量子關聯性是量子資訊科學的研究核心。一般來說，量子關聯性描述測量不同子系統之 間的統計關聯性。然而，Leggett 和 Garg 在 1985 年指出，量子關聯性的概念可以擴 展到對單一系統不同時間的測量。在現代術語中，我們稱之為時間量子相關性。
在本論文中，我們將時間量子關聯性應用於測量量子因果關係以及量子資訊置亂 (quantum information scrambling)。另外，我們也研究透過量子干涉技術來控制時 間量子關聯性。
對於第一個應用，我們考慮的模型是一個在空腔內做等加速運動的量子位元。透過動力 學分析，我們發現此系統會產生契忍可夫輻射以及契忍可夫速度閾值。我們觀察到此閾 值會強烈抑制量子位元的同調性。因此，我們引入以時間量關聯性為基礎的量子因果關 係測量。我們首先考慮量子位元只與共振的空腔模態交互作用，我們發現在某些參數下 (包含量子位元的加速度與其和空腔模態的耦合強度)，量子因果關係會被完全的抑制。 我們進一步延伸分析至多空腔模態的情況。我們發現引入更多的模態會加強對量子因果 關係的抑制。
對於第二個應用，我們以量子資訊置亂作為研究課題。量子資訊置亂描述在量子演化當 中，局部量子資訊以量子糾纏的形式分散至所有可能的自由度。我們以時間量子操縱性 為基礎，提出了一個新的量子資訊置亂測量。我們也證明了，在不會產生量子資訊置亂 的演化下，此測量的值為零。
最後，我們透過干涉儀產生路徑的量子疊加，並探討了它對時間量子相關性的潛在影響。 我們考慮耗散和消相干性自旋玻色子交互作用模型。我們發現，路徑的量子疊加可以控 制量子動力學的非馬可夫性。特別是，在消相干性自旋玻色子模型中，我們可以發現從 馬可夫到非馬爾可夫的過渡轉變以及相干性捕獲。

Quantum correlations lie at the heart of modern quantum information science. Usually, quantum correlations are characterized by measurements on different subsystems. Nevertheless, it was pointed out by Leggett and Garg in 1985 that the concept of quantum correlations can be extended to measurements at different times of a single system. In modern terminology, the correlations that demonstrate non-classical nature of time-like separated measurements are termed temporal quantum correlations.
In this thesis, we apply the temporal quantum correlations on quantum causality and quantum information scrambling. Moreover, we consider an interferometric engineering scheme to modulate temporal quantum correlations.
For the first application, we consider an accelerating qubit inside a cavity. By analyzing the qubit dynamics, we can observe the Cherenkov radiation and the speed threshold. In addition, the threshold can strongly suppress the qubit coherence. We consider measurements of the quantum causality based on temporal quantum correlations. When choosing proper values for qubit acceleration and qubit-field coupling in a single-mode model, the Cherenkov threshold can eliminate quantum causal relations. We further extend the investigations to a multi-mode model. The results indicate that introducing extra modes can lead to further suppression of the quantum causality.
For the second application, we consider the topic called quantum information scrambling that describes the delocalization of local information to global information in the form of entanglement throughout all possible degrees of freedom. We propose a quantity as a scrambling witness, based on the measures of temporal steering. We justify the scrambling measure for unitary qubit channels by proving that the quantity vanishes whenever the channel is nonscrambling.
Finally, we consider a novel interferometric engineering scheme called superposed trajectories and explore its potential impacts on temporal quantum correlations. We consider the dissipative and the pure dephasing spin-boson models. The results suggest that the superposed trajectories can modulate the non-Markovianity of the quantum dynamics. We can observe a Markovian to non-Markovian transition for the pure dephasing model.

[1] Lin, J.-D. & Chen, Y.-N. Quantum direct cause across the Cherenkov threshold in circuit QED. Phys. Rev. A 102, 042223 (2020).
[2] Lin, J.-D. et al. Quantum steering as a witness of quantum scrambling. Phys. Rev. A 104, 022614 (2021).
[3] Huang, Y.-T., Lin, J.-D., Ku, H.-Y. & Chen, Y.-N. Benchmarking quantum state transfer on quantum devices. Phys. Rev. Research 3, 023038 (2021).
[4] Einstein, A., Podolsky, B. & Rosen, N. Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935).
[5] Bell, J. S. On the Einstein Podolsky Rosen paradox. Physics 1, 195 (1964).
