography with Gaussian postselection, Physical Review A 87, 020303(R) (2013).

• Matthew A. Broome, Alessandro Fedrizzi, Saleh Rahimi-Keshari, Justin Dove, Scott Aaronson, Timothy C. Ralph, Andrew G. White, Photonic Boson Sampling in a Tunable Circuit, Science 339, 794-798 (2013).

• J. L. Pienaar, T. C. Ralph, and C. R. Myers, Open Timelike Curves Violate Heisenberg’s Uncertainty Principle, Physical Review Letters 110, 060501 (2013).

• Saleh Rahimi-Keshari, Carlton M. Caves, and Timothy C. Ralph, Measurement-based method for verifying quantum discord, Physical Review A 87, 012119 (2013).

• S. Kocsis, G. Y. Xiang, T. C. Ralph & G. J. Pryde, Heralded noiseless amplification of a photon polarization qubit, Nature Physics 9, 23–28 (2013).

• T. G. Downes, T. C. Ralph, and N. Walk, Quantum communication with an accelerated partner, Physical Review A 87, 012327 (2013).

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2012

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• Magdalena Zych, Fabio Costa, Igor Pikovski, Timothy C. Ralph, and Časlav Brukner, General relativistic effects in quantum interference of photons, Classical and Quantum Gravity 29, (2012).

• R. B. Mann and T. C. Ralph, Relativistic quantum information, Classical and Quantum Gravity 29, (2012).

• Hidehiro Yonezawa, Daisuke Nakane, Trevor A. Wheatley, Kohjiro Iwasawa, Shuntaro Takeda, Hajime Arao, Kentaro Ohki, Koji Tsumura, Dominic W. Berry, Timothy C. Ralph, Howard M. Wiseman, Elanor H. Huntington, and Akira Furusawa, Quantum-Enhanced Optical-Phase Tracking, Science 337, 1514-1517 (2012).

• Mile Gu, Helen M. Chrzanowski, Syed M. Assad, Thomas Symul, Kavan Modi, Timothy C. Ralph, Vlatko Vedral, and Ping Koy Lam, Observing the operational significance of discord consumption, Nature Physics 8, 671–675 (2012).

• Christian Weedbrook, Stefano Pirandola, and Timothy C. Ralph, Continuous-variable quantum key distribution using thermal states, Physical Review A 86, 022318 (2012).

• Peter P. Rohde, Alessandro Fedrizzi, and Timothy C. Ralph, Entanglement dynamics and quasi-periodicity in discrete quantum walks, Journal of Modern Optics 59, 710-720 (2012).

• Christian Weedbrook, Stefano Pirandola, Raúl García-Patrón, Nicolas J. Cerf, Timothy C. Ralph, Jeffrey H. Shapiro, and Seth Lloyd, Gaussian quantum information, Review Modern Physics 84, 621 (2012).

• Peter P. Rohde and Timothy C. Ralph, Error tolerance of the boson-sampling model for linear optics quantum computing, Physical Review A 85, 022332 (2012).

• Timothy C. Ralph and Tony G. Downes, Relativistic quantum information and time machines, Contemporary Physics 53, 1-16 (2012).

• S. Jay Olson and Timothy C. Ralph, Extraction of timelike entanglement from the quantum vacuum, Physical Review A 85, 012306 (2012).