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Quantum Information Processing
Published in: Quantum Information Processing 2/2024

01-02-2024

Remote state preparation by multiple observers using a single copy of a two-qubit entangled state

Authors: Shounak Datta, Shiladitya Mal, Arun K. Pati, A. S. Majumdar

Published in: Quantum Information Processing | Issue 2/2024

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Abstract

We consider a scenario of remote state preparation (RSP) of qubits in the context of sequential network scenario. A single copy of an entangled state is shared between Alice on one side, and several Bobs on the other, who sequentially perform unsharp single-particle measurements in order to prepare a specific state. In the given scenario without any shared randomness between the various Bobs, we first determine the classical bound of fidelity for the preparation of remote states by the Bobs. We then show that there can be at most 6 number of Bobs who can sequentially and independently prepare the remote qubit state in Alice’s lab with fidelity exceeding the classical bound in the presence of shared quantum correlations. The upper bound is achieved when the singlet state is initially shared between Alice and the first Bob and every Bob prepares a state chosen from the equatorial circle of the Bloch sphere. Then, we introduce a new RSP protocol for non-equatorial ensemble of states. The maximum number of Bobs starts to decrease from six when either the choice of remote states is shifted from the equatorial circle towards the poles of the Bloch sphere, or when the initial state shifts towards non-maximally entangled pure and mixed states.
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Appendix
Available only for authorised users
Footnotes
1
If Alice chooses two pure states, e.g. \(|\psi ^p_1\rangle = \cos (\frac{\theta }{2})|0\rangle +e^{i\phi ^p_1} \sin (\frac{\theta }{2})|1\rangle \) (\(0\le \phi ^p_1\le 2\pi \)) and \(|\psi ^p_2\rangle = \cos (\frac{\theta }{2})|0\rangle +e^{i\phi ^p_2} \sin (\frac{\theta }{2})|1\rangle \) (\(0\le \phi ^p_2\le 2\pi \)) randomly from the specified circle with fixed polar angle, \(\theta \) of the Bloch sphere depending upon the CC from Bob, then we have \(f_{cl} = \frac{3}{4} + \frac{\cos 2\theta }{4} + \frac{\sin ^3\theta ~\sin \theta _B}{8} [\cos (\phi _B - \phi ^p_1)-\cos (\phi _B - \phi ^p_2) ] \le \frac{3}{4} + \frac{\cos 2\theta + \sin ^3 \theta }{4}\) where the maximum occurs when \(\theta _B= \frac{\pi }{2}, \phi _B - \phi ^p_1 = 0 ~\text {or}~ 2\pi , \phi _B - \phi ^p_2 = \pm \pi \).
 
2
Let us consider that, Alice applies a general 2\(\times \)2 unitary matrix having the form, \(U=\begin{pmatrix} \cos (\frac{\zeta }{2}) ~e^{i(\frac{\iota +\kappa }{2})} &{} \sin (\frac{\zeta }{2}) ~e^{-i(\frac{\iota -\kappa }{2})}\\ -\sin (\frac{\zeta }{2}) ~e^{i(\frac{\iota -\kappa }{2})} &{} \cos (\frac{\zeta }{2}) ~e^{-i(\frac{\iota +\kappa }{2})}\\ \end{pmatrix}\) next to her prefixed chosen set of unitaries \(\lbrace \mathbb {I}_2, \sigma _z \rbrace \). Hence, the average fidelity in the given scenario between Alice and Bob\(^i\) (\(i\ge 2\)) becomes, \(f_{av}^{AB^i} \big (\rho _{A|E_{+(-)}^{\lambda _i}}^i, |\psi ^i_{(\bot )}\rangle \big ) = \frac{1}{2} + \frac{\lambda _i}{2^i} ~\prod _{k=1}^{i-1} \big (1+\sqrt{1-\lambda _k^2}\big ) ~[\cos ^2(\frac{\zeta }{2}) ~\cos (\iota +\kappa ) - \sin ^2(\frac{\zeta }{2}) ~\cos (\iota -\kappa -2\phi _i)]\), which is maximum when \(\zeta =\iota =\kappa = 0 ~\text {or} ~2\pi \), i.e., \(U=\mathbb {I}_2\).
 