[6] Hensen, B. et al. Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometers. Nature 526, 682–686 (2015).
[7] Giustina, M. et al. Significant-loophole-free test of Bell's theorem with entangled photons. Phys. Rev. Lett. 115, 250401 (2015).
[8] Shalm, L. K. et al. Strong loophole-free test of local realism. Phys. Rev. Lett.
115, 250402 (2015).
[9] Bennett, C. H., Brassard, G. & Ekert, A. K. Quantum cryptography. Scientific American 267, 50–57 (1992).
[10] Pirandola, S., Eisert, J., Weedbrook, C., Furusawa, A. & Braunstein, S. L. Advances in quantum teleportation. Nat. Photon. 9, 641–652 (2015).
[11] Giovannetti, V., Lloyd, S. & Maccone, L. Quantum metrology. Phys. Rev. Lett. 96, 010401 (2006).
[12] Vinjanampathy, S. & Anders, J. Quantum thermodynamics. Contemp. Phys.
57, 545–579 (2016).
[13] Eisert, J., Friesdorf, M. & Gogolin, C. Quantum many-body systems out of equilibrium. Nat. Phys. 11, 124–130 (2015).
[14] Hayden, P. & Preskill, J. Black holes as mirrors: quantum information in random subsystems. J. High Energy Phys. 2007, 120 (2007).
[15] Leggett, A. J. & Garg, A. Quantum mechanics versus macroscopic realism: Is the flux there when nobody looks? Phys. Rev. Lett. 54, 857–860 (1985).
[16] Markiewicz, M. et al. Unified approach to contextuality, nonlocality, and temporal correlations. Phys. Rev. A 89, 042109 (2014).
[17] Ringbauer, M., Costa, F., Goggin, M. E., White, A. G. & Fedrizzi, A. Multi-time quantum correlations with no spatial analog. npj Quantum Inf. 4, 1–6 (2018).
[18] Brukner, C., Taylor, S., Cheung, S. & Vedral, V. Quantum entanglement in time. arXiv 0402127 (2004).
[19] Zukowski, M. Temporal inequalities for sequential multi-time actions in quantum information processing. Front. Phys. 9, 629–633 (2014).
[20] Choi, M.-D. Completely positive linear maps on complex matrices. Linear Algebra Appl. 10, 285–290 (1975).
[21] Koashi, M. & Winter, A. Monogamy of quantum entanglement and other correlations. Phys. Rev. A 69, 022309 (2004).
[22] Breuer, H.-P. & Petruccione, F. The theory of open quantum systems (Oxford University Press on Demand, 2002).
[23] Fitzsimons, J. F., Jones, J. A. & Vedral, V. Quantum correlations which imply causation. Sci. Rep. 5, 18281 (2015).
[24] Pisarczyk, R., Zhao, Z., Ouyang, Y., Vedral, V. & Fitzsimons, J. F. Causal limit on quantum communication. Phys. Rev. Lett. 123, 150502 (2019).
[25] Pisarczyk, R., Zhao, Z., Ouyang, Y., Vedral, V. & Fitzsimons, J. F. Causal limit on quantum communication. Physical review letters 123, 150502 (2019).
[26] Ku, H.-Y. et al. Temporal steering in four dimensions with applications to coupled qubits and magnetoreception. Phys. Rev. A 94, 062126 (2016).
[27] Chen, Y.-N. et al. Temporal steering inequality. Phys. Rev. A 89, 032112 (2014).
[28] Schr¨odinger, E. Probability relations between separated systems. In Math. Proc. Cambridge Philos. Soc., vol. 31, 446 (Cambridge University Press, 1936).
[29] Uola, R., Costa, A. C. S., Nguyen, H. C. & Gu¨hne, O. Quantum steering. Rev. Mod. Phys. 92, 015001 (2020).
[30] Cavalcanti, D. & Skrzypczyk, P. Quantum steering: a review with focus on semidefinite programming. Rep. Prog. Phys. 80, 024001 (2016).
[31] Chen, S.-L. et al. Quantifying Non-Markovianity with Temporal Steering.
Phys. Rev. Lett. 116, 020503 (2016).
[32] Cherenkov, P. A. Visible emission of clean liquids by action of radiation.
Dokl. Akad. Nauk SSSR 2, 451 (1934).
