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We study the behaviour of two different measures of the complexity of multipartite correlation patterns, weaving and neural complexity, for symmetric quantum states. Weaving is the weighted sum of genuine multipartite correlations of any…
Quantum state discrimination is an important problem in many information processing tasks. In this work we are concerned with finding its best possible sample complexity when the states are preprocessed by a quantum channel that is required…
The quantum capacity of a noisy quantum channel determines the maximal rate at which we can code reliably over asymptotically many uses of the channel, and it characterizes the channel's ultimate ability to transmit quantum information…
Quantum complexity is a measure of the minimal number of elementary operations required to approximately prepare a given state or unitary channel. Recently, this concept has found applications beyond quantum computing -- in studying the…
We initiate a study of the complexity of quantum field theories (QFTs) by proposing a measure of information contained in a QFT and its observables. We show that from minimal assertions, one is naturally led to measure complexity by two…
We show how to compute or at least to estimate various capacity-related quantities for Bosonic Gaussian channels. Among these are the coherent information, the entanglement assisted classical capacity, the one-shot classical capacity, and a…
We investigate how the addition of quantum resources changes the statistical complexity of quantum circuits by utilizing the framework of quantum resource theories. Measures of statistical complexity that we consider include the Rademacher…
We study the computational complexity of quantum-mechanical expectation values of single-particle operators in bosonic and fermionic multi-particle product states. Such expectation values appear, in particular, in full-counting-statistics…
The goal of quantum channel discrimination and estimation is to determine the identity of an unknown channel from a discrete or continuous set, respectively. The query complexity of these tasks is equal to the minimum number of times one…
Quantum channels describe subsystem or open system evolution. Using the classical Koopman operator that evolves functions on phase space, 4 classical Koopman channels are identified that are analogs of the 4 possible quantum channels in a…
We use multi-time correlation functions of quantum systems to construct random variables with statistical properties that reflect the degree of complexity of the underlying quantum dynamics.
This thesis deals with the study of quantum communication protocols with Continuous Variable (CV) systems. Continuous Variable systems are those described by canonical conjugated coordinates x and p endowed with infinite dimensional Hilbert…
We extend a recent method to detect lower bounds to the quantum capacity of quantum communication channels by considering realistic scenarios with general input probe states and arbitrary detection procedures at the output. Realistic…
We present a both simple and comprehensive graphical calculus for quantum computing. In particular, we axiomatize the notion of an environment, which together with the earlier introduced axiomatic notion of classical structure enables us to…
The impact of a noisy Gaussian channel on a wide range of non-Gaussian input states is studied in this work. The nonclassical nature of the states, both input and output, is developed by studying the corresponding photon statistics and…
The purpose of this work is to extend the result of previous papers quant-ph/9611023, quant-ph/9703013 to quantum channels with additive constraints onto the input signal, by showing that the capacity of such channel is equal to the…
Gaussian quantum channels constitute a cornerstone of continuous-variable quantum information science, underpinning a wide array of protocols in quantum optics and quantum metrology. While the action of such channels on arbitrary states is…
The creation complexity of a quantum state is the minimum number of elementary gates required to create it from a basic initial state. The creation complexity of quantum states is closely related to the complexity of quantum circuits, which…
The zero-error capacity of quantum channels was defined as the least upper bound of rates at which classical information can be transmitted through a quantum channel with probability of error equal to zero. This paper investigates some…
Recent years have seen significant activity on the problem of using data for the purpose of learning properties of quantum systems or of processing classical or quantum data via quantum computing. As in classical learning, quantum learning…