arXiv subjects

Matthias Freyberger

Publications and source records attributed to Matthias Freyberger.

At least 19 recordsLinked to original sources

arXiv2023

The Wave Functional of the Vacuum in a Resonator

We show that despite the fundamentally different situations, the wave functional of the vacuum in a resonator is identical to that of free space. The infinite product of Gaussian ground state wave functions defining the wave functional of the vacuum translates into an exponential of a sum rather than an integral over the squares of mode amplitudes weighted by the mode volume and a power of the mode wave number. We express this sum by an integral of a bilinear form of the field containing a kernel given by a function of the square root of the negative Laplacian acting on a transverse delta function. For transverse fields it suffices to employ the familiar delta function which allows us to obtain explicit expressions for the kernels of the vector potential, the electric field and the magnetic induction. We show for the example of the vector potential that different mode expansions lead to different kernels. Lastly, we show that the kernels have a close relationship with the Wightman correlation functions of the fields.

physics.gen-ph↗

arXiv2021

Qubit-based momentum measurement of a particle

An early approach to include pointers representing measurement devices into quantum mechanics was given by von Neumann. Based on this idea, we model such pointers by qubits and couple them to a free particle, in analogy to a classical time-of-flight arrangement. The corresponding Heisenberg dynamics leads to pointer observables whose expectation values allow us to reconstruct the particle's momentum distribution via the characteristic function. We investigate different initial qubit states and find that such a reconstruction can be considerably simplified by initially entangled pointers.

quant-ph↗

arXiv2019

Pointer-based model for state reduction in momentum space

We revisit the pointer-based measurement concept of von Neumann which allows us to model a quantum counterpart of the classical time-of-flight (ToF) momentum. Our approach is based on the Hamiltonian for a particle interacting with two quantum pointers serving as basic measurement devices. The corresponding dynamics leads to a pointer-based ToF observable for the operational momentum of the particle. We can consider single measurements of our quantum pointers and show that this process will result in a state reduction for a single particle being downstream of the time-of-flight setup.

quant-ph↗

arXiv2015

Steady-state entanglement enhanced by a dissipative ancilla

We investigate how to enhance entanglement in the steady state of interacting two-level systems. The steady state is reached by spontaneous decay of the individual systems. When we additionally couple them to a dissipative two-level ancilla with variable eigenfrequency and coupling strength, we observe a considerable enhancement effect in the entanglement of this steady state. Moreover, we see that the increased entanglement is directly connected to the selection of certain excited states via the environment disturbing the ancilla. This effect could be used in dissipative state preparation schemes as well as a testbed for decoherence models.

quant-ph↗

arXiv2015

Entropic uncertainty bound for open pointer-based simultaneous measurements of conjugate observables

We discuss the information entropy for a general open pointer-based simultaneous measurement and show how it is bound from below. This entropic uncertainty bound is a direct consequence of the structure of the entropy and can be obtained from the formal solution of the measurement dynamics. Furthermore, the structural properties of the entropy allow us to give an intuitive interpretation of the noisy influence of the pointers and the environmental heat bath on the measurement results.

quant-ph↗

arXiv2014

Pointer-based simultaneous measurements of conjugate observables in a thermal environment

We combine traditional pointer-based simultaneous measurements of conjugate observables with the concept of quantum Brownian motion of multipartite systems to phenomenologically model simultaneous measurements of conjugate observables in a thermal environment. This approach provides us with a formal solution of the complete measurement dynamics for quadratic Hamiltonians and we can therefore discuss the measurement uncertainty and optimal measurement times. As a main result, we obtain a lower bound for the uncertainty of a noisy measurement, which is an extension of a previously known uncertainty relation and in which the squeezing of the system state to be measured plays an important role. This also allows us to classify minimal uncertainty states in more detail.

quant-ph↗

arXiv2013

Entropic uncertainty relation for pointer-based simultaneous measurements of conjugate observables

We present a family of entropic uncertainty relations for pointer-based simultaneous measurements of conjugate observables. The lower bounds of these relations explicitly incorporate the influence of the measurement apparatus. We achieve this by using a mathematical theorem which states that the information entropy of convoluted probability distributions is bound from below. As a consequence of these results we can straightforwardly show that appropriately squeezed states are minimal entropy states for simultaneous measurements.

