Tensor Representation of Spin States ; ; Baguette, Dorian et al in Physical Review Letters (2015), 114 We propose a generalization of the Bloch sphere representation for arbitrary spin states. It provides a compact and elegant representation of spin density matrices in terms of tensors that share the most ... [more ▼] We propose a generalization of the Bloch sphere representation for arbitrary spin states. It provides a compact and elegant representation of spin density matrices in terms of tensors that share the most important properties of Bloch vectors. Our representation, based on covariant matrices introduced by Weinberg in the context of quantum field theory, allows for a simple parametrization of coherent spin states, and a straightforward transformation of density matrices under local unitary and partial tracing operations. It enables us to provide a criterion for anticoherence, relevant in a broader context such as quantum polarization of light. [less ▲] Detailed reference viewed: 10 (2 ULg)Multiqubit symmetric states with maximally mixed one-qubit reductions Baguette, Dorian ; Bastin, Thierry ; Martin, John in Physical Review. A (2014), 90 We present a comprehensive study of maximally entangled symmetric states of arbitrary numbers of qubits in the sense of the maximal mixedness of the one-qubit reduced density operator. A general criterion ... [more ▼] We present a comprehensive study of maximally entangled symmetric states of arbitrary numbers of qubits in the sense of the maximal mixedness of the one-qubit reduced density operator. A general criterion is provided to easily identify whether given symmetric states are maximally entangled in that respect or not. We show that these maximally entangled symmetric (MES) states are the only symmetric states for which the expectation value of the associated collective spin of the system vanishes, as well as in corollary the dipole moment of the Husimi function. We establish the link between this kind of maximal entanglement, the anticoherence properties of spin states, and the degree of polarization of light fields. We analyze the relationship between the MES states and the classes of states equivalent through stochastic local operations with classical communication (SLOCC). We provide a nonexistence criterion of MES states within SLOCC classes of qubit states and show in particular that the symmetric Dicke state SLOCC classes never contain such MES states, with the only exception of the balanced Dicke state class for even numbers of qubits. The 4-qubit system is analyzed exhaustively and all MES states of this system are identified and characterized. Finally the entanglement content of MES states is analyzed with respect to the geometric and barycentric measures of entanglement, as well as to the generalized N-tangle. We show that the geometric entanglement of MES states is ensured to be larger than or equal to 1/2, but also that MES states are not in general the symmetric states that maximize the investigated entanglement measures. [less ▲] Detailed reference viewed: 38 (7 ULg)Generation of artificial magnetic fields using dipole-dipole interactions Cesa, Alexandre ; Martin, John Poster (2014, June 23) In 1996, Lloyd [1] showed that the dynamics of complex many-body quantum systems can be efficiently simulated by quantum computers, an idea first put forward by Manin [2] and further developed by Feynman ... [more ▼] In 1996, Lloyd [1] showed that the dynamics of complex many-body quantum systems can be efficiently simulated by quantum computers, an idea first put forward by Manin [2] and further developed by Feynman [3]. Although the first quantum computers of a few qubits have been realised experimentally [4, 5], the advent of scalable quantum computers might take another few decades. An alternative tool in the context of simulation is a highly controllable quantum system able to mimic the dynamics of other complex quantum systems, known as an analog quantum simulator. Cold neutral atoms and trapped ions have been shown to be versatile quantum simulators [6, 7] thanks to their high flexibility, controllability, and scalability. They permit one to study a wide range of problems arising from atomic physics, relativistic quantum physics, or cosmology [8]. Since neutral atoms do not carry any net charge, the simulation of electric and magnetic condensed matter phenomena, such as the spin Hall effect, seems out of reach. To overcome this apparent difficulty, the idea has been proposed to create artificial electromagnetic potentials for neutral atoms based on atom-light interaction [9– 12]. These artificial potentials act on neutral atoms as real electromagnetic potentials act on charged particles. Many works on artificial gauge potentials induced by atom-light interactions