×

Entanglement in quantum process algebra. (English) Zbl 1468.81017

Summary: We explicitly model entanglement in quantum processes by treating entanglement as a kind of parallelism. We introduce a shadow constant quantum operation and a so-called entanglement merge into quantum process algebra qACP. The transition rules of the shadow constant quantum operation and entanglement merge are designed. We also do a sound and complete axiomatization modulo the so-called quantum bisimilarity for the shadow constant quantum operation and entanglement merge. Then, this new type entanglement merge is extended into the full qACP. The new qACP has wide use in verification for quantum protocols, since most quantum protocols have mixtures with classical and quantum information, and also there are many quantum protocols adopting entanglement.

MSC:

81P40 Quantum coherence, entanglement, quantum correlations

References:

[1] Baeten, JCM, A brief history of process algebra, Theor. Comput. Sci. Process Algebra, 335, 131-146 (2005) · Zbl 1080.68072 · doi:10.1016/j.tcs.2004.07.036
[2] Milner, R.: Communication and Concurrency. Prentice Hall (1989) · Zbl 0683.68008
[3] Milner, R.; Parrow, J.; Walker, D., A calculus of mobile processes, Parts I and II, Inf. Comput., 1992, 1-77 (1992) · Zbl 0752.68036 · doi:10.1016/0890-5401(92)90008-4
[4] Hoare, C.A.R.: Communicating Sequential Processes. http://www.usingcsp.com/ (1985) · Zbl 0637.68007
[5] Fokkink, W.: Introduction to Process Algebra, 2nd edn. Springer (2007) · Zbl 0941.68087
[6] Plotkin, G.D.: A structural approach to operational semantics. Aarhus University, Tech Report DAIMIFN-19 (1981)
[7] Feng, Y.; Duan, RY; Ji, ZF; Ying, MS, Probabilistic bisimulations for quantum processes, Inf. Comput., 2007, 1608-1639 (2007) · Zbl 1130.68079 · doi:10.1016/j.ic.2007.08.001
[8] Gay, S.J., Nagarajan, R.: Communicating quantum processes. In: Proceedings of the 32nd ACM Symposium on Principles of Programming Languages, pp. 145-157. ACM Press, Long Beach (2005) · Zbl 1369.68207
[9] Gay, SJ; Nagarajan, R., Typechecking communicating quantum processes, Math. Struct. Comput. Sci., 2006, 375-406 (2006) · Zbl 1122.68059 · doi:10.1017/S0960129506005263
[10] Jorrand, P., Lalire, M.: Toward a quantum process algebra. In: Proceedings of the 1st ACM Conference on Computing Frontiers, pp. 111-119. ACM Press, Ischia (2005)
[11] Jorrand, P.; Lalire, M., From quantum physics to programming languages: A process algebraic approach, Lect. Notes Comput. Sci, 2005, 1-16 (2005)
[12] Lalire, M., Relations among quantum processes: Bisimilarity and congruence, Math. Struct. Comput. Sci., 2006, 407-428 (2006) · Zbl 1122.68060 · doi:10.1017/S096012950600524X
[13] Lalire, M., Jorrand, P.: A process algebraic approach to concurrent and distributed quantum computation: Operational semantics. In: Proceedings of the 2nd International Workshop on Quantum Programming Languages, pp. 109-126. TUCS General Publications (2004)
[14] Ying, M.; Feng, Y.; Duan, R.; Ji, Z., An algebra of quantum processes, ACM Trans. Comput. Logic (TOCL), 10, 1-36 (2009) · Zbl 1351.68187 · doi:10.1145/1507244.1507249
[15] Feng, Y., Duan, R., Ying, M.: Bisimulations for quantum processes. In: Proceedings of the 38th ACM Symposium on Principles of Programming Languages (POPL 11), pp. 523-534. ACM Press (2011) · Zbl 1284.68425
[16] Ekert, AK, Quantum cryptography based on Bell’s theorem, Phys. Rev. Lett., 67, 661-663 (1991) · Zbl 0990.94509 · doi:10.1103/PhysRevLett.67.661
[17] Deng, Y., Feng, Y.: Open bisimulation for quantum processes. Manuscript, arXiv:1201.0416 (2012) · Zbl 1362.68210
[18] Feng, Y., Deng, Y., Ying, M.: Symbolic bisimulation for quantum processes. Manuscript, arXiv:1202.3484 (2012)
[19] Wang, Y.: An axiomatization for quantum processes to unifying quantum and classical computing. Manuscript, arXiv:1311.2960 (2013)
[20] Duncan, R.: Types for Quantum Computing. Ph.D. Dessertation, Oxford University (2006)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.