Showing papers on "Coherent states published in 2020"

Stabilization and operation of a Kerr-cat qubit

Abstract: Quantum superpositions of macroscopically distinct classical states-so-called Schrodinger cat states-are a resource for quantum metrology, quantum communication and quantum computation. In particular, the superpositions of two opposite-phase coherent states in an oscillator encode a qubit protected against phase-flip errors1,2. However, several challenges have to be overcome for this concept to become a practical way to encode and manipulate error-protected quantum information. The protection must be maintained by stabilizing these highly excited states and, at the same time, the system has to be compatible with fast gates on the encoded qubit and a quantum non-demolition readout of the encoded information. Here we experimentally demonstrate a method for the generation and stabilization of Schrodinger cat states based on the interplay between Kerr nonlinearity and single-mode squeezing1,3 in a superconducting microwave resonator4. We show an increase in the transverse relaxation time of the stabilized, error-protected qubit of more than one order of magnitude compared with the single-photon Fock-state encoding. We perform all single-qubit gate operations on timescales more than sixty times faster than the shortest coherence time and demonstrate single-shot readout of the protected qubit under stabilization. Our results showcase the combination of fast quantum control and robustness against errors, which is intrinsic to stabilized macroscopic states, as well as the potential of of these states as resources in quantum information processing5-8.

Collective Excitations of Quantum Anomalous Hall Ferromagnets in Twisted Bilayer Graphene.

Abstract: We present a microscopic theory for collective excitations of quantum anomalous Hall ferromagnets (QAHF) in twisted bilayer graphene. We calculate the spin magnon and valley magnon spectra by solving Bethe-Salpeter equations and verify the stability of QAHF. We extract the spin stiffness from the gapless spin wave dispersion and estimate the energy cost of a skyrmion-antiskyrmion pair, which is found to be comparable in energy with the Hartree-Fock gap. The valley wave mode is gapped, implying that the valley polarized state is more favorable compared to the valley coherent state. Using a nonlinear sigma model, we estimate the valley ordering temperature, which is considerably reduced from the mean-field transition temperature due to thermal excitations of valley waves.

Coherent many-body exciton in van der Waals antiferromagnet NiPS3.

Abstract: An exciton is the bosonic quasiparticle of electron–hole pairs bound by the Coulomb interaction1. Bose–Einstein condensation of this exciton state has long been the subject of speculation in various model systems2,3, and examples have been found more recently in optical lattices and two-dimensional materials4–9. Unlike these conventional excitons formed from extended Bloch states4–9, excitonic bound states from intrinsically many-body localized states are rare. Here we show that a spin–orbit-entangled exciton state appears below the Neel temperature of 150 kelvin in NiPS3, an antiferromagnetic van der Waals material. It arises intrinsically from the archetypal many-body states of the Zhang–Rice singlet10,11, and reaches a coherent state assisted by the antiferromagnetic order. Using configuration-interaction theory, we determine the origin of the coherent excitonic excitation to be a transition from a Zhang–Rice triplet to a Zhang–Rice singlet. We combine three spectroscopic tools—resonant inelastic X-ray scattering, photoluminescence and optical absorption—to characterize the exciton and to demonstrate an extremely narrow excitonic linewidth below 50 kelvin. The discovery of the spin–orbit-entangled exciton in antiferromagnetic NiPS3 introduces van der Waals magnets as a platform to study coherent many-body excitons. A spin–orbit-entangled exciton state in the van der Waals material NiPS3 is observed, and found to arise from many-body states of a Zhang–Rice singlet.

Onsager's Scars in Disordered Spin Chains.

Abstract: We propose a class of nonintegrable quantum spin chains that exhibit quantum many-body scars even in the presence of disorder. With the use of the so-called Onsager symmetry, we construct scarred models for arbitrary spin quantum number S. There are two types of scar states, namely, coherent states associated with an Onsager-algebra element and one-magnon scar states. While both of them are highly excited states, they have area-law entanglement and can be written as a matrix product state. Therefore, they explicitly violate the eigenstate thermalization hypothesis. We also investigate the dynamics of the fidelity and entanglement entropy for several initial states. The results clearly show that the scar states are trapped in a perfectly periodic orbit in the Hilbert subspace and never thermalize, whereas other generic states do rapidly. To our knowledge, our model is the first explicit example of disordered quantum many-body scarred models.

Orbital angular momentum multiplexed deterministic all-optical quantum teleportation.

