# Quantum Blockchain Using Entanglement in Time

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Classical Blockchain

## 3. Quantum Blockchain

## 4. Quantum Network

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Nielsen, M.A.; Chuang, I.L. Quantum Computation and Quantum Information; Cambridge University Press: Cambridge, UK, 2010. [Google Scholar]
- Castelvecchi, D. Quantum computers ready to leap out of the lab in 2017. Nat. News
**2017**, 541, 9. [Google Scholar] [CrossRef] - Castelvecchi, D. The quantum internet has arrived (and it hasn’t). Nature
**2018**, 554, 289. [Google Scholar] [CrossRef] - Bedington, R.; Arrazola, J.M.; Ling, A. Progress in satellite quantum key distribution. NPJ Quantum Inf.
**2017**, 3, 30. [Google Scholar] [CrossRef] - Bennett, C.H.; Wiesner, S.J. Communication via one-and two-particle operators on Einstein–Podolsky–Rosen states. Phys. Rev. Lett.
**1992**, 69, 2881. [Google Scholar] [CrossRef] [PubMed] - Simon, C. Towards a global quantum network. Nat. Photonics
**2017**, 11, 678. [Google Scholar] [CrossRef] - Nakamoto, S. Bitcoin: A Peer-to-Peer electronic Cash System. Available online: https://bitcoin.org/bitcoin.pdf (accessed on 17 April 2019).
- Aggarwal, D.; Brennen, G.K.; Lee, T.; Santha, M.; Tomamichel, M. Quantum attacks on Bitcoin, and how to protect against them. arXiv
**2017**, arXiv:1710.10377. [Google Scholar] - Kiktenko, E.O.; Pozhar, N.O.; Anufriev, M.N.; Trushechkin, A.S.; Yunusov, R.R.; Kurochkin, Y.V.; Lvovsky, A.I.; Fedorov, A.K. Quantum-secured blockchain. arXiv
**2017**, arXiv:1705.09258. [Google Scholar] - King, S.; Nadal, S. Ppcoin: Peer-to-Peer Crypto-Currency with Proof-of-Stake. 2012. Available online: https://decred.org/research/king2012.pdf (accessed on 17 April 2019).
- Witte, J.H. The Blockchain: A Gentle Four Page Introduction. arXiv
**2016**, arXiv:1612.06244. [Google Scholar] - Buterin, V. Chain Interoperability. Available online: https://www.r3cev.com/s/Chain-Interoperability-8g6f.pdf (accessed on 17 April 2019).
- McMahon, D. Quantum Computing Explained; John Wiley & Sons: Hoboken, NJ, USA, 2007. [Google Scholar]
- Montananao, A. Quantum algorithms: An overview. NPJ Quantum Inf.
**2016**, 2, 15023. [Google Scholar] [CrossRef] - Zeng, W.; Johnson, B.; Smith, R.; Rubin, N.; Reagor, M.; Ryan, C.; Rigetti, C. First quantum computers need smart software. Nature
**2017**, 549, 149. [Google Scholar] [CrossRef] [PubMed] - Jogenfors, J. Quantum bitcoin: An anonymous and distributed currency secured by the no-cloning theorem of quantum mechanics. arXiv
**2016**, arXiv:1604.01383. [Google Scholar] - Sapaev, D.; Bulychkov, D.; Ablayev, F.; Vasiliev, A.; Ziatdinov, M. Quantum-assisted Blockchain. arXiv
**2018**, arXiv:1802.06763. [Google Scholar] - Behera, A.; Paul, G. Quantum to classical one way function and its applications in quantum money authentication. arXiv
**2018**, arXiv:1801.01910. [Google Scholar] - Tessler, L.; Byrnes, T. Bitcoin and quantum computing. arXiv
**2017**, arXiv:1711.04235. [Google Scholar] - Ikeda, K. qBitcoin: A Peer-to-Peer Quantum Cash System. arXiv
**2017**, arXiv:1708.04955. [Google Scholar] - Kalinin, K.P.; Berloff, N.G. Blockchain platform with proof-of-work based on analog Hamiltonian optimisers. arXiv
**2018**, arXiv:1802.10091. [Google Scholar] - Aharonov, Y.; Popescu, S.; Tollaksen, J.; Vaidman, L. Multiple-time states and multiple-time measurements in quantum mechanics. Phys. Rev. A
**2009**, 79, 052110. [Google Scholar] [CrossRef] - Brukner, Č.; Taylor, S.; Cheung, S.; Vedral, V. Quantum entanglement in time. arXiv
**2004**, arXiv:quant-ph/0402127. [Google Scholar] - Ringbauer, M.; Costa, F.; Goggin, M.E.; White, A.G.; Fedrizzi, A. Multi-time quantum correlations with no spatial analog’. NPJ Quantum Inf.
