arXiv subjects

Daniel Braun

Publications and source records attributed to Daniel Braun.

At least 73 records · Page 4Linked to original sources

arXiv2021

Symmetric Multiqudit States: Stars, Entanglement, Rotosensors

A constellation of $N=d-1$ Majorana stars represents an arbitrary pure quantum state of dimension $d$ or a permutation-symmetric state of a system consisting of $n$ qubits. We generalize the latter construction to represent in a similar way an arbitrary symmetric pure state of $k$ subsystems with $d$ levels each. For $d\geq 3$, such states are equivalent, as far as rotations are concerned, to a collection of various spin states, with definite relative complex weights. Following Majorana's lead, we introduce a multiconstellation, consisting of the Majorana constellations of the above spin states, augmented by an auxiliary, "spectator" constellation, encoding the complex weights. Examples of stellar representations of symmetric states of four qutrits, and two spin-$3/2$ systems, are presented. We revisit the Hermite and Murnaghan isomorphisms, which relate multipartite states of various spins, number of parties, and even symmetries. We show how the tools introduced can be used to analyze multipartite entanglement and to identify optimal quantum rotosensors, i.e., pure states which are maximally sensitive to rotations around a specified axis, or averaged over all axes.

quant-ph↗

arXiv2020

P2D: a self-supervised method for depth estimation from polarimetry

Monocular depth estimation is a recurring subject in the field of computer vision. Its ability to describe scenes via a depth map while reducing the constraints related to the formulation of perspective geometry tends to favor its use. However, despite the constant improvement of algorithms, most methods exploit only colorimetric information. Consequently, robustness to events to which the modality is not sensitive to, like specularity or transparency, is neglected. In response to this phenomenon, we propose using polarimetry as an input for a self-supervised monodepth network. Therefore, we propose exploiting polarization cues to encourage accurate reconstruction of scenes. Furthermore, we include a term of polarimetric regularization to state-of-the-art method to take specific advantage of the data. Our method is evaluated both qualitatively and quantitatively demonstrating that the contribution of this new information as well as an enhanced loss function improves depth estimation results, especially for specular areas.

cs.CV↗

arXiv2020

Truncated moment sequences and a solution to the channel separability problem

We consider the problem of separability of quantum channels via the Choi matrix representation given by the Choi-Jamiołkowski isomorphism. We explore three classes of separability across different cuts between systems and ancillae and we provide a solution based on the mapping of the coordinates of the Choi state (in a fixed basis) to a truncated moment sequence (tms) $y$. This results in an algorithm which gives a separability certificate using semidefinite programming. The computational complexity and the performance of it depend on the number of variables $n$ in the tms and on the size of the moment matrix $M_t(y)$ of order $t$. We exploit the algorithm to numerically investigate separability of families of 2-qubit and single-qutrit channels; in the latter case we can provide an answer for examples explored earlier through the criterion based on the negativity $N$, a criterion which remains inconclusive for Choi matrices with $N=0$.

quant-ph↗

arXiv2020

Stoner-Wohlfarth switching of the condensate magnetization in a dipolar spinor gas and the metrology of excitation damping

We consider quasi-one-dimensional dipolar spinor Bose-Einstein condensates in the homogeneous-local-spin-orientation approximation, that is with unidirectional local magnetization. By analytically calculating the exact effective dipole-dipole interaction, we derive a Landau-Lifshitz-Gilbert equation for the dissipative condensate magnetization dynamics, and show how it leads to the Stoner-Wohlfarth model of a uni-axial ferro-magnetic particle, where the latter model determines the stable magnetization patterns and hysteresis curves for switching between them. For an external magnetic field pointing along the axial, long direction, we analytically solve the Landau-Lifshitz-Gilbert equation. The solution explicitly demonstrates that the magnetic dipole-dipole interaction {\it accelerates} the dissipative dynamics of the magnetic moment distribution and the associated dephasing of the magnetic moment direction. Under suitable conditions, dephasing of the magnetization direction due to dipole-dipole interactions occurs within time scales up to two orders of magnitude smaller than the lifetime of currently experimentally realized dipolar spinor condensates, e.g., produced with the large magnetic-dipole-moment atoms ${}^{166} \textrm{Er}$. This enables experimental access to the dissipation parameter $Γ$ in the Gross-Pitaevski\vı~mean-field equation, for a system currently lacking a complete quantum kinetic treatment of dissipative processes and, in particular, an experimental check of the commonly used assumption that $Γ$ is a single scalar independent of spin indices.

