Related papers: Absolute dimensionality of quantum ensembles

The notion of computability is stable (i.e. independent of the choice of an indexing) over infinite-dimensional vector spaces provided they have a finite "tensorial dimension". Such vector spaces with a finite tensorial dimension permit to…

Quantum state exclusion is the task of determining which states from a given set a system was not prepared in. We provide a complete solution to optimal quantum state exclusion for arbitrary sets of pure states generated by finite groups,…

We consider the problem of determining the state of an unknown quantum sequence without error. The elements of the given sequence are drawn with equal probability from a known set of linearly independent pure quantum states with the…

Experimental determination of an unknown quantum state usually requires several incompatible measurements. However, it is also possible to determine the full quantum state from a single, repeated measurement. For this purpose, the quantum…

Quantum coherence quantifies the amount of superposition in a quantum system, and is the reason and resource behind several phenomena and technologies. It depends on the natural basis in which the quantum state of the system is expressed,…

Quantum theory is traditionally formulated using complex numbers. This imaginarity of quantum theory has been quantified as a resource with applications in discrimination tasks, pseudorandomness generation, and quantum metrology. Here we…

If a one-phrase summary of the subject of this thesis were required, it would be something like: miscellaneous large (but finite) dimensional phenomena in quantum information theory. That said, it could nonetheless be helpful to briefly…

We present a scalable, robust approach to creating quantum programs of arbitrary size and complexity. The approach is based on the true abstraction of the problem. The quantum program is expressed in terms of a high-level model together…

The determination of the quantum properties of a single mode radiation field by heterodyne or double homodyne detection is studied. The realistic case of not fully efficient photodetectors is considered. It is shown that a large amount of…

The concept of supersymmetry in a quantum mechanical system is extended, permitting the recognition of many more supersymmetric systems, including very familiar ones such as the free particle. Its spectrum is shown to be supersymmetric,…

Quantum states that remain separable (i.e., not entangled) under any global unitary transformation are known as absolutely separable and form a convex set. Despite extensive efforts, the complete characterization of this set remains largely…

Entanglement is a non local property of quantum states which has no classical counterpart and plays a decisive role in quantum information theory. Several protocols, like the teleportation, are based on quantum entangled states. Moreover,…

High-dimensional quantum steering can be seen as a test for the dimensionality of entanglement, where the devices at one side are not characterized. As such, it is an important component in quantum informational protocols that make use of…

In this paper, we investigate the classicality and quantumness of a quantum ensemble. We define a quantity called classicality to characterize how classical a quantum ensemble is. An ensemble of commuting states that can be manipulated…

We address the problem of testing the dimensionality of classical and quantum systems in a `black-box' scenario. We develop a general formalism for tackling this problem. This allows us to derive lower bounds on the classical dimension…

Based on phase-space structures of quantum states, we propose a novel measure to quantify macroscopic quantum superpositions. Our measure simultaneously quantifies two different kinds of essential information for a given quantum state in a…

We argue that the dimensionality of the space of quantum systems' states should be considered as a legitimate resource for quantum information tasks. The assertion is supported by the fact that quantum states with discord-like capacities…

The main purpose of this tutorial is to elucidate in details what should be meant by ensemble of states in quantum mechanics, and to properly address the problem of discriminating, exactly or approximately, two different ensembles. To this…

Determining the state of a quantum system is a consuming procedure. For this reason, whenever one is interested only in some particular property of a state, it would be desirable to design a measurement setup that reveals this property with…

Machine learning is a fascinating and exciting field within computer science. Recently, this excitement has been transferred to the quantum information realm. Currently, all proposals for the quantum version of machine learning utilize the…