**2018**, 4, 37. [Google Scholar] [CrossRef] - Megidish, E.; Halevy, A.; Shacham, T.; Dvir, T.; Dovrat, L.; Eisenberg, H.S. Entanglement swapping between photons that have never coexisted. Phys. Rev. Lett.
**2013**, 110, 210403. [Google Scholar] [CrossRef] [PubMed] - Katz, J.; Lindell, Y. Introduction to Modern Cryptography; CRC Press: Boca Raton, FL, USA, 2014. [Google Scholar]
- Greenberger, D.; Horne, M.A.; Zeilinger, A. Going Beyond Bell’s Theorem. arXiv
**2007**, arXiv:0712.0921. [Google Scholar] - Carvacho, G.; Graffitti, F.; D’Ambrosio, V.; Hiesmayr, B.C.; Sciarrino, F. Experimental investigation on the geometry of GHZ states. Sci. Rep.
**2017**, 7, 13265. [Google Scholar] [CrossRef] [PubMed] - Megidish, E.; Shacham, T.; Halevy, A.; Dovrat, L.; Eisenberg, H.S. Resource efficient source of multiphoton polarization entanglement. Phys. Rev. Lett.
**2012**, 109, 080504. [Google Scholar] [CrossRef] - Megidish, E.; Halevy, A.; Pilnyak, Y.; Slapa, A.; Eisenberg, H.S. Quantum tomography of inductively-created large multiphoton states. arXiv
**2017**, arXiv:1712.03633. [Google Scholar] - Deutsch, D. Quantum theory, the Church–Turing principle and the universal quantum computer. Proc. R. Soc. Lond. A Math. Phys. Sci.
**1985**, 4, 97. [Google Scholar] [CrossRef] - Deutsch, D.; Jozsa, R. Rapid solution of problems by quantum computation. Proc. R. Soc. Lond. A Math. Phys. Sci.
**1992**, 439, 553. [Google Scholar] [CrossRef] - Grover, L. Quantum Mechanics Helps in Searching for a Needle in a Haystack. Phys. Rev. Lett.
**1997**, 79, 325. [Google Scholar] [CrossRef] - McCutcheon, W.; Pappa, A.; Bell, B.A.; McMillan, A.; Chailloux, A.; Lawson, T.; Mafu, M.; Markham, D.; Diamanti, E.; Kerenidis, I.; et al. Experimental verification of multipartite entanglement in quantum networks. Nat. Commun.
**2016**, 7, 13251. [Google Scholar] [CrossRef] - Cachin, C.; Vukolić, M. Blockchain Consensus Protocols in the Wild. arXiv
**2017**, arXiv:1707.01873. [Google Scholar] - Vukolić, M. The quest for scalable blockchain fabric: Proof-of-work vs. BFT replication. In Proceedings of the International Workshop on Open Problems in Network Security, Zurich, Switzerland, 29 October 2015. [Google Scholar]
- Gramoli, V. From blockchain consensus back to Byzantine consensus. Future Gener. Comput. Syst.