adopt a single-particle approach [12]. The predicted potentials are then supposed to be valid for a system of weakly interacting atoms. So far, the consequences of atom-atom interactions on the generation of artificial gauge fields has little been studied. The aim of this work is to study the artificial gauge fields arising from the interaction of two Rydberg atoms driven by a common laser field [13]. In this situation, we show that the combined atom-atom and atom-field interactions give rise to nonuniform, artificial gauge potentials. We identify the mechanism responsible for the emergence of these gauge potentials. Analytical expressions for the latter indicate that the strongest artificial magnetic fields are reached in the regime intermediate between the dipole blockade regime and the regime in which the atoms are sufficiently far apart such that atom-light interaction dominates over atom-atom interactions. We discuss the differences and similarities of artificial gauge fields originating from resonant dipole-dipole [14] and van der Waals [15] interactions. We also give an estimation of experimentally attainable artificial magnetic fields resulting from this mechanism and we discuss their detection through the deflection of the atomic motion. [1] S. Lloyd, Science 273, 1073 (1996). [2] Yu. I. Manin, Computable and uncomputable, Sovetskoye Radio, Moscow, 1980. [3] R. P. Feynman, Int. J. Theor. Phys. 21, 467 (1982). [4] L. DiCarlo, J. M. Chow, J. M. Gambetta, Lev S. Bishop, B. R. Johnson, D. I. Schuster, J. Majer, A. Blais, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, Nature 460, 240 (2009). [5] N. Xu, J. Zhu, D. Lu, X. Zhou, X. Peng, and J. Du, Phys. Rev. Lett. 108, 130501 (2012). [6] I. Buluta and F. Nori, Science 326, 108 (2009). [7] I. Bloch, J. Dalibard and S. Nascimbéne, Nature Physics 8, 267 (2012). [8] R. Blatt and C. F. Roos, Nature Physics 8, 277 (2012). [9] G. Juzeliunas and P. Öhberg, Phys. Rev. Lett. 93, 033602 (2004). [10] G. Juzeliunas, P. Öhberg, J. Ruseckas, and A. Klein, Phys. Rev. A 71, 053614 (2005). [11] G. Juzeliunas, J. Ruseckas, P. Öhberg, and M. Fleischhauer, Phys. Rev. A 73, 025602 (2006). [12] J. Dalibard, F. Gerbier, G. Juzeliu ̄nas, and P. Öhberg, Rev. Mod. Phys. 83, 1523 (2011). [13] A. Cesa and J. Martin, Phys. Rev. A 88,062703 (2013). [14] A. Gaëtan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, Nature Physics 5, 115 (2009). [15] L. Béguin, A. Vernier, R. Chicireanu, T. Lahaye, and A. Browaeys, Phys. Rev. Lett. 110, 263201 (2013). [less ▲] Detailed reference viewed: 68 (6 ULg)Alteration of decoherence-free states caused by dipole-dipole interactions Damanet, François ; Martin, John Poster (2014, June 23) Decoherence, known as the consequence of the coupling of any quantum system to its environment, causes information loss in the system and represents a major problem in the physical realization of quantum ... [more ▼] Decoherence, known as the consequence of the coupling of any quantum system to its environment, causes information loss in the system and represents a major problem in the physical realization of quantum computers [1]. Decoherence-Free States (DFS) are considered as a possible solution to this problem. A set of trapped cold atoms placed in a DFS state will be immune against decoherence due to spontaneous emission. However, because of dipole-dipole interactions between atoms, induced dephasing effects are likely to destroy the coherence and drive the system out of its DFS [1, 2]. In this work, we study numerically the dynamics of a set of two-level atoms initially in a DFS with respect to dissipative processes by solving the master equation including both dissipative dynamics and dipole dipole interactions. We fo- cus our attention on the infuence of dipolar coupling on the radiated energy rate and coherence of the system as in [3]. In particular, by averaging over many realizations of close randomly distributed atomic positions, we show the formation of a superradiant-like pulse and we study its properties as a function of the dipolar coupling strength. [1] D. A. Lidar & K. B. Whaley, Lectures Notes in Phys., Vol. 622, p83-120, Springer (2003). [2] M. Gross & S. Haroche, Physics reports 93, 301-396 (1982). [3] W. Feng, Y. Li & S-Y. Zhu, Phys. Rev. A 88, 033856 (2013). [less ▲] Detailed reference viewed: 18 (1 ULg)Symmetric N-qubit anticoherent states Baguette, Dorian ; Bastin, Thierry ; Martin, John Poster (2014, June 23) Entanglement is among the key features of quantum mechanics. In the last decade, a lot of efforts has been made to quantify the amount of entanglement of various multipartite states, either pure or mixed ... [more ▼] Entanglement is among the key features of quantum mechanics. In the last decade, a lot of efforts has been made to