Related papers: Bayesian retrodiction of quantum supermaps
In the context of irreversible dynamics, associating to a physical process its intuitive reverse can result to be a quite ambiguous task. It is a standard choice to define the reverse process using Bayes' theorem, but, in general, this…
Bayes' rule, which is routinely used to update beliefs based on new evidence, can be derived from a principle of minimum change. This principle states that updated beliefs must be consistent with new data, while deviating minimally from the…
A mixed quantum state can be taken as capturing an unspecified form of ignorance; or as describing the lack of knowledge about the true pure state of the system ("proper mixture"); or as arising from entanglement with another system that…
Prediction is the making of statements, usually probabilistic, about future events based on current information. Retrodiction is the making of statements about past events based on current information. We present the foundations of quantum…
We derive on the basis of Bayes' theorem a simple but general expression for the retrodicted premeasurement state associated with the result of any measurement. The retrodictive density operator is the normalised probability operator…
In both classical and quantum physics, irreversible processes are described by maps that contract the space of states. The change in volume has often been taken as a natural quantifier of the amount of irreversibility. In Bayesian…
We study quantum measurement retrodiction using the principle of minimum change. For quantum-to-classical measurement channels, we show that all standard quantum divergences select the same retrodictive update, yielding a unique and…
Estimating the state of an open quantum system monitored over time requires incorporating information from past measurements (filtering) and, for improved accuracy, also from future measurements (smoothing). While classical smoothing is…
Bayes' rule $\mathbb{P}(B|A)\mathbb{P}(A)=\mathbb{P}(A|B)\mathbb{P}(B)$ is one of the simplest yet most profound, ubiquitous, and far-reaching results of classical probability theory, with applications in any field utilizing statistical…
Quantum retrodiction is a time-symmetric approach to quantum mechanics with applications in a number of important problems. One of the major challenges to its more widespread applicability is the restriction of its symmetric formalism to…
The reconstruction of the state of a multipartite quantum mechanical system represents a fundamental task in quantum information science. At its most basic, it concerns a state of a bipartite quantum system whose subsystems are subjected to…
Recently, there has been focus on determining the conditions under which the data processing inequality for quantum relative entropy is satisfied with approximate equality. The solution of the exact equality case is due to Petz, who showed…
Irreversibility, crucial in both thermodynamics and information theory, is naturally studied by comparing the evolution -- the (forward) channel -- with an associated reverse -- the reverse channel. There are two natural ways to define this…
Bayes' rule is widely regarded as the canonical prescription for belief updating. We show, however, that one can arbitrarily preserve pre-specified beliefs while appearing to perform Bayesian updates via "prior hacking": engineering a…
Quantum retrodiction involves finding the probabilities for various preparation events given a measurement event. This theory has been studied for some time but mainly as an interesting concept associated with time asymmetry in quantum…
By introducing an operator sum representation for arbitrary linear maps, we develop a generalized theory of quantum error correction (QEC) that applies to any linear map, in particular maps that are not completely positive (CP). This theory…
Bayes' rule connects forward and reverse processes in classical probability theory, and its quantum analogue has been discussed in terms of the Petz (transpose) map. For quantum dynamics governed by the Lindblad equation, the corresponding…
The Petz recovery channel plays an important role in quantum information science as an operation that approximately reverses the effect of a quantum channel. The pretty good measurement is a special case of the Petz recovery channel, and it…
We introduce the concept of quantum supermap, describing the most general transformation that maps an input quantum operation into an output quantum operation. Since quantum operations include as special cases quantum states, effects, and…
A recovery map effectively cancels the action of a quantum operation to a partial or full extent. We study the Petz recovery map in the case where the quantum channel and input states are fermionic and Gaussian. Gaussian states are…