**2017**. [Google Scholar] [CrossRef] - Narayanan, A.; Clark, J. Bitcoin’s academic pedigree. Commun. ACM
**2017**, 15, 36–45. [Google Scholar] [CrossRef] - Bruschi, D.E.; Ralph, T.; Fuentes, I.; Jennewein, T.; Razavi, M. Spacetime effects on satellite-based quantum communications. Phys. Rev. D
**2014**, 90, 045041. [Google Scholar] [CrossRef] - Bruschi, D.E.; Sabín, C.; White, A.; Baccetti, V.; Oi, D.K.L.; Fuentes, I. Testing the effects of gravity and motion on quantum entanglement in space-based experiments. New J. Phys.
**2014**, 16, 053041. [Google Scholar] [CrossRef] - Olson, J.S.; Ralph, T.C. Entanglement between the future and the past in the quantum vacuum. Phys. Rev. Lett.
**2011**, 106, 110404. [Google Scholar] [CrossRef] [PubMed] - Olson, J.S.; Ralph, T.C. Extraction of timelike entanglement from the quantum vacuum. Phys. Rev. A
**2012**, 85, 012306. [Google Scholar] [CrossRef] - Sabín, C.; Peropadre, B.; del Rey, M.; Martín-Martínez, E. Extracting past-future vacuum correlations using circuit QED. Phys. Rev. Lett.
**2012**, 109, 033602. [Google Scholar] [CrossRef] - Oreshkov, O.; Costa, F.; Brukner, Č. Quantum correlations with no causal order. Nat. Commun.
**2012**, 3, 1092. [Google Scholar] [CrossRef] [PubMed] - Brukner, Č. Quantum causality. Nat. Phys.
**2014**, 10, 259. [Google Scholar] [CrossRef] - Chaves, R.; Majenz, C.; Gross, D. Information–theoretic implications of quantum causal structures. Nat. Commun.
**2015**, 6, 5766. [Google Scholar] [CrossRef] - Nowakowski, M. Quantum entanglement in time. AIP Conf. Proc.
**2017**, 1841, 020007. [Google Scholar] - Nowakowski, M.; Cohen, E.; Horodecki, P. Entangled histories versus the two-state-vector formalism: Towards a better understanding of quantum temporal correlations. Phys. Rev. A
**2018**, 98, 032312. [Google Scholar] [CrossRef] - Lloyd, S.; Maccone, L.; Garcia-Patron, R.; Giovannetti, V.; Shikano, Y.; Pirandola, S.; Rozema, L.A.; Darabi, A.; Soudagar, Y.; Shalm, L.K.; et al. Closed timelike curves via post-selection: Theory and experimental demonstration. Phys. Rev. Lett.
**2011**, 106, 040403. [Google Scholar] [CrossRef] [PubMed] - Lloyd, S.; Maccone, L.; Garcia-Patron, R.; Giovannetti, V.; Shikano, Y. Quantum mechanics of time travel through post-selected teleportation. Phys. Rev.
**2011**, D84, 025007. [Google Scholar] [CrossRef] - Visser, M. Lorentzian Wormholes: From Einstein to Hawking; Springer: Berlin, Germany, 1995. [Google Scholar]
- Hawking, S.W. The chronology protection conjecture. Phys. Rev.
**1992**, D46, 603–611. [Google Scholar] [CrossRef] - Visser, M. The quantum physics of chronology protection. In The future of Theoretical Physics and Cosmology: Celebrating Stephen Hawking’s 60th Birthday, Proceedings of the Workshop and Symposium, Cambridge, UK, 7–10 January 2002; Cambridge University Press: Cambridge, UK, 2002; pp. 161–176. [Google Scholar]
- Visser, M. From wormhole to time machine: Comments on Hawking’s chronology protection conjecture. Phys. Rev.
**1993**, D47, 554–565. [Google Scholar] - Ringbauer, M.; Giarmatzi, C.; Chaves, R.; Costa, F.; White, A.G.; Fedrizzi, A. Experimental test of nonlocal causality. Sci. Adv.
**2016**, 2, e1600162. [Google Scholar] [CrossRef] [PubMed]

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Rajan, D.; Visser, M.
Quantum Blockchain Using Entanglement in Time. *Quantum Rep.* **2019**, *1*, 3-11.
https://doi.org/10.3390/quantum1010002

**AMA Style**

Rajan D, Visser M.
Quantum Blockchain Using Entanglement in Time. *Quantum Reports*. 2019; 1(1):3-11.
https://doi.org/10.3390/quantum1010002

**Chicago/Turabian Style**

Rajan, Del, and Matt Visser.
2019. "Quantum Blockchain Using Entanglement in Time" *Quantum Reports* 1, no. 1: 3-11.
https://doi.org/10.3390/quantum1010002