arXiv subjects

Florian Fröwis

Publications and source records attributed to Florian Fröwis.

27 records · Page 2Linked to original sources

arXiv2015

Noise in optical quantum memories based on dynamical decoupling of spin states

Long-lived optical quantum memories are of great importance for scalable distribution of entanglement over remote networks (e.g. quantum repeaters). Long-lived storage generally relies on storing the optical states as spin excitations since these often exhibit long coherence times. To extend the storage time beyond the intrinsic spin dephasing time one can use dynamical decoupling techniques. However, it has been shown that dynamical decoupling introduces noise in optical quantum memories based on ensembles of atoms. In this article a simple model is proposed to calculate the resulting signal-to-noise ratio, based on intrinsic quantum memory parameters such as the optical depth of the ensemble. We also characterize several dynamical decoupling sequences that are efficient in reducing this particular noise. Our calculations indicate that it should be feasible to reach storage times well beyond one second under reasonable experimental conditions.

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arXiv2015

Tighter quantum uncertainty relations follow from a general probabilistic bound

Uncertainty relations (URs) like the Heisenberg-Robertson or the time-energy UR are often considered to be hallmarks of quantum theory. Here, a simple derivation of these URs is presented based on a single classical inequality from estimation theory, a Cramér-Rao-like bound. The Heisenberg-Robertson UR is then obtained by using the Born rule and the Schrödinger equation. This allows a clear separtion of the probabilistic nature of quantum mechanics from the Hilbert space structure and the dynamical law. It also simplifies the interpretation of the bound. In addition, the Heisenberg-Robertson UR is tightened for mixed states by replacing one variance by the so-called quantum Fisher information. Thermal states of Hamiltonians with evenly-gapped energy levels are shown to saturate the tighter bound for natural choices of the operators. This example is further extended to Gaussian states of a harmonic oscillator. For many-qubit systems, we illustrate the interplay between entanglement and the structure of the operators that saturate the UR with spin-squeezed states and Dicke states.

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arXiv2015

Algebraic metrology: Pretty good states and bounds

We investigate quantum metrology using a Lie algebraic approach for a class of Hamiltonians, including local and nearest-neighbor interaction Hamiltonians. Using this Lie algebraic formulation, we identify and construct highly symmetric states that admit Heisenberg scaling in precision in the absence of noise, and investigate their performance in the presence of noise. To this aim we perform a numerical scaling analysis, and derive upper bounds on the quantum Fisher information.

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arXiv2013

Certifiability criterion for large-scale quantum systems

Can one certify the preparation of a coherent, many-body quantum state by measurements with bounded accuracy in the presence of noise and decoherence? Here, we introduce a criterion to assess the fragility of large-scale quantum states which is based on the distinguishability of orthogonal states after the action of very small amounts of noise. States which do not pass this criterion are called asymptotically incertifiable. We show that, if a coherent quantum state is asymptotically incertifiable, there exists an incoherent mixture (with entropy at least log 2) which is experimentally indistinguishable from the initial state. The Greenberger-Horne-Zeilinger states are examples of such asymptotically incertifiable states. More generally, we prove that any so-called macroscopic superposition state is asymptotically incertifiable. We also provide examples of quantum states that are experimentally indistinguishable from highly incoherent mixtures, i.e., with an almost-linear entropy in the number of qubits. Finally we show that all unique ground states of local gapped Hamiltonians (in any dimension) are certifiable.

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arXiv2013

Effective noise channels for encoded quantum systems

We investigate effective noise channels for encoded quantum systems with and without active error correction. Noise acting on physical qubits forming a logical qubit is thereby described as a logical noise channel acting on the logical qubits, which leads to a significant decrease of the effective system dimension. This provides us with a powerful tool to study entanglement features of encoded quantum systems. We demonstrate this framework by calculating lower bounds on the lifetime of distillable entanglement and the negativity for encoded multipartite qubit states with different encodings. At the same time, this approach leads to a simple understanding of the functioning of (concatenated) error correction codes.

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arXiv2012

Measures of macroscopicity for quantum spin systems

We investigate the notion of "macroscopicity" in the case of large quantum spin systems and provide two main results. First, we motivate the Fisher information as a measure for the macroscopicity of quantum states. Second, we compare the existing literature of this topic. We report on a hierarchy among the measures and we conclude that one should carefully distinguish between "macroscopic quantum states" and "macroscopic superpositions", which is a strict subclass of the former.

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arXiv2012

Kind of entanglement that speeds up quantum evolution

The "speed" of unitary quantum evolution was recently shown to be connected to entanglement in multipartite quantum systems. Here, we discuss a tighter version of the Mandelstam-Tamm uncertainty relation that depends on the Fisher information. The passage time is estimated by a lower bound that depends inversely proportional to the square root of the Fisher information. This leads to a better understanding of the origin of a fast quantum time evolution of entangled states.

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arXiv2012

Stability of encoded macroscopic quantum superpositions

The multipartite Greenberger-Horne-Zeilinger (GHZ) state is a paradigmatic example of a highly entangled multipartite states with distinct quantum features. However, the GHZ state is very sensitive to generic decoherence processes, where its quantum features and in particular its entanglement diminish rapidly, thereby hindering possible practical applications e.g. in the context of quantum metrology. In this paper, we discuss GHZ-like quantum states with a block-local structure and show that they exhibit a drastically increased stability against noise for certain choices of block-encoding. We analyze in detail the decay of the interference terms, the entanglement in terms of distillable entanglement and Negativity as well as the notion of macroscopicity as measured by the so-called q-index, and provide general bounds on these quantities. We focus on an encoding where logical qubits are themselves encoded as GHZ states, which leads to so-called concatenated GHZ (C-GHZ) states. We compare the stability of C-GHZ states with other types of encodings, thereby showing the superior stability of the C-GHZ states. Analytic results are complemented by numerical studies, where tensor network techniques are used to investigate the quantum properties of multipartite entangled states under the influence of decoherence.

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arXiv2008

Fleming's bound for the decay of mixed states

Fleming's inequality is generalized to the decay function of mixed states. We show that for any symmetric hamiltonian $h$ and for any density operator $ρ$ on a finite dimensional Hilbert space with the orthogonal projection $Π$ onto the range of $ρ$ there holds the estimate $\Tr(Π\rme^{-\rmi ht}ρ\rme^{\rmi ht}) \geq\cos^{2}((Δh)_ρt) $ for all real $t$ with $(Δh)_ρ| t| \leqπ/2.$ We show that equality either holds for all $t\in\mathbb{R}$ or it does not hold for a single $t$ with $0<(Δh)_ρ| t| \leqπ/2.$ All the density operators saturating the bound for all $t\in\mathbb{R},$ i.e. the mixed intelligent states, are determined.

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