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We introduce a systematic protocol for constructing quantum Hilbert-space-fragmented Hamiltonians, whose Krylov-sector structure, unlike in classically fragmented models, can be fully resolved only in an entangled basis. The protocol takes…

We introduce a ``Statistical Query Sampling'' model, in which the goal of an algorithm is to produce an element in a hidden set $Ssubseteqbit^n$ with reasonable probability. The algorithm gains information about $S$ through oracle calls…

Quantum Key Distribution (QKD) is rapidly transitioning from cutting-edge laboratory research to real-world deployment in established communication networks. Although QKD promises future-proof security, practical challenges stil exist due…

Image hashing is a principled approximate nearest neighbor approach to find similar items to a query in a large collection of images. Hashing aims to learn a binary-output function that maps an image to a binary vector. For optimal…

Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…

We construct approximately local observables, or "overlapping qubits", using non-isometric maps and show that processes in local effective theories can be spoofed with a quantum system with fewer degrees of freedom, similar to our…

In the distribution of quantum states over a long distance, not only are quantum states corrupted by interactions with an environment but also a measurement setting should be re-aligned such that detection events can be ensured for the…

We consider two quantum cryptographic schemes relying on encoding the key into qudits, i.e. quantum states in a d-dimensional Hilbert space. The first cryptosystem uses two mutually unbiased bases (thereby extending the BB84 scheme), while…

The field of quantum algorithms is vibrant. Still, there is currently a lack of programming languages for describing quantum computation on a practical scale, i.e., not just at the level of toy problems. We address this issue by introducing…

Because of its mathematical tractability, the Gaussian mixture model holds a special place in the literature for clustering and classification. For all its benefits, however, the Gaussian mixture model poses problems when the data is skewed…

This paper studies iterative schemes for measure transfer and approximation problems, which are defined through a slicing-and-matching procedure. Similar to the sliced Wasserstein distance, these schemes benefit from the availability of…

We study the mapping which occurs when a single qubit in an arbitrary state interacts with another qubit in a given, fixed state resulting in some unitary transformation on the two qubit system which, in effect, makes two copies of the…

Quantum coherence and distributed correlations among subparties are often considered as separate, although operationally linked to each other, properties of a quantum state. Here, we propose a measure able to quantify the contributions…

Quantum metrology typically demands the preparation of exotic quantum probe states, such as entangled or squeezed states, to surpass classical limits. However, the need for carefully calibrated system parameters and finely optimized quantum…

Covert and secret quantum key distribution aims at generating information-theoretically secret bits between distant legitimate parties in a manner that remains provably undetectable by an adversary. We propose a framework in which to…

Measurements in the quantum domain can exceed classical notions. This concerns fundamental questions about the nature of the measurement process itself, as well as applications, such as their function as building blocks of quantum…

In recent work we have shown how an accurate reduced model can be utilized to perform mesh refinement in random space. That work relied on the explicit knowledge of an accurate reduced model which is used to monitor the transfer of activity…

Estimating the dimension of an Hilbert space is an important component of quantum system identification. In quantum technologies, the dimension of a quantum system (or its corresponding accessible Hilbert space) is an important resource, as…

In this article, we use the theory of quantum channels and open quantum systems to provide an efficient unitary characterization of a class of stochastic generators known as quantum hidden Markov models (QHMMs). By utilizing the unitary…

Cryptography is the science of using mathematics to encrypt and decrypt data. Cryptography enables you to store sensitive information or transmit it across insecure networks so that it cannot be read by anyone except the intended recipient.…