Localizing and excluding quantum information; or, how to share a quantum secret in spacetime

Patrick Hayden1 and Alex May2

1Stanford University
2The University of British Columbia

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.


When can quantum information be localized to each of a collection of spacetime regions, while also excluded from another collection of regions? We answer this question by defining and analyzing the localize-exclude task, in which a quantum system must be localized to a collection of authorized regions while also being excluded from a set of unauthorized regions. This task is a spacetime analogue of quantum secret sharing, with authorized and unauthorized regions replacing authorized and unauthorized sets of parties. Our analysis yields the first quantum secret sharing scheme for arbitrary access structures for which the number of qubits required scales polynomially with the number of authorized sets. We also study a second related task called state-assembly, in which shares of a quantum system are requested at sets of spacetime points. We fully characterize the conditions under which both the localize-exclude and state-assembly tasks can be achieved, and give explicit protocols. Finally, we propose a cryptographic application of these tasks which we call party-independent transfer.

► BibTeX data

► References

[1] Ivette Fuentes-Schuller and Robert B Mann. Alice falls into a black hole: entanglement in noninertial frames. Physical Review Letters, 95 (12): 120404, 2005. URL https:/​/​doi.org/​10.1103/​PhysRevLett.95.120404.

[2] David Rideout, Thomas Jennewein, Giovanni Amelino-Camelia, Tommaso F Demarie, Brendon L Higgins, Achim Kempf, Adrian Kent, Raymond Laflamme, Xian Ma, Robert B Mann, et al. Fundamental quantum optics experiments conceivable with satellites reaching relativistic distances and velocities. Classical and Quantum Gravity, 29 (22): 224011, 2012. URL https:/​/​doi.org/​10.1088/​0264-9381/​29/​22/​224011.

[3] Eduardo Martin-Martinez, David Aasen, and Achim Kempf. Processing quantum information with relativistic motion of atoms. Physical Review Letters, 110 (16): 160501, 2013. URL https:/​/​doi.org/​10.1103/​PhysRevLett.110.160501.

[4] Marcin Pawłowski, Tomasz Paterek, Dagomir Kaszlikowski, Valerio Scarani, Andreas Winter, and Marek Żukowski. Information causality as a physical principle. Nature, 461 (7267): 1101–1104, 2009. https:/​/​doi.org/​10.1038/​nature08400.

[5] David Beckman, Daniel Gottesman, MA Nielsen, and John Preskill. Causal and localizable quantum operations. Physical Review A, 64 (5): 052309, 2001. https:/​/​doi.org/​10.1103/​PhysRevA.64.052309.

[6] Patrick Hayden and Alex May. Summoning information in spacetime, or where and when can a qubit be? Journal of Physics A: Mathematical and Theoretical, 49 (17): 175304, 2016. https:/​/​doi.org/​10.1088/​1751-8113/​49/​17/​175304.

[7] Emily Adlam and Adrian Kent. Quantum paradox of choice: More freedom makes summoning a quantum state harder. Physical Review A, 93 (6): 062327, 2016. https:/​/​doi.org/​10.1103/​PhysRevA.93.062327.

[8] Patrick Hayden, Sepehr Nezami, Grant Salton, and Barry C Sanders. Spacetime replication of continuous variable quantum information. New Journal of Physics, 18 (8): 083043, 2016. https:/​/​doi.org/​10.1088/​1367-2630/​18/​8/​083043.

[9] Adrian Kent. Unconstrained summoning for relativistic quantum information processing. Physical Review A, 98 (6): 062332, 2018. https:/​/​doi.org/​10.1103/​PhysRevA.98.062332.

[10] Adrian Kent. Quantum tasks in minkowski space. Classical and Quantum Gravity, 29 (22): 224013, 2012a. https:/​/​doi.org/​10.1088/​0264-9381/​29/​22/​224013.

[11] Adrian Kent. A no-summoning theorem in relativistic quantum theory. Quantum information processing, 12 (2): 1023–1032, 2013. https:/​/​doi.org/​10.1007/​s11128-012-0431-6.

[12] Patrick Hayden and John Preskill. Black holes as mirrors: quantum information in random subsystems. Journal of High Energy Physics, 2007 (09): 120, 2007. https:/​/​doi.org/​10.1088/​1126-6708/​2007/​09/​120.

[13] Ahmed Almheiri, Donald Marolf, Joseph Polchinski, and James Sully. Black holes: complementarity or firewalls? Journal of High Energy Physics, 2013 (2): 62, 2013. https:/​/​doi.org/​10.1007/​JHEP02(2013)062.

[14] Adrian Kent. Unconditionally secure bit commitment by transmitting measurement outcomes. Physical Review Letters, 109: 130501, Sep 2012b. https:/​/​doi.org/​10.1103/​PhysRevLett.109.130501.

[15] Adrian Kent. Unconditionally secure bit commitment with flying qudits. New Journal of Physics, 13 (11): 113015, 2011a. https:/​/​doi.org/​10.1088/​1367-2630/​13/​11/​113015.

[16] Adrian Kent. Coin tossing is strictly weaker than bit commitment. Physical Review Letters, 83: 5382–5384, Dec 1999. https:/​/​doi.org/​10.1103/​PhysRevLett.83.5382.