[33] Vavilov, S. I. On the possible causes of blue-glow of liquids. CR Dokl. Akad. Nauk SSSR 2, 8 (1934).
[34] Tamm, I. E. & Frank, I. M. Coherent visible radiation from fast electrons passing through matter. Dokl. Akad. Nauk SSSR 14, 107 (1937).
[35] Ginzburg, V. L. Quantum theory of radiation of electron uniformly moving in medium. Zh. Eksp. Teor. Fiz 10, 589–600 (1940).
[36] Marino, J., Recati, A. & Carusotto, I. Casimir Forces and Quantum Friction from Ginzburg Radiation in Atomic Bose-Einstein Condensates. Phys. Rev. Lett. 118, 045301 (2017).
[37] Belgiorno, F., Cacciatori, S. L., Ortenzi, G., Sala, V. G. & Faccio, D. Quantum Radiation from Superluminal Refractive-Index Perturbations. Phys. Rev. Lett. 104, 140403 (2010).
[38] Kaminer, I. et al. Quantum Cˇerenkov radiation: Spectral cutoffs and the role of spin and orbital angular momentum. Phys. Rev. X 6, 011006 (2016).
[39] Scully, M. O., Kocharovsky, V. V., Belyanin, A., Fry, E. & Capasso, F. En- hancing Acceleration Radiation from Ground-State Atoms via Cavity Quantum Electrodynamics. Phys. Rev. Lett. 91, 243004 (2003).
[40] Hu, B. L. & Roura, A. Comment on “Enhancing Acceleration Radiation from Ground-State Atoms via Cavity Quantum Electrodynamics”. Phys. Rev. Lett. 93, 129301 (2004).
[41] Scully, M. O., Kocharovsky, V. V., Belyanin, A., Fry, E. & Capasso, F. Scully et al. Reply:. Phys. Rev. Lett. 93, 129302 (2004).
[42] Belyanin, A. et al. Quantum electrodynamics of accelerated atoms in free space and in cavities. Phys. Rev. A 74, 023807 (2006).
[43] Wang, H., Blencowe, M. P., Wilson, C. M. & Rimberg, A. J. Mechanically generating entangled photons from the vacuum: A microwave circuit-acoustic resonator analog of the oscillatory Unruh effect. Phys. Rev. A 99, 053833 (2019).
[44] Johansson, J. R., Johansson, G., Wilson, C. M. & Nori, F. Dynamical Casimir Effect in a Superconducting Coplanar Waveguide. Phys. Rev. Lett. 103, 147003 (2009).
[45] Sab´ın, C., Peropadre, B., Lamata, L. & Solano, E. Simulating superluminal physics with superconducting circuit technology. Phys. Rev. A 96, 032121 (2017).

[46] Felicetti, S. et al. Relativistic motion with superconducting qubits. Phys. Rev. B 92, 064501 (2015).
[47] Garc´ıa-A´lvarez, L., Felicetti, S., Rico, E., Solano, E. & Sab´ın, C. Entanglement of superconducting qubits via acceleration radiation. Sci. Rep. 7, 657 (2017).
[48] Agust´ı, A., Solano, E. & Sab´ın, C. Entanglement through qubit motion and the dynamical casimir effect. Phys. Rev. A 99, 052328 (2019).
[49] Mun˜oz, C. S., Nori, F. & De Liberato, S. Resolution of superluminal signalling in non-perturbative cavity quantum electrodynamics. Nat. Commun. 9, 1924 (2018).
[50] Jonsson, R. H., Mart´ın-Mart´ınez, E. & Kempf, A. Quantum signaling in cavity QED. Phys. Rev. A 89, 022330 (2014).
[51] Sab´ın, C., del Rey, M., Garc´ıa-Ripoll, J. J. & Leo´n, J. Fermi problem with artificial atoms in circuit QED. Phys. Rev. Lett. 107, 150402 (2011).
[52] Zohar, E. & Reznik, B. The Fermi problem in discrete systems. New J. Phys.
13, 075016 (2011).
[53] Fermi, E. Quantum theory of radiation. Rev. Mod. Phys. 4, 87–132 (1932).
[54] Srinivasan, S. J., Hoffman, A. J., Gambetta, J. M. & Houck, A. A. Tunable coupling in circuit quantum electrodynamics using a superconducting charge qubit with a v-shaped energy level diagram. Phys. Rev. Lett. 106, 083601 (2011).
