Distillation of maximally correlated bosonic matter from many-body quantum coherence

Tyler J. Volkoff

Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA

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


We construct quantum coherence resource theories in symmetrized Fock space (QCRTF), thereby providing an information-theoretic framework that connects analyses of quantum coherence in discrete-variable (DV) and continuous variable (CV) bosonic systems. Unlike traditional quantum coherence resource theories, QCRTF can be made independent of the single-particle basis and allow to quantify coherence within and between particle number sectors. For example, QCRTF can be formulated in such a way that neither Bose-Einstein condensates nor Heisenberg-Weyl coherent states are considered as quantum many-body coherence resources, whereas spin-squeezed and quadrature squeezed states are. The QCRTF framework is utilized to calculate the optimal asymptotic distillation rate of maximally correlated bosonic states both for particle number conserving resource states and resource states of indefinite particle number. In particular, we show how to generate a uniform superposition of maximally correlated bosonic states from a state of maximal bosonic coherence with asymptotically unit efficiency using only free operations in the QCRTF.

► BibTeX data

► References

[1] U. L. Andersen, J. S. Neergaard-Nielsen, P. van Loock, and A. Furusawa, ``Hybrid discrete- and continuous-variable quantum information,'' Nat. Phys. 11, 713 (2015).

[2] K. Xia and J. Twamley, ``Generating spin squeezing states and Greenberger-Horne-Zeilinger entanglement using a hybrid phonon-spin ensemble in diamond,'' Phys. Rev. B 94, 205118 (2016).

[3] X.-Q. Xiao, J. Zhu, G. Guangqiang He, and G. Zeng, ``A scheme for generating a multi-photon NOON state based on cavity QED,'' Quantum Inf. Process. 12, 449 (2013).

[4] N. Killoran, F. E. S. Steinhoff, and M. B. Plenio, ``Converting nonclassicality into entanglement,'' Phys. Rev. Lett. 116, 080402 (2016).

[5] I. Marvian and R. W. Spekkens, ``How to quantify coherence: Distinguishing speakable and unspeakable notions,'' Phys. Rev. A 94, 052324 (2016).

[6] T. Baumgratz, M. Cramer, and M. B. Plenio, ``Quantifying coherence,'' Phys. Rev. Lett. 113, 140401 (2014).

[7] D. E. Browne, J. Eisert, S. Scheel, and M. B. Plenio, ``Driving non-Gaussian to Gaussian states with linear optics,'' Phys. Rev. A 67, 062320 (2003).

[8] K. C. Tan, T. Volkoff, H. Kwon, and H. Jeong, ``Quantifying the coherence between coherent states,'' Phys. Rev. Lett. 119, 190405 (2017).

[9] Y.-R. Zhang, L.-H. Shao, Y. Li, and H. Fan, ``Quantifying coherence in infinite-dimensional systems,'' Phys. Rev. A 93, 012334 (2016).

[10] J. Xu, ``Quantifying coherence of Gaussian states,'' Phys. Rev. A 93, 032111 (2016).

[11] R. Bartosz, M. Piani, M. Cianciaruso, T. R. Bromley, A. Streltsov, and G. Adesso, ``Converting multilevel nonclassicality into genuine multipartite entanglement,'' New J. Phys. 20, 033012 (2018).

[12] A. Winter and D. Yang, ``Operational resource theory of coherence,'' Phys. Rev. Lett. 116, 120404 (2016).

[13] Y. Yao, X. Xiao, L. Ge, and C. P. Sun, ``Quantum coherence in multipartite systems,'' Phys. Rev. A 92, 022112 (2015).

[14] C. Radhakrishnan, M. Parthasarathy, S. Jambulingam, and T. Byrnes, ``Distribution of quantum coherence in multipartite systems,'' Phys. Rev. Lett. 116, 150504 (2016).

[15] J. Sperling, A. Perez-Leija, K. Busch, and I. A. Walmsley, ``Quantum coherences of indistinguishable particles,'' Phys. Rev. A 96, 032334 (2017).

[16] N. Killoran, M. Cramer, and M. B. Plenio, ``Extracting entanglement from identical particles,'' Phys. Rev. Lett. 112, 150501 (2014).

[17] T. J. Volkoff and Y. Kwon, ``Spatial distribution of superfluidity and superfluid distillation of Bose liquids,'' Phys. Rev. B 98, 014519 (2018).

[18] Z. Jiang, A. B. Tacla, and C. M. Caves, ``Bosonic particle-correlated states: A nonperturbative treatment beyond mean field,'' Phys. Rev. A 96, 023621 (2017).

[19] A. Harrow, ``The church of the symmetric subspace,'' arXiv 1308.6595 (2011).

[20] S. Aaronson and A. Arkhipov, ``The computational complexity of linear optics,'' in Proceedings of the 43rd Annual ACM Symposium on Theory of Computing (ACM, 2011) p. 333.

[21] H. M. Wiseman and J. A. Vaccaro, ``Entanglement of indistinguishable particles shared between two parties,'' Phys. Rev. Lett. 91, 097902 (2003).

[22] O. Bratteli and D. W. Robinson, Operator algebras and quantum statistical mechanics 2 (Springer, New York, 1997).

[23] E. Chitambar and G. Gour, ``Critical examination of incoherent operations and a physically consistent resource theory of quantum coherence,'' Phys. Rev. Lett. 117, 030401 (2016).

[24] A. Serafini, Quantum Continuous Variables (CRC Press, Florida, 2017).

[25] K. R. Parthasarathy, Probability measures on metric spaces (Academic Press, New York, 1967).