Abstract: Quantum teleportation is one of the most essential protocol in quantum information. In addition to increasing the scale of teleportation distance, improving its information transmission capacity is also vital importance for its practical applications. Recently, the orbital angular momentum (OAM) of light has attracted wide attention as an important degree of freedom for realizing multiplexing to increase information transmission capacity. Here we show that by utilizing the OAM multiplexed continuous variable entanglement, 9 OAM multiplexed channels of parallel all-optical quantum teleportation can be deterministically established in experiment. More importantly, our parallel all-optical quantum teleportation scheme can teleport OAM-superposition-mode coded coherent state, which demonstrates the teleportation of more than one optical mode with fidelity beating the classical limit and thus ensures the increase of information transmission capacity. Our results open the avenue for deterministically implementing parallel quantum communication protocols and provide a promising paradigm for constructing high-capacity all-optical quantum communication networks.

Laser-Damage Attack Against Optical Attenuators in Quantum Key Distribution

Abstract: Many quantum key distribution systems employ a laser followed by an optical attenuator to prepare weak coherent states in the source. Their mean photon number must be precalibrated to guarantee the security of key distribution. Here we experimentally show that this calibration can be broken with a high-power laser attack. We test four fiber-optic attenuator types used in quantum key distribution systems, and find that two of them exhibit a permanent decrease in attenuation after laser damage. This results in higher mean photon numbers in the prepared states and may allow an eavesdropper to compromise the key.

Geometry of variational methods: dynamics of closed quantum systems

Abstract: We present a systematic geometric framework to study closed quantum systems based on suitably chosen variational families. For the purpose of (A) real time evolution, (B) excitation spectra, (C) spectral functions and (D) imaginary time evolution, we show how the geometric approach highlights the necessity to distinguish between two classes of manifolds: Kahler and non-Kahler. Traditional variational methods typically require the variational family to be a Kahler manifold, where multiplication by the imaginary unit preserves the tangent spaces. This covers the vast majority of cases studied in the literature. However, recently proposed classes of generalized Gaussian states make it necessary to also include the non-Kahler case, which has already been encountered occasionally. We illustrate our approach in detail with a range of concrete examples where the geometric structures of the considered manifolds are particularly relevant. These go from Gaussian states and group theoretic coherent states to generalized Gaussian states.

Demonstration of Controlled-Phase Gates between Two Error-Correctable Photonic Qubits.

Abstract: To realize fault-tolerant quantum computing, it is necessary to store quantum information in logical qubits with error correction functions, realized by distributing a logical state among multiple physical qubits or by encoding it in the Hilbert space of a high-dimensional system. Quantum gate operations between these error-correctable logical qubits, which are essential for implementation of any practical quantum computational task, have not been experimentally demonstrated yet. Here we demonstrate a geometric method for realizing controlled-phase gates between two logical qubits encoded in photonic fields stored in cavities. The gates are realized by dispersively coupling an ancillary superconducting qubit to these cavities and driving it to make a cyclic evolution depending on the joint photonic state of the cavities, which produces a conditional geometric phase. We first realize phase gates for photonic qubits with the logical basis states encoded in two quasiorthogonal coherent states, which have important implications for continuous-variable-based quantum computation. Then we use this geometric method to implement a controlled-phase gate between two binomially encoded logical qubits, which have an error-correctable function.

S -Matrix for massless particles

Abstract: The traditional $S$-matrix does not exist for theories with massless particles, such as quantum electrodynamics. The difficulty in isolating asymptotic states manifests itself as infrared divergences at each order in perturbation theory. Building on insights from the literature on coherent states and factorization, we construct an $S$-matrix that is free of singularities order-by-order in perturbation theory. Factorization guarantees that the asymptotic evolution in gauge theories is universal, i.e., independent of the hard process. Although the hard $S$-matrix element is computed between well-defined few particle Fock states, dressed/coherent states can be seen to form as intermediate states in the calculation of hard $S$-matrix elements. We present a framework for the perturbative calculation of hard $S$-matrix elements combining Lorentz-covariant Feynman rules for the dressed-state scattering with time-ordered perturbation theory for the asymptotic evolution. With hard cutoffs on the asymptotic Hamiltonian, the cancellation of divergences can be seen explicitly. In dimensional regularization, where the hard cutoffs are replaced by a renormalization scale, the contribution from the asymptotic evolution produces scaleless integrals that vanish. A number of illustrative examples are given in QED, QCD, and $\mathcal{N}=4$ super-Yang-Mills theory.