[55] Gambetta, J. M., Houck, A. A. & Blais, A. Superconducting qubit with Purcell protection and tunable coupling. Phys. Rev. Lett. 106, 030502 (2011).
[56] Zhang, G., Liu, Y., Raftery, J. J. & Houck, A. A. Suppression of photon shot noise dephasing in a tunable coupling superconducting qubit. npj Quant. Inf. 3, 1–4 (2017).
[57] Kockum, A. F., Miranowicz, A., De Liberato, S., Savasta, S. & Nori, F. Ultrastrong coupling between light and matter. Nat. Rev. Phys. 1, 19 (2019).
[58] Johansson, J. R., Nation, P. & Nori, F. Qutip: An open-source Python framework for the dynamics of open quantum systems. Computer Physics Communications 183, 1760–1772 (2012).
[59] Johansson, J. R., Nation, P. D. & Nori, F. Qutip 2: A python framework for the dynamics of open quantum systems. Computer Physics Communications 184, 1234–1240 (2013).
[60] Brenna, W. G., Mann, R. B. & Mart´ın-Mart´ınez, E. Anti-unruh phenomena.
Phys. Lett. B 757, 307–311 (2016).
[61] Garay, L. J., Mart´ın-Mart´ınez, E. & de Ram´on, J. Thermalization of particle detectors: The Unruh effect and its reverse. Phys. Rev. D 94, 104048 (2016).
[62] Liu, P.-H. & Lin, F.-L. Decoherence of topological qubit in linear and circular motions: decoherence impedance, anti-Unruh and information backflow. J. High Energy Phys. 2016, 84 (2016).
[63] Li, T., Zhang, B. & You, L. Would quantum entanglement be increased by anti-Unruh effect? Phys. Rev. D 97, 045005 (2018).
[64] Breuer, H.-P., Laine, E.-M. & Piilo, J. Measure for the degree of non- Markovian behavior of quantum processes in open systems. Phys. Rev. Lett. 103, 210401 (2009).
[65] de Vega, I. & Alonso, D. Dynamics of non-Markovian open quantum systems.
Rev. Mod. Phys. 89, 015001 (2017).
[66] Ku, H.-Y., Chen, S.-L., Lambert, N., Chen, Y.-N. & Nori, F. Hierarchy in temporal quantum correlations. Phys. Rev. A 98, 022104 (2018).
[67] Maldacena, J. & Stanford, D. Remarks on the Sachdev-Ye-Kitaev model.
Phys. Rev. D 94, 106002 (2016).
[68] Nahum, A., Ruhman, J., Vijay, S. & Haah, J. Quantum Entanglement Growth under Random Unitary Dynamics. Phys. Rev. X 7, 031016 (2017).
[69] von Keyserlingk, C. W., Rakovszky, T., Pollmann, F. & Sondhi, S. L. Opera- tor Hydrodynamics, OTOCs, and Entanglement Growth in Systems without Conservation Laws. Phys. Rev. X 8, 021013 (2018).
[70] Cotler, J., Hunter-Jones, N., Liu, J. & Yoshida, B. Chaos, complexity, and random matrices. J. High Energy Phys. 2017, 48 (2017).
[71] Fan, R., Zhang, P., Shen, H. & Zhai, H. Out-of-time-order correlation for many-body localization. Science bulletin 62, 707–711 (2017).
[72] Khemani, V., Vishwanath, A. & Huse, D. A. Operator Spreading and the Emergence of Dissipative Hydrodynamics under Unitary Evolution with Conservation Laws. Phys. Rev. X 8, 031057 (2018).
[73] Page, D. N. Average entropy of a subsystem. Phys. Rev. Lett. 71, 1291–1294 (1993).
[74] Gu, Y., Qi, X.-L. & Stanford, D. Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models. J. High Energy Phys. 2017, 125 (2017).
[75] Sekino, Y. & Susskind, L. Fast scramblers. J. High Energy Phys. 2008, 065 (2008).
[76] Lashkari, N., Stanford, D., Hastings, M., Osborne, T. & Hayden, P. Towards the fast scrambling conjecture. J. High Energy Phys. 2013, 22 (2013).
[77] Gao, P., Jafferis, D. L. & Wall, A. C. Traversable wormholes via a double trace deformation. J. High Energy Phys. 2017, 151 (2017).
[78] Shenker, S. H. & Stanford, D. Black holes and the butterfly effect. J. High Energy Phys. 2014, 67 (2014).
