Related papers: Negative probabilities and counter-factual reasoni…
Weak measurements performed between quantum state preparation and post-selection result in complex values for self-adjoint operators, corresponding to complex conditional probabilities for the projections on specific eigenstates. In this…
Testing quantum theory on macroscopic scales is a longstanding challenge that might help to revolutionise physics. For example, laboratory tests (such as those anticipated in nanomechanical or biological systems) may look to rule out…
The counterfactuality of recently proposed protocols is analyzed. A definition of `counterfactuality' is offered and it is argued that an interaction-free measurement of the presence of an opaque object can be named `counterfactual', while…
In this paper we consider the phenomenon of superpositions in quantum mechanics and suggest a way to deal with the idea in a logical setting from a syntactical point of view, that is, as subsumed in the language of the formalism, and not…
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.…
Accepting information as a physical category and ascribing to inanimate matter some spirit (consciousness, intelligence) allows to explain quantum-mechanical phenomena, including delayed-choice and EPR-Bohm-Bell experiments, as well as…
Current quantum computer technology is sufficient to realize weak measurements and the corresponding concept of weak values. We demonstrate how the weak value anomaly can be tested, along with consistency and simultaneity of weak values,…
We study the two dual quantum information effects to manipulate the amount of information in quantum computation: hiding and allocation. The resulting type-and-effect system is fully expressive for irreversible quantum computing, including…
A central feature of quantum mechanics is the non-commutativity of operators used to describe physical observables. In this article, we present a critical analysis on the role of non-commutativity in quantum theory, focusing on its…
We present an experimental realisation of Hardy's thought experiment [Phys. Rev. Lett. {\bf 68}, 2981 (1992)], using photons. The experiment consists of a pair of Mach-Zehnder interferometers that interact through photon bunching at a beam…
We investigate the limitations of random trials when the cause of interest is confounded with the effect by formalizing a counterfactual policy-space where the agent's natural predilection is input to a soft-intervention.
We describe quantum tomography as an inverse statistical problem and show how entropy methods can be used to study the behaviour of sieved maximum likelihood estimators. There remain many open problems, and a main purpose of the paper is to…
Quantum kernel methods are a proposal for achieving quantum computational advantage in machine learning. They are based on a hybrid classical-quantum computation where a function called the quantum kernel is estimated by a quantum device…
We study the quasiprobability representation of quantum light, as introduced by Glauber and Sudarshan, for the unified characterization of quantum phenomena. We begin with reviewing the past and current impact of this technique.…
Quasi-set theory $\cal Q$ allows us to cope with certain collections of objects where the usual notion of identity is not applicable, in the sense that $x = x$ is not a formula, if $x$ is an arbitrary term. $\cal Q$ was partially motivated…
Inverse Ising inference allows pairwise interactions of complex binary systems to be reconstructed from empirical correlations. Typical estimators used for this inference, such as Pseudo-likelihood maximization (PLM), are biased. Using the…
We consider highly inaccurate measurements made on classical stochastic and quantum systems. In the quantum case such a \e{weak} measurement preserves coherence between the system's alternatives. We demonstrate that in both cases the…
We expand the scope of the statistical notion of error probability, i.e., how often large deviations are observed in an experiment, in order to make it directly applicable to quantum tomography. We verify that the error probability can…
Quantum mechanical weak values of projection operators have been used to answer which-way questions, e.g. to trace which arms in a multiple Mach-Zehnder setup a particle may have traversed from a given initial to a prescribed final state. I…
Quantum tomography is the main method used to assess the quality of quantum information processing devices, but its complexity presents a major obstacle for the characterization of even moderately large systems. The number of experimental…