Effective dynamics from coherent state path integral of full loop quantum gravity

Abstract: A new routine is proposed to relate loop quantum cosmology (LQC) to loop quantum gravity (LQG) from the perspective of effective dynamics. We derive the big-bang singularity resolution and big bounce from the first principle of full canonical LQG. Our results are obtained in the framework of the reduced phase space quantization of LQG. As a key step in our work, we derive with coherent states a new discrete path integral formula of the transition amplitude generated by the physical Hamiltonian. The semiclassical approximation of the path integral formula gives an interesting set of effective equations of motion (EOMs) for full LQG. When solving the EOMs with homogeneous and isotropic ansatz, we reproduce the LQC effective dynamics in the ${\ensuremath{\mu}}_{0}$-scheme. The solution replaces the big-bang singularity by a big bounce. In the end, we comment on the possible relation between the $\overline{\ensuremath{\mu}}$-scheme of effective dynamics and the continuum limit of the path integral formula.

Coherence distillation machines are impossible in quantum thermodynamics.

Abstract: The role of coherence in quantum thermodynamics has been extensively studied in the recent years and it is now well-understood that coherence between different energy eigenstates is a resource independent of other thermodynamics resources, such as work. A fundamental remaining open question is whether the laws of quantum mechanics and thermodynamics allow the existence of a coherence distillation machine, i.e., a machine that, by possibly consuming work, obtains pure coherent states from mixed states, at a nonzero rate. This is related to another fundamental question: Starting from many copies of noisy quantum clocks which are (approximately) synchronized with a reference clock, can one distill synchronized clocks in pure states, at a non-zero rate? Surprisingly, we find that the answer to both questions is negative for generic (full-rank) mixed states. However, at the same time, it is possible to distill a sub-linear number of pure coherent states with a vanishing error. Can an idealised machine obtain pure coherent quantum states from mixed ones at a non-zero rate, or equivalently, can a machine distill synchronized quantum clocks starting from noisy ones? Iman Marvian demonstrates that this is impossible, even if the machine is allowed to spend an arbitrary amount of work.

Tuning between photon-number and quadrature measurements with weak-field homodyne detection

Abstract: Variable measurement operators enable the optimization of strategies for testing quantum properties and the preparation of a range of quantum states. Here, we experimentally implement a weak-field homodyne detector that can continuously tune between measuring photon numbers and field quadratures. We combine a quantum signal with a coherent state on a balanced beam splitter and detect light at both output ports using photon-number-resolving transition edge sensors. We observe that the discrete difference statistics converge to the quadrature distribution of the signal as we increase the coherent state amplitude. Moreover, in a proof-of-principle demonstration of state engineering, we show the ability to control the photon-number distribution of a state that is heralded using our weak-field homodyne detector.

Circuit complexity for generalized coherent states in thermal field dynamics

Abstract: In this work, we study the circuit complexity for generalized coherent states in thermal systems by adopting the covariance matrix approach. We focus on the coherent thermal (CT) state, which is non-Gaussian and has a nonvanishing one-point function. We find that even though the CT state cannot be fully determined by the symmetric two-point function, the circuit complexity can still be computed in the framework of the covariance matrix formalism by properly enlarging the covariance matrix. Now the group generated by the unitary is the semiproduct of translation and the symplectic group. If the reference state is Gaussian, the optimal geodesic is still be generated by a horizontal generator such that the circuit complexity can be read from the generalized covariance matrix associated to the target state by taking the cost function to be ${F}_{2}$. For a single harmonic oscillator, we discuss carefully the complexity and its formation in the cases that the reference states are Gaussian and the target space is excited by a single mode or double modes. We show that the study can be extended to the free scalar field theory.

Aspects of The First Law of Complexity.

Abstract: We investigate the first law of complexity proposed in arXiv:1903.04511, i.e., the variation of complexity when the target state is perturbed, in more detail. Based on Nielsen's geometric approach to quantum circuit complexity, we find the variation only depends on the end of the optimal circuit. We apply the first law to gain new insights into the quantum circuits and complexity models underlying holographic complexity. In particular, we examine the variation of the holographic complexity for both the complexity=action and complexity=volume conjectures in perturbing the AdS vacuum with coherent state excitations of a free scalar field. We also examine the variations of circuit complexity produced by the same excitations for the free scalar field theory in a fixed AdS background. In this case, our work extends the existing treatment of Gaussian coherent states to properly include the time dependence of the complexity variation. We comment on the similarities and differences of the holographic and QFT results.