[79] Maldacena, J., Stanford, D. & Yang, Z. Diving into traversable wormholes.
Fortschr. Phys. 65, 1700034 (2017).
[80] Roberts, D. A., Stanford, D. & Susskind, L. Localized shocks. J. High Energy Phys. 2015, 51 (2015).
[81] Shenker, S. H. & Stanford, D. Multiple shocks. J. High Energy Phys. 2014, 46 (2014).
[82] Roberts, D. A. & Stanford, D. Diagnosing chaos using four-point functions in two-dimensional conformal field theory. Phys. Rev. Lett. 115, 131603 (2015).
[83] Blake, M. Universal charge diffusion and the butterfly effect in holographic theories. Phys. Rev. Lett. 117, 091601 (2016).
[84] Kitaev, A. Hidden correlations in the Hawking radiation and thermal noise. In contribution to the Fundamental Physics Prize Symposium, vol. 10 (2014).
[85] Hosur, P., Qi, X.-L., Roberts, D. A. & Yoshida, B. Chaos in quantum channels.
J. High Energy Phys. 2016, 4 (2016).
[86] Ding, D., Hayden, P. & Walter, M. Conditional mutual information of bipartite unitaries and scrambling. J. High Energy Phys. 2016, 145 (2016).
[87] Seshadri, A., Madhok, V. & Lakshminarayan, A. Tripartite mutual information, entanglement, and scrambling in permutation symmetric systems with an application to quantum chaos. Phys. Rev. E 98, 052205 (2018).
[88] Iyoda, E. & Sagawa, T. Scrambling of quantum information in quantum many-body systems. Phys. Rev. A 97, 042330 (2018).
[89] Shen, H., Zhang, P., You, Y.-Z. & Zhai, H. Information scrambling in quantum neural networks. Phys. Rev. Lett. 124, 200504 (2020).
[90] Li, Y., Li, X. & Jin, J. Information scrambling in a collision model. Phys. Rev. A 101, 042324 (2020).
[91] Pappalardi, S. et al. Scrambling and entanglement spreading in long-range spin chains. Phys. Rev. B 98, 134303 (2018).
[92] Landsman, K. A. et al. Verified quantum information scrambling. Nature 567, 61 (2019).
[93] Ku, H.-Y., Chen, S.-L., Lambert, N., Chen, Y.-N. & Nori, F. Hierarchy in temporal quantum correlations. Phys. Rev. A 98, 022104 (2018).
[94] Chitambar, E. & Gour, G. Quantum resource theories. Reviews of Modern Physics 91, 025001 (2019).
[95] Myatt, C. J. et al. Decoherence of quantum superpositions through coupling to engineered reservoirs. Nature 403, 269–273 (2000).
[96] Liu, B.-H. et al. Experimental control of the transition from Markovian to non-Markovian dynamics of open quantum systems. Nat. Phys. 7, 931–934 (2011).
[97] Chiuri, A., Greganti, C., Mazzola, L., Paternostro, M. & Mataloni, P. Lin- ear optics simulation of quantum non-Markovian dynamics. Sci. Rep. 2, 968 (2012).
[98] Zou, C.-L. et al. Photonic simulation of system-environment interaction: Non-Markovian processes and dynamical decoupling. Phys. Rev. A 88, 063806 (2013).
[99] Yuan, J.-B., Xing, H.-J., Kuang, L.-M. & Yi, S. Quantum non-Markovian reservoirs of atomic condensates engineered via dipolar interactions. Phys. Rev. A 95, 033610 (2017).
[100] Liu, Z.-D. et al. Experimental implementation of fully controlled dephasing dynamics and synthetic spectral densities. Nat. Commun. 9, 3453 (2018).
[101] Khurana, D., Agarwalla, B. K. & Mahesh, T. S. Experimental emulation of quantum non-Markovian dynamics and coherence protection in the presence of information backflow. Phys. Rev. A 99, 022107 (2019).
[102] Garc´ıa-P´erez, G., Rossi, M. A. & Maniscalco, S. IBM Q experience as a versatile experimental testbed for simulating open quantum systems. npj Quantum Inf. 6, 1–10 (2020).
[103] Lu, Y.-N. et al. Observing information backflow from controllable non- Markovian multichannels in diamond. Phys. Rev. Lett. 124, 210502 (2020).