Literature
1.
Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70, 1895 (1993)ADSMathSciNetPubMedCrossRef
2.
Pan, J.-W., Chen, Z.-B., Lu, C.-Y., Weinfurter, H., Zeilinger, A., Żukowski, M.: Multiphoton entanglement and interferometry. Rev. Mod. Phys. 84, 777 (2012)ADSCrossRef
3.
4.
Pati, A.K.: Minimum classical bit for remote preparation and measurement of a qubit. Phys. Rev. A 63, 014302 (2000)ADSCrossRef
5.
Bennett, C.H., DiVincenzo, D.P., Shor, P.W., Smolin, J.A., Terhal, B.M., Wootters, W.K.: Remote state preparation. Phys. Rev. Lett. 87, 077902 (2001)ADSPubMedCrossRef
6.
7.
8.
Peng, X., Zhu, X., Fang, X., Feng, M., Liu, M., Gao, K.: Experimental implementation of remote state preparation by nuclear magnetic resonance. Phys. Lett. A 306(5), 271 (2003)ADSCrossRef
9.
Babichev, S.A., Brezger, B., Lvovsky, A.I.: Remote preparation of a single-mode photonic qubit by measuring field quadrature noise. Phys. Rev. Lett. 92, 047903 (2004)ADSPubMedCrossRef
10.
Liu, W.-T., Wu, W., Ou, B.-Q., Chen, P.-X., Li, C.-Z., Yuan, J.-M.: Experimental remote preparation of arbitrary photon polarization states. Phys. Rev. A 76, 022308 (2007)ADSCrossRef
11.
Xiang, G.-Y., Li, J., Yu, B., Guo, G.-C.: Remote preparation of mixed states via noisy entanglement. Phys. Rev. A 72, 012315 (2005)ADSCrossRef
12.
Christ, A., Silberhorn, C.: Limits on the deterministic creation of pure single-photon states using parametric down-conversion. Phys. Rev. A 85, 023829 (2012)ADSCrossRef
13.
Jiao, X.-F., Zhou, P., Lv, S.-X., Wang, Z.-Y.: Remote preparation for single-photon two-qubit hybrid state with hyperentanglement via linear-optical elements. Sci. Rep. 9, 4663 (2019)ADSPubMedPubMedCentralCrossRef
14.
Rosenfeld, W., Berner, S., Volz, J., Weber, M., Weinfurter, H.: Remote preparation of an atomic quantum memory. Phys. Rev. Lett. 98, 050504 (2007)ADSPubMedCrossRef
15.
Nguyen, B.A., Kim, J.: Joint remote state preparation. J. Phys. B: At. Mol. Opt. Phys. 41(9), 095501 (2008)ADSCrossRef
16.
Chaudhary, M., Fadel, M., Ilo-Okeke, E.O., Pyrkov, A.N., Ivannikov, V., Byrnes, T.: Remote state preparation of two-component Bose-Einstein condensates. Phys. Rev. A 103, 062417 (2021)ADSMathSciNetCrossRef
17.
Wang, M.-Y., Yan, F., Gao, T.: Remote preparation for single-photon state in two degrees of freedom with hyper-entangled states. Front. Phys. 16, 41501 (2021)ADSCrossRef
18.
Cameron, A.R., Cheng, S.W.L., Schwarz, S., Kapahi, C., Sarenac, D., Grabowecky, M., Cory, D.G., Jennewein, T., Pushin, D.A., Resch, K.J.: Remote state preparation of single-photon orbital-angular-momentum lattices. Phys. Rev. A 104, 051701 (2021)ADSCrossRef
19.
Paris, M.G.A., Cola, M., Bonifacio, R.: Remote state preparation and teleportation in phase space. J. Opt. B: Quantum Semiclass. Opt. 5(3), 360 (2003)ADSCrossRef
20.
Dakić, B., Lipp, Y.O., Ma, X., Ringbauer, M., Kropatschek, S., Barz, S., Paterek, T., Vedral, V., Zeilinger, A., Brukner, C., Walther, P.: Quantum discord as resource for remote state preparation. Nat. Phys. 8(9), 666 (2012)CrossRef
21.
22.
Kanjilal, S., Khan, A., Jebarathinam, C., Home, D.: Remote state preparation using correlations beyond discord. Phys. Rev. A 98, 062320 (2018)ADSCrossRef
