arXiv subjects

R. Demkowicz-Dobrzanski

Publications and source records attributed to R. Demkowicz-Dobrzanski.

10 recordsLinked to original sources

arXiv2018

Quantum limits in optical interferometry

Non-classical states of light find applications in enhancing the performance of optical interferometric experiments, with notable example of gravitational wave-detectors. Still, the presence of decoherence hinders significantly the performance of quantum-enhanced protocols. In this review, we summarize the developments of quantum metrology with particular focus on optical interferometry and derive fundamental bounds on achievable quantum-enhanced precision in optical interferometry taking into account the most relevant decoherence processes including: phase diffusion, losses and imperfect interferometric visibility. We introduce all the necessary tools of quantum optics as well as quantum estimation theory required to derive the bounds. We also discuss the practical attainability of the bounds derived and stress in particular that the techniques of quantum-enhanced interferometry which are being implemented in modern gravitational wave detectors are close to the optimal ones.

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arXiv2018

Adaptive quantum metrology under general Markovian noise

We consider a general model of unitary parameter estimation in presence of Markovian noise, where the parameter to be estimated is associated with the Hamiltonian part of the dynamics. In absence of noise, unitary parameter can be estimated with precision scaling as $1/T$, where $T$ is the total probing time. We provide a simple algebraic condition involving solely the operators appearing in the quantum Master equation, implying at most $1/\sqrt{T}$ scaling of precision under the most general adaptive quantum estimation strategies. We also discuss the requirements a quantum error-correction like protocol must satisfy in order to regain the $1/T$ precision scaling in case the above mentioned algebraic condition is not satisfied. Furthermore, we apply the developed methods to understand fundamental precision limits in atomic interferometry with many-body effects taken into account, shedding new light on the performance of non-linear metrological models.

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arXiv2017

Discrete-to-continuous transition in quantum phase estimation

We analyze the problem of quantum phase estimation where the set of allowed phases forms a discrete $N$ element subset of the whole $[0,2π]$ interval, $φ_n = 2πn/N$, $n=0,\dots N-1$ and study the discrete-to-continuous transition $N\rightarrow\infty$ for various cost functions as well as the mutual information. We also analyze the relation between the problems of phase discrimination and estimation by considering a step cost functions of a given width $σ$ around the true estimated value. We show that in general a direct application of the theory of covariant measurements for a discrete subgroup of the $U(1)$ group leads to suboptimal strategies due to an implicit requirement of estimating only the phases that appear in the prior distribution. We develop the theory of sub-covariant measurements to remedy this situation and demonstrate truly optimal estimation strategies when performing transition from a discrete to the continuous phase estimation regime.

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arXiv2013

Experimental generation of complex noisy photonic entanglement

We present an experimental scheme based on spontaneous parametric down-conversion to produce multiple photon pairs in maximally entangled polarization states using an arrangement of two type-I nonlinear crystals. By introducing correlated polarization noise in the paths of the generated photons we prepare mixed entangled states whose properties illustrate fundamental results obtained recently in quantum information theory, in particular those concerning bound entanglement and privacy.

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arXiv2012

Quantum Key Distribution with Qubits Encoded in Qutrit

We present a novel one-way quantum key distribution protocol based on 3-dimensional quantum state, a qutrit, that encodes two qubits in its 2-dimensional subspaces. The qubits hold the classical bit information that has to be shared between the legitimate users. Alice sends such a qutrit to Bob where he decodes one of the qubit and measures it along the random Pauli basis. This scheme has higher secure key rate at longer transmission distance than the standard BB84 protocol.

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arXiv2009

Experimental quantum-enhanced estimation of a lossy phase shift

When standard light sources are employed, the precision of the phase determination is limited by the shot noise. Quantum entanglement provides means to exceed this limit with the celebrated example of N00N states that saturate the ultimate Heisenberg limit on precision, but at the same time are extremely fragile to losses. In contrast, we provide experimental evidence that appropriately engineered quantum states outperform both standard and N00N states in the precision of phase estimation when losses are present.

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arXiv2009

Quantum phase estimation with lossy interferometers

We give a detailed discussion of optimal quantum states for optical two-mode interferometry in the presence of photon losses. We derive analytical formulae for the precision of phase estimation obtainable using quantum states of light with a definite photon number and prove that maximization of the precision is a convex optimization problem. The corresponding optimal precision, i.e. the lowest possible uncertainty, is shown to beat the standard quantum limit thus outperforming classical interferometry. Furthermore, we discuss more general inputs: states with indefinite photon number and states with photons distributed between distinguishable time bins. We prove that neither of these is helpful in improving phase estimation precision.

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arXiv2009

Optimal Quantum Phase Estimation

By using a systematic optimization approach we determine quantum states of light with definite photon number leading to the best possible precision in optical two mode interferometry. Our treatment takes into account the experimentally relevant situation of photon losses. Our results thus reveal the benchmark for precision in optical interferometry. Although this boundary is generally worse than the Heisenberg limit, we show that the obtained precision beats the standard quantum limit thus leading to a significant improvement compared to classical interferometers. We furthermore discuss alternative states and strategies to the optimized states which are easier to generate at the cost of only slightly lower precision.

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arXiv2006

The Quantum Cocktail Party

We consider the problem of decorrelating states of coupled quantum systems. The decorrelation can be seen as separation of quantum signals, in analogy to the classical problem of signal-separation rising in the so-called cocktail-party context. The separation of signals cannot be achieved perfectly, and we analyse the optimal decorrelation map in terms of added noise in the local separated states. Analytical results can be obtained both in the case of two-level quantum systems and for Gaussian states of harmonic oscillators.

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arXiv2006

How to hide a secret direction

We present a procedure to share a secret spatial direction in the absence of a common reference frame using a multipartite quantum state. The procedure guarantees that the parties can determine the direction if they perform joint measurements on the state, but fail to do so if they restrict themselves to local operations and classical communication (LOCC). We calculate the fidelity for joint measurements, give bounds on the fidelity achievable by LOCC, and prove that there is a non-vanishing gap between the two of them, even in the limit of infinitely many copies. The robustness of the procedure under particle loss is also studied. As a by-product we find bounds on the probability of discriminating by LOCC between the invariant subspaces of total angular momentum N/2 and N/2-1 in a system of N elementary spins.

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