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Kolmogorov's foundation of probability takes measure spaces, $\sigma$-algebras, and probability measures as basic objects. It is, however, widely recognized that this classical framework is inadequate for random phenomena involving quantum…

In classical physics, memoryless dynamics and Markovian statistics are one and the same. This is not true for quantum dynamics, first and foremost because quantum measurements are invasive. Going beyond measurement invasiveness, here we…

The usual conjectures of quantum measurements approaches, inspired from the traditional interpretation of Heisenberg's ("uncertainty") relations, are proved as being incorrect. A group of reconsidered conjectures and a corresponding new…

Residue arithmetic is an elegant and convenient way of computing with integers that exceed the natural word size of a computer. The algorithms are highly parallel and hence naturally adapted to quantum computation. The process differs from…

Random-access quantum memories may offer computational advantages for quantum computers and networks. In this paper, we advance arrays of solid-state quantum memories towards their usage as random-access quantum memory. We perform quantum…

A bit-quantum map relates probabilistic information for Ising spins or classical bits to quantum spins or qubits. Quantum systems are subsystems of classical statistical systems. The Ising spins can represent macroscopic two-level…

The uncertainty principle restricts potential information one gains about physical properties of the measured particle. However, if the particle is prepared in entanglement with a quantum memory, the corresponding entropic uncertainty…

We design machines that learn how to rotate a quantum bit about an initially unknown direction, encoded in the state of a spin-j particle. We show that a machine equipped with a quantum memory of O(log j) qubits can outperform all machines…

Quantum computers are promising tools for the simulation of many-body systems, and among those, QCD stands out by its rich phenomenology. Every simulation starts with a codification, and here we succently review a newly developed compact…

The classification of big data usually requires a mapping onto new data clusters which can then be processed by machine learning algorithms by means of more efficient and feasible linear separators. Recently, Lloyd et al. have advanced the…

Over decades traditional information theory of source and channel coding advances toward learning and effective extraction of information from data. We propose to go one step further and offer a theoretical foundation for learning classical…

Richard Feynman's observation that quantum mechanical effects could not be simulated efficiently on a computer led to speculation that computation in general could be done more efficiently if it used quantum effects. This speculation…

Quantum communication leads to strong correlations, that can outperform classical ones. Complementary to previous works in this area, we investigate correlations in prepare-and-measure scenarios assuming a bound on the information content…

Quantum and classical mechanics share a common algebraic formalism which is expressed naturally in the language of category theory. A third realization of this formalism is the so-called hyperbolic quantum mechanics where split-complex…

Forgetfulness is a common feature of nature. Moreover, without forgetfulness, repeatability would be impossible. Despite this, small systems constantly leak information about their state to their surroundings, and quantum mechanics tells us…

Quantum Random Access Memory (QRAM) has the potential to revolutionize the area of quantum computing. QRAM uses quantum computing principles to store and modify quantum or classical data efficiently, greatly accelerating a wide range of…

Quantum information science currently poses a troubling contradiction. It can be summarized as: (1) To factor efficiently, quantum computers must perform exponentially precise energy estimation. (2) Exponentially precise energy estimation…

Quantum models of computation are widely believed to be more powerful than classical ones. Efforts center on proving that, for a given problem, quantum algorithms are more resource efficient than any classical one. All this, however,…

Cumulative memory -- the sum of space used per step over the duration of a computation -- is a fine-grained measure of time-space complexity that was introduced to analyze cryptographic applications like password hashing. It is a more…

The idea of the quantum computation is based on paradoxical principles of quantum physics, superposition and entanglement of quantum states. This idea looks well-founded on the microscopic level in spite of the absence of an universally…