cond-mat.quant-gas↗

arXiv2020

Improving the dynamics of quantum sensors with reinforcement learning

Recently proposed quantum-chaotic sensors achieve quantum enhancements in measurement precision by applying nonlinear control pulses to the dynamics of the quantum sensor while using classical initial states that are easy to prepare. Here, we use the cross-entropy method of reinforcement learning to optimize the strength and position of control pulses. Compared to the quantum-chaotic sensors with periodic control pulses in the presence of superradiant damping, we find that decoherence can be fought even better and measurement precision can be enhanced further by optimizing the control. In some examples, we find enhancements in sensitivity by more than an order of magnitude. By visualizing the evolution of the quantum state, the mechanism exploited by the reinforcement learning method is identified as a kind of spin-squeezing strategy that is adapted to the superradiant damping.

quant-ph↗

arXiv2020

Time-evolution of nonlinear optomechanical systems: Interplay of mechanical squeezing and non-Gaussianity

We solve the time evolution of a nonlinear optomechanical Hamiltonian with arbitrary time-dependent mechanical displacement, mechanical single-mode squeezing and a time-dependent optomechanical coupling up to the solution of two second-order differential equations. The solution is based on identifying a minimal and finite Lie algebra that generates the time-evolution of the system. This reduces the problem to considering a finite set of coupled ordinary differential equations of real functions. To demonstrate the applicability of our method, we compute the degree of non-Gaussianity of the time-evolved state of the system by means of a measure based on the relative entropy of the non-Gaussian state and its closest Gaussian reference state. We find that the addition of a constant mechanical squeezing term to the standard optomechanical Hamiltonian generally decreases the overall non-Gaussian character of the state. For sinusoidally modulated squeezing, the two second-order differential equations mentioned above take the form of the Mathieu equation. We derive perturbative solutions for a small squeezing amplitude at parametric resonance and show that they correspond to the rotating-wave approximation at times larger than the scale set by the mechanical frequency. We find that the non-Gaussianity of the state increases with both time and the squeezing parameter in this specific regime.

quant-ph↗

arXiv2020

Optimal estimation with quantum optomechanical systems in the nonlinear regime

We study the fundamental bounds on precision measurements of parameters contained in a time-dependent nonlinear optomechanical Hamiltonian, which includes the nonlinear light-matter coupling, a mechanical displacement term, and a single-mode mechanical squeezing term. By using a recently developed method to solve the dynamics of this system, we derive a general expression for the quantum Fisher information and demonstrate its applicability through three concrete examples: estimation of the strength of a nonlinear light-matter coupling, the strength of a time-modulated mechanical displacement, and a single-mode mechanical squeezing parameter, all of which are modulated at resonance. Our results can be used to compute the sensitivity of a nonlinear optomechanical system to a number of external and internal effects, such as forces acting on the system or modulations of the light--matter coupling.

quant-ph↗

arXiv2019

Maximal Quantum Fisher Information for Mixed States

We study quantum metrology for unitary dynamics. Analytic solutions are given for both the optimal unitary state preparation starting from an arbitrary mixed state and the corresponding optimal measurement precision. This represents a rigorous generalization of known results for optimal initial states and upper bounds on measurement precision which can only be saturated if pure states are available. In particular, we provide a generalization to mixed states of an upper bound on measurement precision for time-dependent Hamiltonians that can be saturated with optimal Hamiltonian control. These results make precise and reveal the full potential of mixed states for quantum metrology.