23.
Horodecki, P., Tuziemski, J., Mazurek, P., Horodecki, R.: Can communication power of separable correlations exceed that of entanglement resource? Phys. Rev. Lett. 112, 140507 (2014)ADSPubMedCrossRef
24.
25.
Hayashi, A., Hashimoto, T., Horibe, M.: Remote state preparation without oblivious conditions. Phys. Rev. A 67, 052302 (2003)ADSCrossRef
26.
Silva, R., Gisin, N., Guryanova, Y., Popescu, S.: Multiple observers can share the nonlocality of half of an entangled pair by using optimal weak measurements. Phys. Rev. Lett. 114, 250401 (2015)ADSPubMedCrossRef
27.
Mal, S., Majumdar, A.S., Home, D.: Sharing of nonlocality of a single member of an entangled pair of qubits is not possible by more than two unbiased observers on the other wing. Mathematics 4(3), 48 (2016)CrossRef
28.
Hu, M.-J., Zhou, Z.-Y., Hu, X.-M., Li, C.-F., Guo, G.-C., Zhang, Y.-S.: Observation of non-locality sharing among three observers with one entangled pair via optimal weak measurement. NPJ Quantum Inf 4(1), 63 (2018)ADSCrossRef
29.
Schiavon, M., Calderaro, L., Pittaluga, M., Vallone, G., Villoresi, P.: Three-observer bell inequality violation on a two-qubit entangled state. Quantum Sci. Technol. 2(1), 015010 (2017)ADSCrossRef
30.
Feng, T., Ren, C., Tian, Y., Luo, M., Shi, H., Chen, J., Zhou, X.: Observation of nonlocality sharing via not-so-weak measurements. Phys. Rev. A 102, 032220 (2020)ADSCrossRef
31.
Das, D., Ghosal, A., Sasmal, S., Mal, S., Majumdar, A.S.: Facets of bipartite nonlocality sharing by multiple observers via sequential measurements. Phys. Rev. A 99, 022305 (2019)ADSCrossRef
32.
33.
Bera, A., Mal, S., Sen, A., Sen, U.: Witnessing bipartite entanglement sequentially by multiple observers. Phys. Rev. A 98, 062304 (2018)ADSCrossRef
34.
Maity, A.G., Das, D., Ghosal, A., Roy, A., Majumdar, A.S.: Detection of genuine tripartite entanglement by multiple sequential observers. Phys. Rev. A 101, 042340 (2020)ADSCrossRef
35.
Srivastava, C., Mal, S., Sen, A., Sen, U.: Sequential measurement-device-independent entanglement detection by multiple observers. Phys. Rev. A 103, 032408 (2021)ADSMathSciNetCrossRef
36.
Sasmal, S., Das, D., Mal, S., Majumdar, A.S.: Steering a single system sequentially by multiple observers. Phys. Rev. A 98, 012305 (2018)ADSCrossRef
37.
Shenoy, H., Designolle, S., Hirsch, F., Silva, R., Gisin, N., Brunner, N.: Unbounded sequence of observers exhibiting Einstein–Podolsky–Rosen steering. Phys. Rev. A 99, 022317 (2019)ADSCrossRef
38.
Gupta, S., Maity, A.G., Das, D., Roy, A., Majumdar, A.S.: Genuine Einstein–Podolsky–Rosen steering of three-qubit states by multiple sequential observers. Phys. Rev. A 103, 022421 (2021)ADSMathSciNetCrossRef
39.
Datta, S., Majumdar, A.S.: Sharing of nonlocal advantage of quantum coherence by sequential observers. Phys. Rev. A 98, 042311 (2018)ADSCrossRef
40.
Roy, S., Bera, A., Mal, S., Sen, A., Sen, U.: Recycling the resource: Sequential usage of shared state in quantum teleportation with weak measurements. Phys. Lett. A 392, 127143 (2021)MathSciNetCrossRef
41.