[104] Wiseman, H. M. Quantum theory of continuous feedback. Phys. Rev. A 49, 2133–2150 (1994).
[105] Doherty, A. C., Habib, S., Jacobs, K., Mabuchi, H. & Tan, S. M. Quantum feedback control and classical control theory. Phys. Rev. A 62, 012105 (2000).
[106] Lloyd, S. & Viola, L. Engineering quantum dynamics. Phys. Rev. A 65, 010101 (2001).
[107] Wiseman, H. M. & Milburn, G. J. Quantum measurement and control (Cam- bridge university press, 2010).
[108] Zhang, J., Liu, Y.-x., Wu, R.-B., Jacobs, K. & Nori, F. Quantum feedback: theory, experiments, and applications. Phys. Rep. 679, 1–60 (2017).
[109] Schirmer, S. G. & Wang, X. Stabilizing open quantum systems by Markovian reservoir engineering. Phys. Rev. A 81, 062306 (2010).
[110] Viola, L., Knill, E. & Lloyd, S. Dynamical decoupling of open quantum systems. Phys. Rev. Lett. 82, 2417–2421 (1999).
[111] Viola, L., Lloyd, S. & Knill, E. Universal control of decoupled quantum systems. Phys. Rev. Lett. 83, 4888–4891 (1999).
[112] Khodjasteh, K. & Lidar, D. A. Fault-tolerant quantum dynamical decoupling. Phys. Rev. Lett. 95, 180501 (2005).
[113] Yang, W., Wang, Z.-Y. & Liu, R.-B. Preserving qubit coherence by dynamical decoupling. Front. Phys. 6, 2–14 (2011).
[114] Du, J. et al. Preserving electron spin coherence in solids by optimal dynamical decoupling. Nature 461, 1265–1268 (2009).
[115] Viola, L. & Knill, E. Robust dynamical decoupling of quantum systems with bounded controls. Phys. Rev. Lett. 90, 037901 (2003).
[116] De Lange, G., Wang, Z. H., Riste, D., Dobrovitski, V. V. & Hanson, R. Universal dynamical decoupling of a single solid-state spin from a spin bath. Science 330, 60–63 (2010).
[117] Liu, G.-Q., Po, H. C., Du, J., Liu, R.-B. & Pan, X.-Y. Noise-resilient quantum evolution steered by dynamical decoupling. Nat. Commun. 4, 2254 (2013).
[118] Alonso, J. et al. Generation of large coherent states by bang-bang control of a trapped-ion oscillator. Nat. Commun. 7, 11243 (2016).
[119] Misra, B. & Sudarshan, E. G. The Zeno’s paradox in quantum theory. J. Math. Phys. 18, 756 (1977).
[120] Itano, W. M., Heinzen, D. J., Bollinger, J. J. & Wineland, D. J. Quantum Zeno effect. Phys. Rev. A 41, 2295–2300 (1990).
[121] Kofman, A. G. & Kurizki, G. Acceleration of quantum decay processes by frequent observations. Nature 405, 546–550 (2000).
[122] Fischer, M. C., Guti´errez-Medina, B. & Raizen, M. G. Observation of the quantum Zeno and anti-Zeno effects in an unstable system. Phys. Rev. Lett. 87, 040402 (2001).
[123] Facchi, P. & Pascazio, S. Quantum Zeno subspaces. Phys. Rev. Lett. 89, 080401 (2002).
[124] Koshino, K. & Shimizu, A. Quantum Zeno effect by general measurements. Phys. Rep. 412, 191–275 (2005).
[125] Chaudhry, A. Z. & Gong, J. Zeno and anti-Zeno effects on dephasing. Phys. Rev. A 90, 012101 (2014).
[126] Chaudhry, A. Z. A general framework for the quantum Zeno and anti-Zeno effects. Sci. Rep. 6, 29497 (2016).
[127] Wang, X.-B., You, J. Q. & Nori, F. Quantum entanglement via two-qubit quantum Zeno dynamics. Phys. Rev. A 77, 062339 (2008).
[128] Zhou, L., Yang, S., Liu, Y.-x., Sun, C. P. & Nori, F. Quantum Zeno switch for single-photon coherent transport. Phys. Rev. A 80, 062109 (2009).
[129] Cao, X., You, J. Q., Zheng, H., Kofman, A. G. & Nori, F. Dynamics and quantum Zeno effect for a qubit in either a low- or high-frequency bath beyond the rotating-wave approximation. Phys. Rev. A 82, 022119 (2010).