quant-ph↗

arXiv2019

Trade--off relations for operation entropy of complementary quantum channels

The entropy of a quantum operation, defined as the von Neumann entropy of the corresponding Choi-Jamiołkowski state, characterizes the coupling of the principal system with the environment. For any quantum channel $Φ$ acting on a state of size $N$ one defines the complementary channel $\tilde Φ$, which sends the input state into the state of the environment after the operation. Making use of subadditivity of entropy we show that for any dimension $N$ the sum of both entropies, $S(Φ)+ S(\tilde Φ)$, is bounded from below. This result characterizes the trade-off between the information on the initial quantum state accessible to the principal system and the information leaking to the environment. For one qubit maps, $N=2$, we describe the interpolating family of depolarising maps, for which the sum of both entropies gives the lower boundary of the region allowed in the space spanned by both entropies.

quant-ph↗

arXiv2019

Outcoupling from a Bose-Einstein condensate in the strong-field limit

Atoms can be extracted from a trapped Bose-Einstein condensate (BEC) by driving spin-flips to untrapped states. The coherence properties of the BEC are transfered to the released atoms, creating a coherent beam of matter refered to as an atom laser. In this work, the extraction of atoms from a BEC is investigated numerically by solving a coupled set of Gross-Pitaevskii equations in up to three dimensions. The result is compared to experimental data and a semiclassical rate model. In the weak-coupling regime, quantitative agreement is reached between theory and experiment and a semiclassical rate model. In the strong-coupling regime, the atom laser enters a trapped state that manifests itself in a saturation of the rate of out-coupled atoms observed in new experimental data. The semiclassical rate model fails, but the numerical descriptions yield qualitative agreement with experimental data at the onset of saturation.

cond-mat.quant-gas↗

arXiv2019

Quantum parameter-estimation of frequency and damping of a harmonic-oscillator

We determine the quantum Cramér-Rao bound for the precision with which the oscillator frequency and damping constant of a damped quantum harmonic oscillator in an arbitrary Gaussian state can be estimated. This goes beyond standard quantum parameter estimation of a single mode Gaussian state for which typically a mode of fixed frequency is assumed. We present a scheme through which the frequency estimation can nevertheless be based on the known results for single-mode quantum parameter estimation with Gaussian states. Based on these results, we investigate the optimal measurement time. For measuring the oscillator frequency, our results unify previously known partial results and constitute an explicit solution for a general single-mode Gaussian state. Furthermore, we show that with existing carbon nanotube resonators (see J. Chaste et al.~Nature Nanotechnology 7, 301 (2012)) it should be possible to achieve a mass sensitivity of the order of an electron mass $\text{Hz}^{-1/2}$.

quant-ph↗

arXiv2019

A quantum-chaotic cesium-vapor magnetometer

Quantum-enhanced measurements represent the path towards the best measurement precision allowed by the laws of quantum mechanics. Known protocols usually rely on the preparation of entangled states and promise high or even optimal precision, but fall short in real-word applications because of the difficulty to generate entangled states and to protect them against decoherence. Here, we refrain from the preparation of entangled states but supplement the integrable parameter-encoding dynamics by non-linear kicks driving the system in the dynamical regime of quantum chaos. We show that large improvements in measurement precision are possible by modeling a spin-exchange relaxation-free alkali-vapor magnetometer where the non-linear kicks are realized by exploiting the ac Stark effect.

quant-ph↗

arXiv2019

The gravitational field of a laser beam beyond the short wavelength approximation

Light carries energy, and therefore, it is the source of a gravitational field. The gravitational field of a beam of light in the short wavelength approximation has been studied by several authors. In this article, we consider light of finite wavelengths by describing a laser beam as a solution of Maxwell's equations and taking diffraction into account. Then, novel features of the gravitational field of a laser beam become apparent, such as frame-dragging due to its spin angular momentum and the deflection of parallel co-propagating test beams that overlap with the source beam. Even though the effects are too small to be detected with current technology, they are of conceptual interest, revealing the gravitational properties of light.

gr-qc↗

arXiv2019

Rotation of polarization in the gravitational field of a laser beam - Faraday effect and optical activity