quant-ph↗

arXiv2012

Quantum optical reconstruction scheme using weak values

A quantum state contains the maximal amount of information available for a given quantum system. In this paper we use weak-value expressions to reconstruct quantum states of continuous-variable systems in the quantum optical domain. The role played by postselecting measured data will be particularly emphasized in the proposed setup, which is based on an interferometer just using simple homodyne detection.

quant-ph↗

arXiv2011

Simple Adaption of Measurements for Qudit Estimation

We present a strategy for estimation of d-level quantum states and for the simple adaption of corresponding measurements. The adaption method is inspired by mutually unbiased measurements, but it is also applicable in cases for which no complete set of mutually unbiased bases is known. We present results of Monte Carlo simulations, that demonstrate the fidelity gain of the adaptive strategy compared to a non-adaptive estimation.

quant-ph↗

arXiv2008

Adaptive estimation of qubits by symmetry measurements

We analyze quantum state estimation for finite samples based on symmetry information. The used measurement concept compares an unknown qubit to a reference state. We describe explicitly an adaptive strategy, that enhances the estimation fidelity of these measurements.

quant-ph↗

arXiv2007

Quantum estimation of a damping constant

We discuss an interferometric approach to the estimation of quantum mechanical damping. We study specific classes of entangled and separable probe states consisting of superpositions of coherent states. Based on the assumption of limited quantum resources we show that entanglement improves the estimation of an unknown damping constant.

quant-ph↗

arXiv2005

Iterative entanglement distillation for finite resources

We discuss a specific entanglement distillation scheme under the constraint of finite samples of entangled qubit pairs. It is shown that an iterative process can be explicitly formulated. The average fidelity of this process can be enhanced by introducing conditional storing of entangled qubit pairs in each step of the iteration. We investigate the corresponding limitations on the size and the initial fidelity of the sample.

quant-ph↗

arXiv2002

Wave Packets can Factorize Numbers

We draw attention to various aspects of number theory emerging in the time evolution of elementary quantum systems with quadratic phases. Such model systems can be realized in actual experiments. Our analysis paves the way to a new, promising and effective method to factorize numbers.

quant-ph↗

arXiv2002

Dynamics of entanglement between two trapped atoms

We investigate the dynamics of entanglement between two continuous variable quantum systems. The model system consists of two atoms in a harmonic trap which are interacting by a simplified s-wave scattering. We show, that the dynamically created entanglement changes in a steplike manner. Moreover, we introduce local operators which allow us to violate a Bell-CHSH inequality adapted to the continuous variable case. The correlations show nonclassical behavior and almost reach the maximal quantum mechanical value. This is interesting since the states prepared by this interaction are very different from any EPR-like state.

quant-ph↗

arXiv2002

Wave packet dynamics and factorization of numbers

We connect three phenomena of wave packet dynamics: Talbot images, revivals of a particle in a box and fractional revivals. The physical origin of these effects is deeply rooted in phase factors which are quadratic in the quantum number. We show that the characteristic structures in the time evolution of these systems allow us to factorize large integers.

quant-ph↗

arXiv2002

Channel Estimation with Noisy Entanglement

We analyze the Pauli-channel estimation with mixed nonseparable states. It turns out that within a specific range entanglement can serve as a nonclassical resource. However, this range is rather small, that is entanglement is not very robust for this application. We further show that Werner states yield the best result of all Bell diagonal states with the same amount of entanglement.

quant-ph↗

arXiv2001

Estimation of quantum channels with finite resources

We investigate the problem of determining the parameters that describe a quantum channel. It is assumed that the users of the channel have at best only partial knowledge of it and make use of a finite amount of resources to estimate it. We discuss simple protocols for the estimation of the parameters of several classes of channels that are studied in the current literature. We define two different quantitative measures of the quality of the estimation schemes, one based on the standard deviation, the other one on the fidelity. The possibility of protocols that employ entangled particles is also considered. It turns out that the use of entangled particles as a new kind of nonclassical resource enhances the estimation quality of some classes of quantum channel. Further, the investigated methods allow us to extend them to higher dimensional quantum systems.

quant-ph↗

arXiv2001

Enhanced Estimation of a Noisy Quantum Channel Using Entanglement

We discuss the estimation of channel parameters for a noisy quantum channel - the so-called Pauli channel - using finite resources. It turns out that prior entanglement considerably enhances the fidelity of the estimation when we compare it to an estimation scheme based on separable quantum states.

quant-ph↗