Abstract:
Many experimental setups in quantum physics use pseudorandomness in places where the theory requires randomness. In this Letter we show that the use of pseudorandomness instead of proper randomness in quantum setups has potentially observable consequences. First, we present a new loophole for Bell-like experiments: if some of the parties choose their measurements pseudorandomly, then the computational resources of the local model have to be limited in order to have a proper observation of nonlocality. Second, we show that no amount of pseudorandomness is enough to produce a mixed state by computably choosing pure states from some basis. © 2016 American Physical Society.
Registro:
Documento: |
Artículo
|
Título: | Algorithmic Pseudorandomness in Quantum Setups |
Autor: | Bendersky, A.; De La Torre, G.; Senno, G.; Figueira, S.; Acín, A. |
Filiación: | ICFO-Institut de Ciencies Fotoniques, Barcelona Institute of Science and Technology, Castelldefels (Barcelona), 08860, Spain Departamento de Computación, FCEN, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina CONICET, Godoy Cruz 2290, Buenos Aires, 1425, Argentina ICREA-Institucio Catalana de Recerca i Estudis Avançats, Lluis Companys 23, Barcelona, 08010, Spain
|
Palabras clave: | Algorithms; Computation theory; Computational resources; Local model; Mixed state; Nonlocalities; Pseudorandomness; Pure state; Quantum physics; Random processes |
Año: | 2016
|
Volumen: | 116
|
Número: | 23
|
DOI: |
http://dx.doi.org/10.1103/PhysRevLett.116.230402 |
Título revista: | Physical Review Letters
|
Título revista abreviado: | Phys Rev Lett
|
ISSN: | 00319007
|
CODEN: | PRLTA
|
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00319007_v116_n23_p_Bendersky |
Referencias:
- Odifreddi, P., Classical Recursion Theory (1999) Studies in Logic and the Foundations of Mathematics, 2. , (Elsevier, Amsterdam, The Netherlands)
- Matsumoto, M., Nishimura, T., Mersenne twister: A 623-dimensionally equidistributed uniform pseudo-random number generator (1998) ACM Trans. Model. Comput. Simul., 8, p. 3
- Figueira, S., Nies, A., Feasible analysis, randomness and base invariance (2015) Theor. Comput. Syst., 56, p. 439
- Einstein, A., Podolsky, B., Rosen, N., Can quantum-mechanical description of physical reality be considered complete? (1935) Phys. Rev., 47, p. 777
- Bohr, N., Can quantum-mechanical description of physical reality be considered complete? (1935) Phys. Rev., 48, p. 696
- Bell, J., On the Einstein Podolsky Rosen paradox (1964) Physics (N.Y.), 1, p. 195
- Conway, J., Kochen, S., The free will theorem (2006) Found. Phys., 36, p. 1441
- Koh, D.E., Hall, M.J.W., Setiawan, Pope, J.E., Marletto, C., Kay, A., Scarani, V., Ekert, A., Effects of Reduced Measurement Independence on Bell-Based Randomness Expansion (2012) Phys. Rev. Lett., 109, p. 160404
- Hall, M.J.W., Local Deterministic Model of Singlet State Correlations Based on Relaxing Measurement Independence (2010) Phys. Rev. Lett., 105, p. 250404
- Barrett, J., Gisin, N., How much Measurement Independence is Needed in Order to Demonstrate Nonlocality? (2011) Phys. Rev. Lett., 106, p. 100406
- Amselem, E., Bourennane, M., Experimental four-qubit bound entanglement (2009) Nat. Phys., 5, p. 748
- Lavoie, J., Kaltenbaek, R., Piani, M., Resch, K.J., Experimental Bound Entanglement in a Four-Photon State (2010) Phys. Rev. Lett., 105, p. 130501
- Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A., Proposed Experiment to Test Local Hidden-Variable Theories (1969) Phys. Rev. Lett., 23, p. 880
- Barrett, J., Collins, D., Hardy, L., Kent, A., Popescu, S., Quantum nonlocality, Bell inequalities, and the memory loophole (2002) Phys. Rev. A, 66, p. 042111
- Pironio, S., Acín, A., Massar, S., De La Giroday, A.B., Matsukevich D, N., Maunz, P., Olmschenk, S., Manning, T.A., Random numbers certified by Bell's theorem (2010) Nature (London), 464, p. 1021
- Pironio, S., Massar, S., Security of practical private randomness generation (2013) Phys. Rev. A, 87, p. 012336
- http://link.aps.org/supplemental/10.1103/PhysRevLett.116.230402; Gold, E.M., Language identification in the limit (1967) Inf. Control, 10, p. 447
- Lloyd, S., Ultimate physical limits to computation (2000) Nature (London), 406, p. 1047
- Boaz Barak, S.A., (2009) Computational Complexity: A Modern Approach, , (Cambridge University Press, Cambridge, UK)
- Zeugmann, T., Zilles, S., Learning recursive functions: A survey (2008) Theor. Comput. Sci., 397, p. 4
- Hensen, B., Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres (2015) Nature (London), 526, p. 682
- Giustina, M., Significant-Loophole-Free Test of Bell's Theorem with Entangled Photons (2015) Phys. Rev. Lett., 115, p. 250401
- Shalm, L.K., Strong Loophole-Free Test of Local Realism (2015) Phys. Rev. Lett., 115, p. 250402
- Abellán, C., Amaya, W., Mitrani, D., Pruneri, V., Mitchell, M.W., Generation of Fresh and Pure Random Numbers for Loophole-Free Bell Tests (2015) Phys. Rev. Lett., 115, p. 250403
- Nies, A., (2009) Computability and Randomness, Oxford Logic Guides, 51. , (Oxford University Press, Oxford, UK)
- Downey, R., Hirschfeldt, D., Algorithmic Randomness and Complexity (2010) Springer Series on Theory and Applications of Computability, , (Springer, New York)
- Li, M., Vitanyi, P., (2008) An Introduction to Kolmogorov Complexity and Its Applications, , (Springer Verlag, New York)
Citas:
---------- APA ----------
Bendersky, A., De La Torre, G., Senno, G., Figueira, S. & Acín, A.
(2016)
. Algorithmic Pseudorandomness in Quantum Setups. Physical Review Letters, 116(23).
http://dx.doi.org/10.1103/PhysRevLett.116.230402---------- CHICAGO ----------
Bendersky, A., De La Torre, G., Senno, G., Figueira, S., Acín, A.
"Algorithmic Pseudorandomness in Quantum Setups"
. Physical Review Letters 116, no. 23
(2016).
http://dx.doi.org/10.1103/PhysRevLett.116.230402---------- MLA ----------
Bendersky, A., De La Torre, G., Senno, G., Figueira, S., Acín, A.
"Algorithmic Pseudorandomness in Quantum Setups"
. Physical Review Letters, vol. 116, no. 23, 2016.
http://dx.doi.org/10.1103/PhysRevLett.116.230402---------- VANCOUVER ----------
Bendersky, A., De La Torre, G., Senno, G., Figueira, S., Acín, A. Algorithmic Pseudorandomness in Quantum Setups. Phys Rev Lett. 2016;116(23).
http://dx.doi.org/10.1103/PhysRevLett.116.230402