Classical Solutions and their Double Copy in Split Signature

Abstract: The three-point amplitude is the key building block in the on-shell approach to scattering amplitudes. We show that the classical objects computed by massive three-point amplitudes in gauge theory and gravity are Newman-Penrose scalars in a split-signature spacetime, where three-point amplitudes can be defined for real kinematics. In fact, the quantum state set up by the particle is a coherent state fully determined by the three-point amplitude due to an eikonal-type exponentiation. Having identified this simplest classical solution from the perspective of scattering amplitudes, we explore the double copy of the Newman-Penrose scalars induced by the traditional double copy of amplitudes, and find that it coincides with the Weyl version of the classical double copy. We also exploit the Kerr-Schild version of the classical double copy to determine the exact spacetime metric in the gravitational case. Finally, we discuss the direct implication of these results for Lorentzian signature via analytic continuation.

Bosonic and fermionic Gaussian states from K\"ahler structures

Abstract: We show that bosonic and fermionic Gaussian states (also known as "squeezed coherent states") can be uniquely characterized by their linear complex structure $J$ which is a linear map on the classical phase space. This extends conventional Gaussian methods based on covariance matrices and provides a unified framework to treat bosons and fermions simultaneously. Pure Gaussian states can be identified with the triple $(G,\Omega,J)$ of compatible Kahler structures, consisting of a positive definite metric $G$, a symplectic form $\Omega$ and a linear complex structure $J$ with $J^2=-1\!\!1$. Mixed Gaussian states can also be identified with such a triple, but with $J^2 eq -1\!\!1$. We apply these methods to show how computations involving Gaussian states can be reduced to algebraic operations of these objects, leading to many known and some unknown identities. We apply these methods to the study of (A) entanglement and complexity, (B) dynamics of stable systems, (C) dynamics of driven systems. From this, we compile a comprehensive list of mathematical structures and formulas to compare bosonic and fermionic Gaussian states side-by-side.

Quantum Oppenheimer-Snyder model

Abstract: We construct two reduced quantum theories for the Oppenheimer-Snyder model, respectively taking the point of view of the comoving and the exterior stationary observer, using affine coherent states quantization. Investigations of the quantum corrected dynamics reveal that both observers can see a bounce, although for the exterior observer certain quantization ambiguities have to be chosen correctly. The minimal radius for this bounce as seen from the stationary observer is then shown to always be outside of the photon sphere. Possible avenues to lower this minimal radius and reclaim black holes as an intermediate state in the collapse are discussed. We demonstrate further that switching between the observers at the level of the quantum theories can be achieved by modifying the commutation relations.

Partially coherent Pearcey–Gauss beams

Abstract: We investigate the dynamics of partially coherent Pearcey-Gauss beams propagating in free space, theoretically and experimentally. They are produced by introducing the degree of coherence (DOC) function with Gaussian Schell-model correlation into the light source in the frequency domain. Under a nearly incoherent state, the oscillation of the sidelobe turns smooth, and the intensity distribution concentrates on the mainlobe. Particularly, partially coherent Pearcey-Gauss beams would maintain the inherent properties of autofocusing performance and inversion effect without diminishing the autofocusing distance and form-invariable propagation. Moreover, the opening angle and the shift of peak intensity of the beams can be controlled by the binary parabola in the spectrum distribution of the Pearcey function. Our experimental results are in great agreement with the theoretical analysis.

Engineering Schrödinger cat states with a photonic even-parity detector

Abstract: When two equal photon-number states are combined on a balanced beam splitter, both output ports of the beam splitter contain only even numbers of photons. Consider the time-reversal of this interference phenomenon: the probability that a pair of photon-number-resolving detectors at the output ports of a beam splitter both detect the same number of photons depends on the overlap between the input state of the beam splitter and a state containing only even photon numbers. Here, we propose using this even-parity detection to engineer quantum states containing only even photon-number terms. As an example, we demonstrate the ability to prepare superpositions of two coherent states with opposite amplitudes, i.e. two-component Schrodinger cat states. Our scheme can prepare cat states of arbitrary size with nearly perfect fidelity. Moreover, we investigate engineering more complex even-parity states such as four-component cat states by iteratively applying our even-parity detector.