[130] Cao, X., Ai, Q., Sun, C.-P. & Nori, F. The transition from quantum Zeno to anti-Zeno effects for a qubit in a cavity by varying the cavity frequency. Phys. Lett. A 349–357.
[131] Zhang, W., Kofman, A., Zhuang, J., You, J. & Nori, F. Quantum Zeno and anti-Zeno effects measured by transition probabilities. Phys. Lett. A 1837– 1843.
[132] Ai, Q. et al. Quantum anti-Zeno effect without wave function reduction. Sci. Rep. 1752.
[133] Oi, D. K. L. Interference of quantum channels. Phys. Rev. Lett. 91, 067902 (2003).
[134] Gisin, N., Linden, N., Massar, S. & Popescu, S. Error filtration and entanglement purification for quantum communication. Phys. Rev. A 72, 012338 (2005).
[135] Chiribella, G. & Kristj´ansson, H. Quantum Shannon theory with superpositions of trajectories. Proc. R. Soc. A 475, 20180903 (2019).
[136] Loizeau, N. & Grinbaum, A. Channel capacity enhancement with indefinite causal order. Phys. Rev. A 101, 012340 (2020).
[137] Abbott, A. A., Wechs, J., Horsman, D., Mhalla, M. & Branciard, C. Communication through coherent control of quantum channels. Quantum 4, 333 (2020).
[138] Kristj´ansson, H., Chiribella, G., Salek, S., Ebler, D. & Wilson, M. Resource theories of communication. New J. Phys. 22, 073014 (2020).
[139] Rubino, G. et al. Experimental quantum communication enhancement by superposing trajectories. Phys. Rev. Research 3, 013093 (2021).
[140] Foo, J., Mann, R. B. & Zych, M. Entanglement amplification between superposed detectors in flat and curved spacetimes. Phys. Rev. D 103, 065013 (2021).
[141] Foo, J., Onoe, S. & Zych, M. Unruh-deWitt detectors in quantum superpositions of trajectories. Phys. Rev. D 102, 085013 (2020).
[142] Henderson, L. J. et al. Quantum temporal superposition: The case of quantum field theory. Phys. Rev. Lett. 125, 131602 (2020).
[143] Ban, M. Two-qubit correlation in two independent environments with indefiniteness. Phys. Lett. A 385, 126936 (2021).
[144] Ban, M. Relaxation process of a two-level system in a coherent superposition of two environments. Quantum Inf. Process. 19, 351 (2020).
[145] Siltanen, O., Kuusela, T. & Piilo, J. Interferometric approach to open quantum systems and non-Markovian dynamics. Phys. Rev. A 103, 032223 (2021).
[146] Reck, M., Zeilinger, A., Bernstein, H. J. & Bertani, P. Experimental realization of any discrete unitary operator. Phys. Rev. Lett. 73, 58–61 (1994).
[147] Bouland, A. & Aaronson, S. Generation of universal linear optics by any beam splitter. Phys. Rev. A 89, 062316 (2014).
[148] Cronin, A. D., Schmiedmayer, J. & Pritchard, D. E. Optics and interferometry with atoms and molecules. Rev. Mod. Phys. 81, 1051–1129 (2009).
[149] Nairz, O., Arndt, M. & Zeilinger, A. Quantum interference experiments with large molecules. American J. Phys. 71, 319 (2003).
[150] Sadana, S., Sanders, B. C. & Sinha, U. Double-slit interferometry as a lossy beam splitter. New J. Phys. 21, 113022 (2019).
[151] Carin˜e, J. et al. Multi-core fiber integrated multi-port beam splitters for quantum information processing. Optica 7, 542–550 (2020).
[152] Margalit, Y. et al. Realization of a complete Stern-Gerlach interferometer: Toward a test of quantum gravity. Sci. Adv. 7, eabg2879 (2021).
[153] Addis, C., Brebner, G., Haikka, P. & Maniscalco, S. Coherence trapping and information backflow in dephasing qubits. Phys. Rev. A 89, 024101 (2014).
[154] Zhang, Y.-J., Han, W., Xia, Y.-J., Yu, Y.-M. & Fan, H. Role of initial system- bath correlation on coherence trapping. Sci. Rep. 5, 13359 (2015).
