Related papers: Necessity of negativity in quantum theory

This article comprises a review of both the quasi-probability representations of infinite-dimensional quantum theory (including the Wigner function) and the more recently defined quasi-probability representations of finite-dimensional…

Several finite dimensional quasi-probability representations of quantum states have been proposed to study various problems in quantum information theory and quantum foundations. These representations are often defined only on restricted…

Quasiprobability representations, such as the Wigner function, play an important role in various research areas. The inevitable appearance of negativity in such representations is often regarded as a signature of nonclassicality, which has…

Building on earlier work, we further develop a formalism based on the mathematical theory of frames that defines a set of possible phase-space or quasi-probability representations of finite-dimensional quantum systems. We prove that an…

Negativity in a quasiprobability representation is typically interpreted as an indication of nonclassical behavior. However, this does not preclude states that are non-negative from exhibiting phenomena typically associated with quantum…

The appearance of negative terms in quasiprobability representations of quantum theory is known to be inevitable, and, due to its equivalence with the onset of contextuality, of central interest in quantum computation and information. Until…

The presence of unique quantum correlations is the core of quantum information processing and general quantum theory. We address the fundamental question of how quantum correlations of a generic quantum system can be probed using…

A web of cohomological facts relates quantum error correction, measurement-based quantum computation, symmetry protected topological order and contextuality. Here we extend this web to quantum computation with magic states. In this…

We describe a scheme of quantum computation with magic states on qubits for which contextuality is a necessary resource possessed by the magic states. More generally, we establish contextuality as a necessary resource for all schemes of…

Polarization quasiprobability distribution defined in the Stokes space shares many important properties with the Wigner function for the position and momentum. Most notably, they both give correct one-dimensional marginal probability…

The Wigner function of quantum systems is an effective instrument to construct the approximate classical description of the systems for which the classical approximation is possible. During the last time, the Wigner function formalism is…

Negativity in certain quasiprobability representations is a necessary condition for a quantum computational advantage. Here we define a quasiprobability representation exhibiting this property with respect to quantum computations in the…

One of the most central and controversial element of quantum mechanics is the use of non zero vectors of a Hilbert space (or, more generally, of one dimension subspaces) for representing the state of a quantum system. In particular, the…

Any bipartite quantum state has quasi-probability representations in terms of separable states. For entangled states these quasi-probabilities necessarily exhibit negativities. Based on the general structure of composite quantum states, one…

A central problem in quantum information is to determine the minimal physical resources that are required for quantum computational speedup and, in particular, for fault-tolerant quantum computation. We establish a remarkable connection…

We argue that Hilbert spaces are not suitable to represent quantum states mathematically, in the sense that they require properties that are untenable by physical entities. We first demonstrate that the requirements posited by complex inner…

Two notions of nonclassicality that have been investigated intensively are: (i) negativity, that is, the need to posit negative values when representing quantum states by quasiprobability distributions such as the Wigner representation, and…

We introduce a general method for the construction of quasiprobability representations for arbitrary notions of quantum coherence. Our technique yields a nonnegative probability distribution for the decomposition of any classical state.…

We study the possibility to describe pure quantum states and evens with classical probability distributions and conditional probabilities and show that the distributions and/or conditional probabilities have to assume negative values,…

Negativity of the Wigner function is arguably one of the most striking non-classical features of quantum states. Beyond its fundamental relevance, it is also a necessary resource for quantum speedup with continuous variables. As quantum…