Phase-Space Inequalities Beyond Negativities.

Abstract: We derive a family of inequalities involving different phase-space distributions of a quantum state which have to be fulfilled by any classical state. The violation of these inequalities is a clear signature of nonclassicality. Our approach combines the characterization of nonclassical effects via negativities in phase-space distributions with inequality conditions usually being formulated for moments of physical observables. Importantly, the obtained criteria certify nonclassicality even when the involved phase-space distributions are non-negative. Moreover, we show how these inequalities are related to correlation measurements. The strength of the derived conditions is demonstrated by different examples, including squeezed states, lossy single-photon states, and even coherent states.

Nonlinear states and dynamics in a synthetic frequency dimension

Abstract: Recent advances in the study of synthetic dimensions revealed a possibility to employ the frequency space as an additional degree of freedom which allows for investigating and exploiting higher-dimensional phenomena in a priori low-dimensional systems. However, the influence of nonlinear effects on the synthetic frequency dimensions was studied only under significant restrictions. In the present paper, we develop a generalized mean-field model for the optical field envelope inside a single driven-dissipative resonator with quadratic and cubic nonlinearities, whose frequencies are coupled via an electro-optical resonant temporal modulation. The leading-order equation takes the form of a driven Gross-Pitaevskii equation with a cosine potential. We numerically investigate the nonlinear dynamics in such a microring resonator with a synthetic frequency dimension in the regime where parametric frequency conversion occurs. We observe that the modulation brings additional control to the system, enabling one to readily create and manipulate bright and dark dissipative solitons inside the cavity. In the case of anomalous dispersion, we find that the presence of electro-optical mode coupling confines and stabilizes the chaotic modulation instability region. This leads to the appearance of an unconventional type of stable coherent structure which emerges in the synthetic space with restored translational symmetry, in a region of parameters where conventionally only chaotic modulation instability states exist. This structure appears in the center of the synthetic band and, therefore, is referred to as the band soliton. Finally, we extend our results to the case of multiple modulation frequencies with controllable relative phases creating synthetic lattices with nontrivial geometry. We show that an asymmetric synthetic band leads to the coexistence of chaotic and coherent states of the electromagnetic field inside the cavity, i.e., dynamics that can be interpreted as chimeralike states. Recently developed ${\ensuremath{\chi}}^{(2)}$ microresonators can open the way to experimentally exploring our findings.

Continuous variable B92 quantum key distribution protocol using single photon added and subtracted coherent states

Abstract: In this paper, a continuous variable B92 quantum key distribution protocol is proposed using single photon added and subtracted coherent states, which are prepared by adding and subsequently subtracting a single photon on a coherent state. It is established that in contrast to the traditional discrete variable B92 protocol, this protocol for quantum key distribution is intrinsically robust against the unambiguous state discrimination attack, which circumvents the requirement for any uninformative states or entanglement used in corresponding discrete variable case as a remedy for this attack. Further, it is shown that the proposed protocol is intrinsically robust against the eavesdropping strategies exploiting classical communication during basis reconciliation, such as beam splitter attack. Security against some individual attacks, key rate, and bit-error rate estimation for the proposed scheme are also provided. Specifically, the proposed scheme ensures very small bit-error rate due to properties of the states used. Thus, the proposed scheme is shown to be preferable over the corresponding discrete variable B92 protocol as well as some similar continuous variable quantum key distribution schemes.

Quantum nonstationary oscillators: Invariants, dynamical algebras and coherent states via point transformations

Abstract: We consider the relations between nonstationary quantum oscillators and their stationary counterpart in view of their applicability to study particles in electromagnetic traps. We develop a consistent model of quantum oscillators with time-dependent frequencies that are subjected to the action of a time-dependent driving force, and have a time-dependent zero point energy. Our approach uses the method of point transformations to construct the physical solutions of the parametric oscillator as mere deformations of the well known solutions of the stationary oscillator. In this form, the determination of the quantum integrals of motion is automatically achieved as a natural consequence of the transformation, without necessity of any ansatz. It yields the mechanism to construct an orthonormal basis for the nonstationary oscillators, so arbitrary superpositions of orthogonal states are available to obtain the corresponding coherent states. We also show that the dynamical algebra of the parametric oscillator is immediately obtained as a deformation of the algebra generated by the conventional boson ladder operators. A number of explicit examples is provided to show the applicability of our approach.

