Related papers: The Operational Choi-Jamiolkowski Isomorphism
One can view quantum mechanics as a generalization of classical probability theory that provides for pairwise interference among alternatives. Adopting this perspective, we ``quantize'' the classical random walk by finding, subject to a…
We add non-linear and state-dependent terms to quantum field theory. We show that the resulting low-energy theory, non-linear quantum mechanics, is causal, preserves probability and permits a consistent description of the process of…
Quantum nonlocality without entanglement (Q-NWE) encapsulates nonlocal behavior of multipartite product states as they may entail global operation for optimal decoding of the classical information encoded within. Here we show that the…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
We introduce and study the notion of steerability for channels. This generalizes the notion of steerability of bipartite quantum states. We discuss a key conceptual difference between the case of states and the case of channels: while state…
Nonlocality is a property of paramount importance both conceptually and computationally exhibited by quantum systems, which has no classical counterpart. Conceptually, it is important because it implies that the evolving system has…
This paper presents a minimal formulation of nonrelativistic quantum mechanics, by which is meant a formulation which describes the theory in a succinct, self-contained, clear, unambiguous and of course correct manner. The bulk of the…
Homomorphisms between relational structures play a central role in finite model theory, constraint satisfaction and database theory. A central theme in quantum computation is to show how quantum resources can be used to gain advantage in…
We propose an exercise in which one attempts to deduce the formalism of quantum mechanics solely from phenomenological observations. The only assumed inputs are the multi-time probability distributions estimated from the results of…
The statistical model of quantum mechanics is based on the mapping between operators on the Hilbert space and functions on the phase space. This map can be implemented by an operator that satisfies physically motivated Stratonovich-Weyl…
Contextuality is a central feature of quantum theory, traditionally understood as the impossibility of reproducing quantum measurement statistics using noncontextual ontological models. We study classical ontological descriptions in which a…
The properties which give quantum mechanics its unique character - unitarity, complementarity, non-commutativity, uncertainty, nonlocality - derive from the algebraic structure of Hermitian operators acting on the wavefunction in complex…
In this paper we develop an operational formulation of General Relativity similar in spirit to existing operational formulations of Quantum Theory. To do this we introduce an operational space (or op-space) built out of scalar fields. A…
We have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
The equivalence postulate of quantum mechanics offers an axiomatic approach to quantum field theories and quantum gravity. The equivalence hypothesis can be viewed as adaptation of the classical Hamilton-Jacobi formalism to quantum…
In this work, we give rigorous operational meaning to superposition of causal orders. This fits within a recent effort to understand how the standard operational perspective on quantum theory could be extended to include indefinite…
We present an alternative formalism of quantum mechanics tailored to statistical ensemble in phase space. The purpose of our work is to show that it is possible to establish an alternative autonomous formalism of quantum mechanics in phase…
We demonstrate that quantum instruments can provide a unified operational foundation for quantum theory. Since these instruments directly correspond to laboratory devices, this foundation provides an alternate, more experimentally grounded,…
We study the possibility of applying statistical mechanics to generally covariant quantum theories with a vanishing Hamiltonian. We show that (under certain appropiate conditions) this makes sense, in spite of the absence of a notion of…