Collective randomized measurements in quantum information processing
Abstract: The concept of randomized measurements on individual particles has proven to be useful for analyzing quantum systems and is central for methods like shadow tomography of quantum states. We introduce $\textit{collective}$ randomized measurements as a tool in quantum information processing. Our idea is to perform measurements of collective angular momentum on a quantum system and actively rotate the directions using simultaneous multilateral unitaries. Based on the moments of the resulting probability distribution, we propose systematic approaches to characterize quantum entanglement in a collective-reference-frame-independent manner. First, we show that existing spin-squeezing inequalities can be accessible in this scenario. Next, we present an entanglement criterion based on three-body correlations, going beyond spin-squeezing inequalities with two-body correlations. Finally, we apply our method to characterize entanglement between spatially-separated two ensembles.
- A. Ketterer, N. Wyderka, and O. Gühne, Physical Review Letters 122, 120505 (2019).
- A. Ketterer, N. Wyderka, and O. Gühne, Quantum 4, 325 (2020).
- S. J. van Enk and C. W. Beenakker, Physical Review Letters 108, 110503 (2012).
- Y. Zhou, P. Zeng, and Z. Liu, Physical Review Letters 125, 200502 (2020).
- X.-D. Yu, S. Imai, and O. Gühne, Physical Review Letters 127, 060504 (2021b).
- S. Aaronson, in Proceedings of the 50th annual ACM SIGACT symposium on theory of computing (2018) pp. 325–338.
- H.-Y. Huang, R. Kueng, and J. Preskill, Nature Physics 16, 1050 (2020).
- M. Kitagawa and M. Ueda, Physical Review A 47, 5138 (1993).
- M. Horodecki, P. Horodecki, and R. Horodecki, Physical Review Letters 80, 5239 (1998).
- D. Gross, K. Audenaert, and J. Eisert, Journal of Mathematical Physics 48, 052104 (2007).
- G. Tóth and O. Gühne, Physical Review Letters 102, 170503 (2009).
- T.-C. Wei, Physical Review A 81, 054102 (2010).
- X. Wang and B. C. Sanders, Physical Review A 68, 012101 (2003).
- J. K. Korbicz, J. I. Cirac, and M. Lewenstein, Physical Review Letters 95, 120502 (2005).
- F. Bohnet-Waldraff, D. Braun, and O. Giraud, Physical Review A 94, 042343 (2016).
- G. Tóth, Physical Review A 69, 052327 (2004).
- B. Collins, S. Matsumoto, and J. Novak, arXiv preprint arXiv:2109.14890 (2022).
- P. D. Seymour and T. Zaslavsky, Advances in Mathematics 52, 213 (1984).
- T. Eggeling and R. F. Werner, Physical Review A 63, 042111 (2001).
- G. Tóth and M. W. Mitchell, New Journal of Physics 12, 053007 (2010).
- A. Peres, Physical Review Letters 77, 1413 (1996).
- M. Horodecki, P. Horodecki, and R. Horodecki, Physics Letters A 283, 1 (2001).
- I. Frérot and T. Roscilde, Physical Review Letters 126, 140504 (2021).
- G. Tóth, Physical Review A 85, 022322 (2012).
- G. Tóth and I. Apellaniz, Journal of Physics A: Mathematical and Theoretical 47, 424006 (2014).
- M. Cramer, M. B. Plenio, and H. Wunderlich, Physical Review Letters 106, 020401 (2011).
- J. Steinberg and O. Gühne, arXiv preprint arXiv:2210.13475 (2022).
- K. R. Parthasarathy, Proceedings Mathematical Sciences 114, 365 (2004).
- M. Demianowicz and R. Augusiak, Physical Review A 98, 012313 (2018).
- J. Kofler and Č. Brukner, Physical Review A 74, 050304 (2006).
- O. Gühne and G. Tóth, Physics Reports 474, 1 (2009).
- M. Gessner, A. Smerzi, and L. Pezzè, Physical Review Letters 122, 090503 (2019).
- G. Kimura, Physics Letters A 314, 339 (2003).
- R. A. Bertlmann and P. Krammer, Journal of Physics A: Mathematical and Theoretical 41, 235303 (2008).
- C. Eltschka and J. Siewert, Quantum 2, 64 (2018).
- L. Zhang, arXiv preprint arXiv:1408.3782 (2014).
- D. A. Roberts and B. Yoshida, Journal of High Energy Physics 2017, 1 (2017).
- R. J. Garcia, Y. Zhou, and A. Jaffe, Physical Review Research 3, 033155 (2021).
- S. Imai, O. Gühne, and S. Nimmrichter, Physical Review A 107, 022215 (2023).
- L. Mirsky, Monatshefte für Mathematik 79, 303 (1975).
- G. Tóth, JOSA B 24, 275 (2007).
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.