[155] Feng, L.-J., Zhang, Y.-J., Xing, G.-C., Xia, Y.-J. & Gong, S.-Q. Trapping of coherence and entanglement in photonic band-gaps. Ann. Phys. 377, 77–86 (2017).
[156] Streltsov, A., Adesso, G. & Plenio, M. B. Colloquium: Quantum coherence as a resource. Rev. Mod. Phys. 89, 041003 (2017).
[157] Rom´an-Ancheyta, R., Kol´aˇr, M., Guarnieri, G. & Filip, R. Enhanced steady-state coherence via repeated system-bath interactions. Phys. Rev. A 104, 062209 (2021).
[158] Megier, N., Chru´scin´ski, D., Piilo, J. & Strunz, W. T. Eternal non- Markovianity: from random unitary to Markov chain realisations. Sci. Rep. 7, 6379 (2017).
[159] Chru´scin´ski, D. & Siudzin´ska, K. Generalized Pauli channels and a class of non-Markovian quantum evolution. Phys. Rev. A 94, 022118 (2016).
[160] Breuer, H.-P., Amato, G. & Vacchini, B. Mixing-induced quantum non- Markovianity and information flow. New J. Phys. 20, 043007 (2018).
[161] Jagadish, V., Srikanth, R. & Petruccione, F. Convex combinations of Pauli semigroups: Geometry, measure, and an application. Phys. Rev. A 101, 062304 (2020).
[162] Siudzin´ska, K. Markovian semigroup from mixing noninvertible dynamical maps. Phys. Rev. A 103, 022605 (2021).
[163] Breuer, H.-P., Laine, E.-M., Piilo, J. & Vacchini, B. Colloquium: Non- Markovian dynamics in open quantum systems. Rev. Mod. Phys. 88, 021002 (2016).
[164] Skrzypczyk, P., Short, A. J. & Popescu, S. Work extraction and thermodynamics for individual quantum systems. Nat. Commun. 5, 1–8 (2014).
[165] Oreshkov, O., Costa, F. & Brukner, Cˇ. Quantum correlations with no causal order. Nat. Commun. 3, 1092 (2012).
[166] Dicke, R. H. Coherence in spontaneous radiation processes. Phys. Rev. 93, 99–110 (1954).
[167] DeVoe, R. G. & Brewer, R. G. Observation of superradiant and subradiant spontaneous emission of two trapped ions. Phys. Rev. Lett. 76, 2049–2052 (1996).
[168] Gross, M. & Haroche, S. Superradiance: An essay on the theory of collective spontaneous emission. Phys. Rep. 93, 301–396 (1982).
[169] Chen, Y.-N., Li, C., Chuu, D.-S. & Brandes, T. Proposal for teleportation of charge qubits via super-radiance. New J. Phys. 7, 172 (2005).
[170] Chen, Y.-N. et al. Entanglement swapping and testing quantum steering into the past via collective decay. Phys. Rev. A 88, 052320 (2013).
[171] Chen, Y. N., Chuu, D. S. & Brandes, T. Current detection of superradiance and induced entanglement of double quantum dot excitons. Phys. Rev. Lett. 90, 166802 (2003).
[172] Brandes, T. Coherent and collective quantum optical effects in mesoscopic systems. Phys. Rep. 408, 315–474 (2005).
[173] Chen, G.-Y., Chen, S.-L., Li, C.-M. & Chen, Y.-N. Examining non-locality and quantum coherent dynamics induced by a common reservoir. Sci. Rep. 3, 2154 (2013).
[174] Yang, D. et al. Realization of superabsorption by time reversal of superradiance. Nat. Photon. 15, 272–276 (2021).
[175] Shammah, N., Ahmed, S., Lambert, N., De Liberato, S. & Nori, F. Open quantum systems with local and collective incoherent processes: Efficient numerical simulations using permutational invariance. Phys. Rev. A 98, 063815 (2018).
[176] See Supplemental Material for detailed derivations of full-time dynamics and the associated non-Markovian effects.
[177] Rubino, G. et al. Experimental verification of an indefinite causal order. Sci. Adv. 3, e1602589 (2017).
[178] Ebler, D., Salek, S. & Chiribella, G. Enhanced communication with the assistance of indefinite causal order. Phys. Rev. Lett. 120, 120502 (2018).
[179] Zych, M., Costa, F., Pikovski, I. & Brukner, Cˇ. Bell's theorem for temporal order. Nat. Commun. 10, 3772 (2019).