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/ √ 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.

We point out a contrasting role the entanglement plays in communication and estimation scenarios. In the first case it brings noticeable benefits at the measurement stage (output super-additivity), whereas in the latter it is the entanglement of the input probes that enables significant performance enhancement (input super-additivity). We identify a weak estimation regime where a strong connection between concepts crucial to the two fields is demonstrated; the accessible information and the Holevo quantity on one side and the quantum Fisher information related quantities on the other. This allows us to shed new light on the problem of super-additivity in communication using the concepts of quantum estimation theory. of merit used in estimation and communication approaches are usually different [14]. The central problem of quantum communication and estimation theories is to identify the potential benefits coming from exploiting entanglement in the input states as well as at the measurement stage of the protocols. Interestingly, unlike in the communication problem, there is a great number of examples demonstrating significant gains coming from the use of entangled input probes in quantum estimation protocols, with applications ranging from optical and atomic interferometry, via magnetometry to spectroscopy and atomic clocks stabilization [17][18][19][20][21][22][23]. At the same time, in a typical estimation protocol utilizing unentangled input probes collective measurements are typically irrelevant. Thus a contrasting picture emerges: when thinking of capacities of quantum channels gains in information processing arising from utilizing entanglement are at the measurement stage whereas it is the input stage where entanglement makes a difference in the estimation scenarios.The goal of this paper is to better understand the connections between the two fields from the point of view of the super-additivity issue, understood here as a general question of utility of entanglement in estimation/ communication protocols. We show that in the weak estimation regime, where the amount of information extractable on the parameter is very small compared to the prior information, i.e. the error of estimation is large compared with the variance of prior distribution, the accessible information as well as the Holevo quantity can be expressed using Fisher information (FI)-like concepts, which allows us to discuss utility of entanglement in communication using the properties of quantities well understood within the field of quantum estimation. We also point out that in a communication problem encoding a large number of independent parameters is favored even at the cost of their limited estimation precision, which makes the estimation strategy of learning a given parameter with highest possible accuracy not likely to be useful for the communication purposes. In order to make the paper self-contained we also recall some of the recent results on applications of rate-distortion theory in quantum estimation, which is another way of connecti...

We investigate the post-quantum security of hash functions based on the sponge construction. A crucial property for hash functions in the post-quantum setting is the collapsing property (a strengthening of collision-resistance). We show that the sponge construction is collapsing (and in consequence quantum collision-resistant) under suitable assumptions about the underlying block function. In particular, if the block function is a random function or a (non-invertible) random permutation, the sponge construction is collapsing. Contents 1 Introduction 1 2 Preliminaries 4 3 Collapsing hash functions 6 3.1 Definitions for concrete security 7 4 The sponge construction 9 5 Collision-resistance of the sponge construction 10 5.1 Random sponges. .. .. .. . 12 6 Sponges are collapsing 13 6.1 Using random oracles or random permutations. .. .. .. 17 6.2 Concrete security results. .. . 19 6.3 Using random oracles or random permutations. .. .. .. 25 7 Quantum Attack 26 7.1 Quantum Collision Finding With Random Oracle. .. .. . 27 Index 29 Symbol index 30 References 30

We study the impact of many-body effects on the fundamental precision limits in quantum metrology. On the one hand such effects may lead to nonlinear Hamiltonians, studied in the field of nonlinear quantum metrology, while on the other hand they may result in decoherence processes that cannot be described using single-body noise models. We provide a general reasoning that allows to predict the fundamental scaling of precision in such models as a function of the number of atoms present in the system. Moreover, we describe a computationally efficient approach that allows for a simple derivation of quantitative bounds. We illustrate these general considerations by a detailed analysis of fundamental precision bounds in a paradigmatic atomic interferometry experiment with standard linear Hamiltonian but with both single and two-body losses taken into account-a model which is motivated by the most recent Bose-Einstein condensate magnetometry experiments. Using this example we also highlight the impact of the atom number super-selection rule on the possibility of protecting interferometric protocols against decoherence.

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