Curchod, F.J., Johansson, M., Augusiak, R., Hoban, M.J., Wittek, P., Acín, A.: Unbounded randomness certification using sequences of measurements. Phys. Rev. A 95, 020102 (2017)ADSCrossRef
42.
Das, A.K., Das, D., Mal, S., Home, D., Majumdar, A.S.: Resource-theoretic efficacy of the single copy of a two-qubit entangled state in a sequential network. Quantum Inf. Process. 21, 1–29 (2022)MathSciNetCrossRef
43.
Brown, P.J., Colbeck, R.: Arbitrarily many independent observers can share the nonlocality of a single maximally entangled qubit pair. Phys. Rev. Lett. 125, 090401 (2020)ADSMathSciNetPubMedCrossRef
44.
45.
Bužek, V., Hillery, M., Werner, R.F.: Optimal manipulations with qubits: Universal-not gate. Phys. Rev. A 60, 2626–2629 (1999)ADSMathSciNetCrossRef
46.
47.
Wu, W., Liu, W.-T., Chen, P.-X., Li, C.-Z.: Deterministic remote preparation of pure and mixed polarization states. Phys. Rev. A 81, 042301 (2010)ADSCrossRef
48.
Costa, A.C.S., Beims, M.W., Angelo, R.M.: Generalized discord, entanglement, Einstein–Podolsky–Rosen steering, and bell nonlocality in two-qubit systems under (non-)markovian channels: Hierarchy of quantum resources and chronology of deaths and births. Phys. A: Stat. Mech. App. 461, 469 (2016)MathSciNetCrossRef
49.
Busch, P., Lahti, P.J., Mittelstaedt, P.: The Quantum Theory of Measurement. Springer, New York (1996)
50.
51.
Dakić, B., Vedral, V., Brukner, V.: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502 (2010)ADSPubMedCrossRef
52.
53.
Werner, R.F.: Quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277–4281 (1989)ADSCrossRef
54.
Hill, S.A., Wootters, W.K.: Entanglement of a pair of quantum bits. Phys. Rev. Lett. 78, 5022–5025 (1997)ADSCrossRef
55.
56.
Bennett, C.H., Brassard, G., Crepeau, C., Maurer, U.M.: Generalized privacy amplification. IEEE Trans. Inf. Theory 41(6), 1915–1923 (1995)MathSciNetCrossRef
57.
Brassard, G., Cleve, R., Tapp, A.: Cost of exactly simulating quantum entanglement with classical communication. Phys. Rev. Lett. 83, 1874–1877 (1999)ADSCrossRef
58.
Bowles, J., Hirsch, F., Quintino, M.T., Brunner, N.: Local hidden variable models for entangled quantum states using finite shared randomness. Phys. Rev. Lett. 114, 120401 (2015)ADSPubMedCrossRef
59.
Guha, T., Alimuddin, M., Rout, S., Mukherjee, A., Bhattacharya, S.S., Banik, M.: Quantum advantage for shared randomness generation. Quantum 5, 569 (2021)CrossRef
60.
An, N.B., Kim, J.: Collective remote state preparation. Int. J. Quant. Inf. 06(05), 1051 (2008)CrossRef
61.
Yang, R.-Y., Liu, J.-M.: Enhancing the fidelity of remote state preparation by partial measurements. Quantum Inf. Process. 16, 1 (2017)ADSMathSciNetCrossRef
62.
Peters, N.A., Wei, T.-C., Kwiat, P.G.: Mixed-state sensitivity of several quantum-information benchmarks. Phys. Rev. A 70, 052309 (2004)ADSCrossRef
Metadata
Title
Remote state preparation by multiple observers using a single copy of a two-qubit entangled state
Authors
Shounak Datta
Shiladitya Mal
Arun K. Pati
A. S. Majumdar
Publication date
01-02-2024
Publisher
Springer US
Published in
Quantum Information Processing / Issue 2/2024
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-024-04263-7

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