quantify the amount of entanglement of various multipartite states, either pure or mixed. In particular, the search for maximally entangled states (states maximizing certain measures of entanglement) has focused a great deal of attention, see e.g. Refs. [1–4]. In this work, we present a comprehensive study of maximally entangled symmetric N-qubit states with respect to the definition of Gisin [1]. According to this definition, a state is maximally entangled if all its one-qubit reduced density matrices are maximally mixed. These states maximize various entanglement measures, such as von Neumann and Meyer-Wallach entropies [5]. They are unique up to local unitaries within the class of states interconvertible under stochastic local operations and classical communication (SLOCC) [3]. Besides, they are conjectured to be maximally entangled with respect to the Negative Partial Transpose measure of entanglement [6]. As appreciated by B. Kraus, they play an important role in the determination of the local unitary equivalence of multiqubit states [7]. Moreover, they are maximally fragile (in the sense that they are the states which are the most sensitive to noise) and therefore have been proposed as ideal candidates for ultrasensitive sensors [1]. We provide general conditions for a symmetric state with an arbitrary number of qubits to be maximally entangled and identify families of SLOCC classes which do not contain any such states. We also compute various measure of entanglement associated with those states in order to characterize them further and find all maximally entangled states up to 4 qubits. We finally prove that maximally entangled states coincide with anticoherent states of order 1. According to the definition of Ref. [8], a symmetric state of N qubits is anticoherent to order t iff 〈(S·n)k〉 is independent of n for k = 1, . . . , t where n is a tridimensional unit vector and S is the collective spin operator associated to the N-qubit system. [1] N. Gisin, H. Bechmann-Pasquinucci, Phys. Lett. A 246 (1998). [2] A. Higuchi, A. Sudbery, Phys. Lett. A, 272, 213 (2000). [3] F. Verstraete, J. Dehaene, B. De Moor, Phys. Rev. A 68, 012103 (2003). [4] J. Martin, O. Giraud, P. A. Braun, D. Braun and T. Bastin, Phys. Rev. A 81, 062347 (2010). [5] D. A. Meyer, N. R. Wallach, J. Math. Phys. 43, 4273 (2002). [6] I. D. K. Brown, S. Stepney, A. Sudbery, and S. L. Braunstein, J. Phys. A 38, 1119 (2005). [7] B. Kraus, Phys. Rev. Lett. 104, 020504 (2010). [8] J. Zimba, EJTP 3, 10 (2006). [less ▲] Detailed reference viewed: 40 (8 ULg)Two Scenarios for Quantum Multifractality Breakdown Dubertrand, Rémy ; ; et al in Physical Review Letters (2014), 112 We expose two scenarios for the breakdown of quantum multifractality under the effect of perturbations. In the first scenario, multifractality survives below a certain scale of the quantum fluctuations ... [more ▼] We expose two scenarios for the breakdown of quantum multifractality under the effect of perturbations. In the first scenario, multifractality survives below a certain scale of the quantum fluctuations. In the other one, the fluctuations of the wave functions are changed at every scale and each multifractal dimension smoothly goes to the ergodic value. We use as generic examples a one-dimensional dynamical system and the three-dimensional Anderson model at the metal-insulator transition. Based on our results, we conjecture that the sensitivity of quantum multifractality to perturbation is universal in the sense that it follows one of these two scenarios depending on the perturbation. We also discuss the experimental implications. [less ▲] Detailed reference viewed: 17 (7 ULg)Two Scenarios for Quantum Multifractality Breakdown Dubertrand, Rémy ; ; et al in Physical Review Letters (2014), 112 We expose two scenarios for the breakdown of quantum multifractality under the effect of perturbations. In the first scenario, multifractality survives below a certain scale of the quantum fluctuations ... [more ▼] We expose two scenarios for the breakdown of quantum multifractality under the effect of perturbations. In the first scenario, multifractality survives below a certain scale of the quantum fluctuations. In the other one, the fluctuations of the wave functions are changed at every scale and each multifractal dimension smoothly goes to the ergodic value. We use as generic examples a one-dimensional dynamical system and the three-dimensional Anderson model at the metal-insulator transition. Based on our results, we conjecture that the sensitivity of quantum multifractality to perturbation is universal in the sense that it follows one of these two scenarios depending on the perturbation. We also discuss the experimental implications. [less ▲] Detailed reference viewed: 17 (7 ULg)Two Scenarios