[17] Jonathan Barrett, Lucien Hardy, and Adrian Kent. No signaling and quantum key distribution. Physical Review Letters, 95: 010503, Jun 2005. https:/​/​doi.org/​10.1103/​PhysRevLett.95.010503.

[18] Jonathan Barrett, Roger Colbeck, and Adrian Kent. Unconditionally secure device-independent quantum key distribution with only two devices. Physical Review A, 86: 062326, Dec 2012. https:/​/​doi.org/​10.1103/​PhysRevA.86.062326.

[19] Adrian Kent. Location-oblivious data transfer with flying entangled qudits. Physical Review A, 84: 012328, Jul 2011b. https:/​/​doi.org/​10.1103/​PhysRevA.84.012328.

[20] Damián Pitalúa-García. Spacetime-constrained oblivious transfer. Physical Review A, 93 (6): 062346, 2016. https:/​/​doi.org/​10.1103/​PhysRevA.93.062346.

[21] Ya-Dong Wu, Abdullah Khalid, and Barry C Sanders. Efficient code for relativistic quantum summoning. New Journal of Physics, 20 (6): 063052, 2018. https:/​/​doi.org/​10.1088/​1367-2630/​aaccae.

[22] Andris Ambainis, Michele Mosca, Alain Tapp, and Ronald De Wolf. Private quantum channels. In Foundations of Computer Science, 2000. Proceedings. 41st Annual Symposium on, pages 547–553. IEEE, 2000. https:/​/​doi.org/​10.1109/​SFCS.2000.892142.

[23] Daniel Gottesman. Theory of quantum secret sharing. Physical Review A, 61 (4): 042311, 2000. https:/​/​doi.org/​10.1103/​PhysRevA.61.042311.

[24] Jérôme Javelle, Mehdi Mhalla, and Simon Perdrix. New protocols and lower bounds for quantum secret sharing with graph states. In Conference on Quantum Computation, Communication, and Cryptography, pages 1–12. Springer, 2012. https:/​/​doi.org/​10.1007/​978-3-642-35656-8_1.

[25] Adi Shamir. How to share a secret. Communications of the ACM, 22 (11): 612–613, 1979. https:/​/​doi.org/​10.1145/​359168.359176.

[26] Damian Markham and Barry C Sanders. Graph states for quantum secret sharing. Physical Review A, 78 (4): 042309, 2008. https:/​/​doi.org/​10.1103/​PhysRevA.78.042309.

[27] Pradeep Sarvepalli and Robert Raussendorf. Matroids and quantum-secret-sharing schemes. Physical Review A, 81 (5): 052333, 2010. https:/​/​doi.org/​10.1103/​PhysRevA.81.052333.

[28] Amos Beimel. Secret-sharing schemes: a survey. In International Conference on Coding and Cryptology, pages 11–46. Springer, 2011. https:/​/​doi.org/​10.1007/​978-3-642-20901-7_2.

[29] Is there a studied notion of party independent transfer? https:/​/​crypto.stackexchange.com/​questions/​44256/​is-there-a-studied-notion-of-party-independent-transfer. [Online; accessed 1-October-2017 ].

[30] Hoi-Kwong Lo and Hoi Fung Chau. Is quantum bit commitment really possible? Physical Review Letters, 78 (17): 3410, 1997. https:/​/​doi.org/​10.1103/​PhysRevLett.78.3410.

[31] Dominic Mayers. Unconditionally secure quantum bit commitment is impossible. Physical Review Letters, 78 (17): 3414, 1997. https:/​/​doi.org/​10.1103/​PhysRevLett.78.3414.

[32] Seth Lloyd. Ultimate physical limits to computation. Nature, 406: 1047–1054, 2000. https:/​/​doi.org/​10.1038/​35023282.

[33] Stephen P Jordan. Fast quantum computation at arbitrarily low energy. Physical Review A, 95 (3): 032305, 2017. https:/​/​doi.org/​10.1103/​PhysRevA.95.032305.

[34] Leonard Susskind, Larus Thorlacius, and John Uglum. The stretched horizon and black hole complementarity. Physical Review D, 48 (8): 3743, 1993. https:/​/​doi.org/​10.1103/​PhysRevD.48.3743.

[35] Daniel Harlow and Patrick Hayden. Quantum computation vs. firewalls. Journal of High Energy Physics, 2013 (6): 85, 2013. https:/​/​doi.org/​10.1007/​JHEP06(2013)085.

[36] Raphael Bousso. The holographic principle. Reviews of Modern Physics, 74 (3): 825, 2002. https:/​/​doi.org/​10.1103/​RevModPhys.74.825.

Cited by

[1] Kfir Dolev, Alex May, and Kianna Wan, "Distributing bipartite quantum systems under timing constraints", Journal of Physics A: Mathematical and Theoretical 54 14, 145301 (2021).

[2] Alex May, "Quantum tasks in holography", Journal of High Energy Physics 2019 10, 233 (2019).

[3] Damián Pitalúa-García, "One-out-of-m spacetime-constrained oblivious transfer", Physical Review A 100 1, 012302 (2019).

The above citations are from Crossref's cited-by service (last updated successfully 2021-04-21 18:48:34) and SAO/NASA ADS (last updated successfully 2021-04-21 18:48:35). The list may be incomplete as not all publishers provide suitable and complete citation data.