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Quantum entanglement and coherence are two fundamental resources for quantum information processing. Recent results clearly demonstrate their relevance in quantum technological tasks, including quantum communication and quantum algorithms.…

We investigate the problem of "nonlocal" computation, in which separated parties must compute a function with nonlocally encoded inputs and output, such that each party individually learns nothing, yet together they compute the correct…

We introduce a new aspect of nonlocality which arises when the task of quantum states distinguishability is considered under local operations and shared entanglement in the absence of classical communication. We find the optimal amount of…

Quantum states are represented by positive semidefinite Hermitian operators with unit trace, known as density matrices. An important subset of quantum states is that of separable states, the complement of which is the subset of…

In the past decades, quantum entanglement has been recognized to be the basic resource in quantum information theory. A fundamental need is then the understanding its qualification and its quantification: Is the quantum state entangled, and…

Quantum entanglement plays an important role in quantum computation and communication. It is necessary for many protocols and computations, but causes unexpected disturbance of computational states. Hence, static analysis of quantum…

We argue that entanglement is the essential non-classical ingredient which provides the computational speed-up in quantum algorithms as compared to algorithms based on the processes of classical physics.

Shor's factoring algorithm uses two quantum registers. By introducing more registers we show that the measured numbers in these registers which are of the same pre-measurement state, should be equal if the original Shor's complexity…

Coherence and entanglement are fundamental properties of quantum systems, promising to power the near future quantum computers, sensors and simulators. Yet, their experimental detection is challenging, usually requiring full reconstruction…

In a quantum computation with pure states, the generation of large amounts of entanglement is known to be necessary for a speedup with respect to classical computations. However, examples of quantum computations with mixed states are known,…

A contemporary technological milestone is to build a quantum device performing a computational task beyond the capability of any classical computer, an achievement known as quantum adversarial advantage. In what ways can the entanglement…

This note shows how quantum entanglement may be simulated in classical computing. The simulated entanglement protocol is implemented using oblivious transfer in the simplest case and other many-to-one mappings in more general cases. For the…

Recently Galv\~{a}o and Hardy have shown that quantum cloning can improve the performance of some quantum computation tasks. However such performance enhancement is possible only if quantum correlations survive the cloning process. We…

In quantum systems, entanglement corresponds to nonclassical correlation of nonlocal observables. Thus, entanglement (or, to the contrary, separability) of a given quantum state is not uniquely determined by properties of the state, but may…

Quantum entanglement is a key resource in quantum computing and quantum information processing tasks. However, its quantification remains a major challenge since it cannot be directly extracted from physical observables. To address this…

We present a necessary and sufficient condition to determine the entanglement status of an arbitrary N-qubit quantum state (may be pure or mixed) represented by the density matrix, (Rho)N. We develop a new approach and a new criterion for…

Entanglement quantification aims to assess the value of quantum states for quantum information processing tasks. A closely related problem is state convertibility, asking whether two remote parties can convert a shared quantum state into…

Resource identification and quantification is an essential element of both classical and quantum information theory. Entanglement is one of these resources, arising when quantum communication and nonlocal operations are expensive to…

In this paper, we study the nature of entanglement in quantum Grover's and Shor's algorithms. So far, the authors who have been interested in this problem have approached the question quantitatively by introducing entanglement measures…

Entanglement is a fundamental aspect of quantum physics, both conceptually and for its many applications. Classifying an arbitrary multipartite state as entangled or separable -- a task referred to as the separability problem -- poses a…