for Quantum Multifractality Breakdown Dubertrand, Rémy ; ; et al in Physical Review Letters (2014), 112 We expose two scenarios for the breakdown of quantum multifractality under the effect of perturbations. In the first scenario, multifractality survives below a certain scale of the quantum fluctuations ... [more ▼] We expose two scenarios for the breakdown of quantum multifractality under the effect of perturbations. In the first scenario, multifractality survives below a certain scale of the quantum fluctuations. In the other one, the fluctuations of the wave functions are changed at every scale and each multifractal dimension smoothly goes to the ergodic value. We use as generic examples a one-dimensional dynamical system and the three-dimensional Anderson model at the metal-insulator transition. Based on our results, we conjecture that the sensitivity of quantum multifractality to perturbation is universal in the sense that it follows one of these two scenarios depending on the perturbation. We also discuss the experimental implications. [less ▲] Detailed reference viewed: 17 (7 ULg)Dubertrand, Rémy ; ; et al in Physical Review Letters (2014), 112 The two scenarios for quantum multifractality breakdown ; ; et al Scientific conference (2014, June) Several types of physical systems are characterized by quantum wave func- tions with multifractal properties. In the quantum chaos field, they cor- respond to pseudointegrable systems, with properties ... [more ▼] Several types of physical systems are characterized by quantum wave func- tions with multifractal properties. In the quantum chaos field, they cor- respond to pseudointegrable systems, with properties intermediate between integrability and chaos. In condensed matter, they include electrons in a disordered potential at the Anderson metal-insulator transition. This multi- fractality leads to particular transport properties and appears in conjunction with specific types of spectral statistics. In parallel, progress in experimental techniques allows to observe finer and finer properties of the wavefunctions of quantum or wave systems, as well as to perform experiments with un- precedented control on the dynamics of the systems studied. In this context, this talk will discuss the robustness of multifractality in presence of footnote- size perturbations. We expose two scenarios for the breakdown of quantum multifractality under the effect of such perturbations. In the first scenario, multifractality survives below a certain scale of the quantum fluctuations. In the other one, the fluctuations of the wave functions are changed at every scale and each multifractal dimension smoothly goes to the ergodic value. We use as generic examples a one-dimensional dynamical system and the three- dimensional Anderson model at the metal-insulator transition, and show that for different types of perturbation the destruction of multifractal properties always follows one of these two ways. Our results thus suggest that quantum multifractality breakdown is universal and obeys one of these two scenarios depending on the perturbation. We also discuss the experimental implica- tions. [less ▲] Detailed reference viewed: 26 (3 ULg)Artificial Abelian gauge potentials induced by dipole-dipole interactions between Rydberg atoms Cesa, Alexandre ; Martin, John Poster (2014, March 19) We analyze the influence of dipole-dipole interactions between Rydberg atoms on the generation of Abelian artificial gauge potentials and fields. When two Rydberg atoms are driven by a uniform laser field ... [more ▼] We analyze the influence of dipole-dipole interactions between Rydberg atoms on the generation of Abelian artificial gauge potentials and fields. When two Rydberg atoms are driven by a uniform laser field, we show that the combined atom-atom and atom-field interactions give rise to nonuniform, artificial gauge potentials. We identify the mechanism responsible for the emergence of these gauge potentials. Analytical expressions for the latter indicate that the strongest artificial magnetic fields are reached in the regime intermediate between the dipole blockade regime and the regime in which the atoms are sufficiently far apart such that atom-light interaction dominates over atom-atom interactions. We discuss the differences and similarities of artificial gauge fields originating from resonant dipole-dipole and van der Waals interactions. We also give an estimation of experimentally attainable artificial magnetic fields resulting from this mechanism and we discuss their detection through the deflection of the atomic motion. [less ▲] Detailed reference viewed: 33 (10 ULg)Influence of dipole-dipole interactions decoherence-free states Damanet, François ; Martin, John Poster (2014, March 18) Decoherence, known