We investigate the rotation of the polarization of a light ray propagating in the gravitational field of a circularly polarized laser beam. The rotation consists of a reciprocal part due to gravitational optical activity, and a non-reciprocal part due to the gravitational Faraday effect. We discuss how to distinguish the two effects: Letting light propagate back and forth between two mirrors, the rotation due to gravitational optical activity cancels while the rotation due to the gravitational Faraday effect accumulates. In contrast, the rotation due to both effects accumulates in a ring cavity and a situation can be created in which gravitational optical activity dominates. Such setups amplify the effects by up to five orders of magnitude, which however is not enough to make them measurable with state of the art technology. The effects are of conceptual interest as they reveal gravitational spin-spin coupling in the realm of classical general relativity, a phenomenon which occurs in perturbative quantum gravity.

gr-qc↗

arXiv2018

Quantum enhanced measurements without entanglement

Quantum-enhanced measurements exploit quantum mechanical effects for increasing the sensitivity of measurements of certain physical parameters and have great potential for both fundamental science and concrete applications. Most of the research has so far focused on using highly entangled states, which are, however, difficult to produce and to stabilize for a large number of constituents. In the following we review alternative mechanisms, notably the use of more general quantum correlations such as quantum discord, identical particles, or non-trivial hamiltonians; the estimation of thermodynamical parameters or parameters characterizing non-equilibrium states; and the use of quantum phase transitions. We describe both theoretically achievable enhancements and enhanced sensitivities, not primarily based on entanglement, that have already been demonstrated experimentally, and indicate some possible future research directions.

quant-ph↗

arXiv2018

Quantum metrology with a quantum-chaotic sensor

Quantum metrology promises high-precision measurements of classical parameters with far reaching implications for science and technology. So far, research has concentrated almost exclusively on quantum-enhancements in integrable systems, such as precessing spins or harmonic oscillators prepared in non-classical states. Here we show that large benefits can be drawn from rendering integrable quantum sensors chaotic, both in terms of achievable sensitivity as well as robustness to noise, while avoiding the challenge of preparing and protecting large-scale entanglement. We apply the method to spin-precession magnetometry and show in particular that the sensitivity of state-of-the-art magnetometers can be further enhanced by subjecting the spin-precession to non-linear kicks that renders the dynamics chaotic.

quant-ph↗

arXiv2018

Two-qubit causal structures and the geometry of positive qubit-maps

We study quantum causal inference in a set-up proposed by Ried et al. [Nat. Phys. 11, 414 (2015)] in which a common-cause scenario can be mixed with a cause-effect scenario, and for which it was found that quantum mechanics can bring an advantage in distinguishing the two scenarios: Whereas in classical statistics, interventions such as randomized trials are needed, a quantum observational scheme can be enough to detect the causal structure if the common cause results from a maximally entangled state. We analyze this setup in terms of the geometry of unital positive but not completely positive qubit-maps, arising from the mixture of qubit-channels and steering maps. We find the range of mixing parameters that can generate given correlations, and prove a quantum advantage in a more general setup, allowing arbitrary unital channels and initial states with fully mixed reduced states. This is achieved by establishing new bounds on signed singular values of sums of matrices. Based on the geometry, we quantify and identify the origin of the quantum advantage depending on the observed correlations, and discuss how additional constraints can lead to a unique solution of the problem.

quant-ph↗

arXiv2018

Nonclassical states of light with a smooth $P$ function

There is a common understanding in quantum optics that nonclassical states of light are states that do not have a positive semidefinite and sufficiently regular Glauber-Sudarshan $P$ function. Almost all known nonclassical states have $P$ functions that are highly irregular which makes working with them difficult and direct experimental reconstruction impossible. Here we introduce classes of nonclassical states with regular, non-positive-definite $P$ functions. They are constructed by "puncturing" regular smooth positive $P$ functions with negative Dirac-delta peaks, or other sufficiently narrow smooth negative functions. We determine the parameter ranges for which such punctures are possible without losing the positivity of the state, as well as the regimes yielding antibunching of light. Finally, we propose some possible experimental realizations of such states.

quant-ph↗