Quantum vs classical dynamics in a spin-boson system: manifestations of spectral correlations and scarring

Abstract: We compare the entire classical and quantum evolutions of the Dicke model in its regular and chaotic domains. This is a paradigmatic interacting spin-boson model of great experimental interest. By studying the classical and quantum survival probabilities of initial coherent states, we identify features of the long-time dynamics that are purely quantum and discuss their impact on the equilibration times. We show that the ratio between the quantum and classical asymptotic values of the survival probability serves as a metric to determine the proximity to a separatrix in the regular regime and to distinguish between two manifestations of quantum chaos: scarring and ergodicity. In the case of maximal quantum ergodicity, our results are analytical and show that quantum equilibration takes longer than classical equilibration.

Geometry of variational methods: dynamics of closed quantum systems

Abstract: We present a systematic geometric framework to study closed quantum systems based on suitably chosen variational families. For the purpose of (A) real time evolution, (B) excitation spectra, (C) spectral functions and (D) imaginary time evolution, we show how the geometric approach highlights the necessity to distinguish between two classes of manifolds: Kahler and non-Kahler. Traditional variational methods typically require the variational family to be a Kahler manifold, where multiplication by the imaginary unit preserves the tangent spaces. This covers the vast majority of cases studied in the literature. However, recently proposed classes of generalized Gaussian states make it necessary to also include the non-Kahler case, which has already been encountered occasionally. We illustrate our approach in detail with a range of concrete examples where the geometric structures of the considered manifolds are particularly relevant. These go from Gaussian states and group theoretic coherent states to generalized Gaussian states.

Plug-and-play continuous-variable quantum key distribution for metropolitan networks

Abstract: We report a plug-and-play continuous variable quantum key distribution system (CV-QKD) with Gaussian modulated quadratures and a true local oscillator. The proposed configuration avoids the need for frequency locking two narrow line-width lasers. To minimize Rayleigh back-scattering, we utilize two independent fiber strands for the distribution of the laser and the transmission of the quantum signals. We further demonstrate the quantum-classical co-existing capability of our system by injecting high-power classical light in both fibers. A secret key rate up to 0.88 Mb/s is obtained by using two fiber links of 13 km and up to 0.3 Mb/s when adding 4 mW of classical light in the optical fiber used for transmitting the quantum signal. The reported performance indicates that the proposed QKD scheme has the potential to become an effective low-cost solution for metropolitan optical networks.

Deterministic Generation of Large Fock States

Abstract: We present a protocol to deterministically prepare the electromagnetic field in a large photon number state. The field starts in a coherent state and, through resonant interaction with one or few two-level systems, it evolves into a coherently displaced Fock state without any postselection. We show the feasibility of the scheme under realistic parameters. The presented method opens a door to reach Fock states, with $n\ensuremath{\sim}100$ and optimal fidelities above 70%, blurring the line between macroscopic and quantum states of the field.

Fundamental limits of quantum illumination

Abstract: In quantum illumination (QI), a signal beam initially entangled with an idler beam held at the receiver interrogates a target region bathed in thermal background light. The returned beam is measured jointly with the idler in order to determine whether a weakly reflecting target is present. Using tools from quantum information theory, we derive lower bounds on the average error probability of detecting both specular and fading targets and on the mean squared error of estimating the reflectance of a detected target, which are obeyed by any QI transmitter satisfying a signal energy constraint. For bright thermal backgrounds, we show that the QI system using multiple copies of low-brightness two-mode squeezed vacuum states is nearly optimal. More generally, our results place limits on the best possible performance achievable using QI systems at all wavelengths, and at all signal and background noise levels.

Quantum black holes in bootstrapped Newtonian gravity

Abstract: We analyze the classical configurations of a bootstrapped Newtonian potential generated by homogeneous spherically symmetric sources in terms of a quantum coherent state. We first compute how the mass and mean wavelength of these solutions scale in terms of the number of quanta in the coherent state. We then note that the classical relation between the ADM mass and the proper mass of the source naturally gives rise to a generalized uncertainty principle (GUP) for the size of the gravitational radius in the quantum theory. Consistency of the mass and wavelength scalings with this GUP requires the compactness remains at most of order one even for black holes, and the corpuscular predictions are thus recovered, with the quantized horizon area expressed in terms of the number of quanta in the coherent state. Our findings could be useful for analyzing the classicalization of gravity in the presence of matter and the avoidance of singularities in the gravitational collapse of compact sources.