as the consequence of the coupling of any quan- tum system to its environment, causes information loss in the system and represents a major problem in the physical realization of quan ... [more ▼] Decoherence, known as the consequence of the coupling of any quan- tum system to its environment, causes information loss in the system and represents a major problem in the physical realization of quan- tum computers [1]. Decoherence-Free States (DFS) are considered as a possible solution to this problem. A set of trapped cold atoms placed in a DFS state will be immune against decoherence due to sponta- neous emission. However, because of dipole-dipole interactions between atoms, induced dephasing effects are likely to destroy the coherence and drive the system out of its DFS [1-2]. In this work, we study nu- merically the dynamics of a set of two-level atoms initially in a DFS with respect to dissipative processes by solving the master equation in- cluding both dissipative dynamics and dipole dipole interactions. We focus our attention on the influence of dipolar coupling on the radiated energy rate and coherence of the system as in [3]. In particular, by av- eraging over many realizations of close randomly distributed atomic positions, we show the formation of a superradiant-like pulse and we study its properties as a function of the dipolar coupling strength. [1] D. A. Lidar & K. B. Whaley, Lectures Notes in Phys., Vol. 622, p83-120, Springer (2003). [2] M. Gross & S. Haroche, Physics reports 93, 301-396 (1982). [3] W. Feng, Y. Li & S. -Y. Zhu, arXiv :1302.0957. (2013). [less ▲] Detailed reference viewed: 25 (5 ULg)On the Identication of Symmetric N-qubit Maximally Entangled States Baguette, Dorian ; Bastin, Thierry ; Martin, John Poster (2014, March 11) Maximally entangled states can serve as a useful resource in many different contexts. It is therefore important to identify those states. Here we are interested in the identification of maximally ... [more ▼] Maximally entangled states can serve as a useful resource in many different contexts. It is therefore important to identify those states. Here we are interested in the identification of maximally entangled states in the symmetric subspace of an N-qubit system. By maximally entangled states, we refer to symmetric states characterized by a one qubit reduced density matrix proportional to the identity. These states maximise various entanglement measures [1] such as von Neumann and Meyer-Wallach entropy and are unique up to LU in their SLOCC class [2]. We identify and characterize all maximally entangled symmetric states up to 4 qubits. We provide general conditions for a symmetric state with an arbitrary number of qubits to be maximally entangled and identify families of SLOCC classes which do not contain any maximally entangled states. [1] F. Verstraete, J. Dehaene, B. De Moor, Phys. Rev. A 68, 012103 (2003). [2] G. Gour, N. Wallach, N. J. Phys. 13, 073013 (2011) [less ▲] Detailed reference viewed: 47 (6 ULg)Robustness of quantum multifractality ; ; et al Scientific conference (2014, March) Several models where quantum wave functions display multifractal properties have been recently identified. In the quantum chaos field, they correspond to pseudointegrable systems, with properties ... [more ▼] Several models where quantum wave functions display multifractal properties have been recently identified. In the quantum chaos field, they correspond to pseudointegrable systems, with properties intermediate between integrability and chaos. In condensed matter, they include electrons in a disordered potential at the Anderson metal-insulator transition. These multifractality properties lead to particular transport properties and appear in conjunction with specific types of spectral statistics. In parallel, progress in experimental techniques allow to observe finer and finer properties of the wavefunctions of quantum or wave systems, as well as to perform experiments with unprecedented control on the dynamics of the systems studied. In this context, this talk will discuss the robustness of multifractality in presence of small perturbations. We identify two distinct processes of multifractality destruction according to the type of perturbation, and specify a range of parameters where multifractality could indeed be observed in physical systems in presence of imperfections. [less ▲] Detailed reference viewed: 23 (4 ULg)Nonlinear Schrödinger wave equation with linear quantum behavior Richardson, Christopher ; Schlagheck, Peter ; Martin, John et al in Physical Review. A (2014), 89 We show that a nonlinear Schro ̈dinger wave equation can reproduce all the features of linear quantum mechanics. This nonlinear wave equation is obtained by exploring, in a uniform language, the ... [more ▼] We show that a nonlinear Schro ̈dinger wave equation can reproduce all the features of linear quantum mechanics. This nonlinear wave equation is obtained by exploring, in a uniform language, the transition from fully classical theory governed by a nonlinear classical wave equation to quantum theory. The classical wave equation includes a nonlinear classicality enforcing potential which when eliminated transforms the wave equation into the linear Schro ̈dinger equation. We show that it is not necessary to completely cancel this nonlinearity to recover the linear behavior of quantum mechanics. Scaling the classicality enforcing potential is sufficient to have quantumlike features appear and is equivalent to scaling Planck’s constant. [less ▲] Detailed reference viewed: 15 (3 ULg)Highly non-classical symmetric states of an N-qubit system Baguette, Dorian ; Martin, John Poster (2013, September 02) In this work, we consider two measures of non-classicality for pure symmetric N-qubit states : Wehrl entropy (S) and Wehrl participation ratio (R). Measures of non-classicality help to the understanding ... [more ▼] In this work, we consider two measures of non-classicality for pure symmetric N-qubit states : Wehrl entropy (S) and Wehrl participation ratio (R). Measures of non-classicality help to the understanding of the mechanisms responsible for the transition from quantum to classical physics and are usefull in the context of information processing and quantum-enhanced measurements. [less ▲] Detailed reference viewed: 30 (7 ULg)Influence of dipole-dipole interactions on superradiance Damanet, François ; Martin, John Poster (2013, September 02) Superradiance, known as the cooperative spontaneous emission of a directional light pulse by excited atoms placed in vacuum, has recently regained attention in the context of photon localization [1] and ... [more ▼] Superradiance, known as the cooperative spontaneous emission of a directional light pulse by excited atoms placed in vacuum, has recently regained attention in the context of photon localization [1] and single photon cooperative emission [2]. The dissipative dynamics of the atoms is known to depend dramatically on the ratio between the typical inter- atomic distance and the atomic transition wavelength, notably because of dipole-dipole interactions [3]. In this work, we study the effects of these interactions on superradiance as in [4] by solving numerically the corresponding master equation. In particular, by averaging over many realizations of the randomly distributed atomic positions, we show that the decay of the radiated energy pulse height with the intensity of the dipolar coupling follows a power law. [1] E. Ackermans, A. Gero & R. Kaiser, Phys. Rev. Lett. 101, 103602 (2008). [2] R. Friedberg & J. T. Manassah, J. Phys. B 43, 035501 (2010). [3] M. Gross & S. Haroche, Physics reports 93, 301-396 (1982). [4] B. Coffey & R. Friedberg, Phys. Rev. A 17, 1033 (1978). [less ▲] Detailed reference viewed: 61 (6 ULg)Multifractality of quantum wave functions ; ; et al Poster (2013, September) Detailed reference viewed: 27 (1 ULg)Influence of dipole-dipole interactions on the superradiant pulse Damanet, François ; Martin, John Poster (2013, May 23) Superradiance, known as the cooperative spontaneous emission of a directional light pulse by excited atoms placed in vacuum, has recently regained attention in the context of photon localization [1] and ... [more ▼] Superradiance, known as the cooperative spontaneous emission of a directional light pulse by excited atoms placed in vacuum, has recently regained attention in the context of photon localization [1] and single photon cooperative emission [2]. The dissipative dynamics of the atoms is known to depend dramatically on the ratio between the typical inter-atomic distance and the atomic transition wavelength, notably because of dipole-dipole interactions [3]. In this work, we study the effects of these interactions on superradiance as in [4] by solving numerically the corresponding master equation. In particular, by averaging over many realizations of the randomly distributed atomic positions, we show that the decay of the radiated energy pulse height with the intensity of the dipolar coupling follows a power law. [1] E. Ackermans, A. Gero & R. Kaiser, Phys. Rev. Lett. 101, 103602 (2008). [2] R. Friedberg & J. T. Manassah, J. Phys. B 43, 035501 (2010). [3] M. Gross & S. Haroche, Physics reports 93, 301-396 (1982). [4] B. Coffey & R. Friedberg, Phys. Rev. A 17, 1033 (1978). [less ▲] Detailed reference viewed: 22 (4 ULg)The most non-classical symmetric states of an N-qubit system Baguette, Dorian ; Martin, John Poster (2013, May 23) Detailed reference viewed: 29 (4 ULg) |
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