[26] D. Braun, ``Invariant integration over the orthogonal group,'' J. Phys. A: Math. Gen. 39, 14581 (2006).

[27] L. Fallani, C. Fort, and M. Inguscio, ``Bose–Einstein Condensates in Disordered Potentials,'' in Advances in Atomic, Molecular, and Optical Physics, Advances In Atomic, Molecular, and Optical Physics, Vol. 56 (Academic Press, 2008) pp. 119 – 160. https:/​/​doi.org/​10.1016/​S1049-250X(08)00012-8.

[28] Q. Zhao, Y. Liu, Y. Yuan, E. Chitambar, and A. Winter, ``One-Shot Coherence Distillation: Towards Completing the Picture,'' IEEE Trans. Inf. Theory 65, 6441 (2018).

[29] C. K. Hong, Z. Y. Ou, and L. Mandel, ``Measurement of subpicosecond time intervals between two photons by interference,'' Phys. Rev. Lett. 59, 2044–2046 (1987).

[30] K. K. Sabapathy and A. Winter, ``Non-Gaussian operations on bosonic modes of light: Photon-added Gaussian channels,'' Phys. Rev. A 95, 062309 (2017).

[31] R. J. Glauber, ``Photon correlations,'' Phys. Rev. Lett. 10, 84–86 (1963a).

[32] R. J. Glauber, ``The quantum theory of optical coherence,'' Phys. Rev. 130, 2529–2539 (1963b).

[33] R. J. Glauber, ``Coherent and incoherent states of the radiation field,'' Phys. Rev. 131, 2766–2788 (1963c).

[34] A. Bach and U. Luxmann-Ellinghaus, ``The simplex structure of the classical states of the quantum harmonic oscillator,'' Comm. Math. Phys. 107, 553–560 (1986).

[35] A. Perelomov, Generalized Coherent States and Their Applications (Springer-Verlag, Berlin, 1986).

[36] M. M. Nieto, ``Displaced and squeezed number states,'' Phys. Lett. A 229, 135 (1997).

[37] L.-F. Qiao, A. Streltsov, J. Gao, S. Rana, R.-J. Ren, Z.-Q. Jiao, C.-Q. Hu, X.-Y. Xu, C.-Y. Wang, H. Tang, A.-L. Yang, Z.-H. Ma, M. Lewenstein, and X.-M. Jin, ``Entanglement activation from quantum coherence and superposition,'' Phys. Rev. A 98, 052351 (2018).

[38] K. C. Tan, S. Choi, H. Kwon, and H. Jeong, ``Coherence, quantum Fisher information, superradiance, and entanglement as interconvertible resources,'' Phys. Rev. A 97, 052304 (2018).

[39] M. M. Wilde, Quantum Information Theory, 2nd Ed. (Cambridge University Press, Cambridge, 2017).

[40] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000).

[41] E. Chitambar, D. Leung, L. Mancinska, M. Ozols, and A. Winter, ``Everything You Always Wanted to Know About LOCC (But Were Afraid to Ask),'' Commun. Math. Phys. 328, 303 (2014).

[42] A. P. Lund, H. Jeong, T. C. Ralph, and M. S. Kim, ``Conditional production of superpositions of coherent states with inefficient photon detection,'' Phys. Rev. A 70, 020101 (2004).

[43] M. Kitagawa and M. Ueda, ``Squeezed spin states,'' Phys. Rev. A 47, 5138–5143 (1993).

[44] X. Yuan, H. Zhou, Z. Cao, and X. Ma, ``Intrinsic randomness as a measure of quantum coherence,'' Phys. Rev. A 92, 022124 (2015).

[45] J. Cichoń and Z. Golebiewski, ``On Bernoulli Sums and Bernstein Polynomials,'' in 23rd Intl. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA 12) (2012) p. 179.

[46] T. M. Cover and J. A. Thomas, Elements of Information Theory (John Wiley and Sons, Inc., New York, 1991).

[47] G. Giedke and J. Ignacio Cirac, ``Characterization of Gaussian operations and distillation of Gaussian states,'' Phys. Rev. A 66, 032316 (2002).

[48] T. J. Volkoff and C. M. Herdman, ``Generating accessible entanglement in bosons via pair-correlated tunneling,'' Phys. Rev. A 100, 022331 (2019).

[49] B. Yadin, F. C. Binder, J. Thompson, V. Narasimhachar, M. Gu, and M. S. Kim, ``Operational resource theory of continuous-variable nonclassicality,'' Phys. Rev. X 8, 041038 (2018).

[50] H. Kwon, K. C. Tan, T. Volkoff, and H. Jeong, ``Nonclassicality as a quantifiable resource for quantum metrology,'' Phys. Rev. Lett. 122, 040503 (2019).

[51] T. J. Volkoff, ``Optimal and near-optimal probe states for quantum metrology of number-conserving two-mode bosonic Hamiltonians,'' Phys. Rev. A 94, 042327 (2016).

[52] T. J. Volkoff, ``Nonclassical properties and quantum resources of hierarchical photonic superposition states,'' J. Exp. Theor. Phys. 121, 770 (2015).

Cited by

[1] T. J. Volkoff and Changhyun Ryu, "Globally optimal interferometry with lossy twin Fock probes", Frontiers in Physics 12, 1369786 (2024).

The above citations are from Crossref's cited-by service (last updated successfully 2024-04-19 08:14:11) and SAO/NASA ADS (last updated successfully 2024-04-19 08:14:13). The list may be incomplete as not all publishers provide suitable and complete citation data.