Related papers: Bayesian retrodiction of quantum supermaps
Bayes' rule plays a crucial piece of logical inference in information and physical sciences alike. Its extension into the quantum regime has been the object of several recent works. These quantum versions of Bayes' rule have been expressed…
The Petz recovery map is a central construct in quantum information theory, providing an explicit, channel-aware prescription for reversing the effects of noise. Unlike standard quantum operations, the Petz map is intrinsically dependent on…
Higher-order quantum theory is an extension of quantum theory where one introduces transformations whose input and output are transformations, thus generalizing the notion of channels and quantum operations. The generalization then goes…
Transformations of quantum channels, such as the transpose, complex conjugate, and adjoint, are fundamental to quantum information theory. Given access to an unknown channel, a central problem is whether these transformations can be…
Bayes' rule tells us how to invert a causal process in order to update our beliefs in light of new evidence. If the process is believed to have a complex compositional structure, we may ask whether composing the inversions of the component…
Implementing quantum error correction (QEC) protocols is a challenging task in today's era of noisy intermediate-scale quantum devices. We present quantum circuits for a universal, noise-adapted recovery map, often referred to as the Petz…
In this paper, we discuss the quantum data processing inequality and its refinements that are physically meaningful in the context of approximate recoverability. An important conjecture regarding this due to Seshadreesan et. al. in J. Phys.…
We show that quantum subdynamics of an open quantum system can always be described by a Hermitian map, irrespective of the form of the initial total system state. Since the theory of quantum error correction was developed based on the…
The fascinating concept of coherent quantum absorber - which can absorb any photon emitted by another system while maintaining entanglement with that system - has found diverse implications in open quantum system theory and quantum…
We investigate the problem of reversing quantum dynamics, specifically via optimal Petz recovery maps. We focus on typical decoherence channels, such as dephasing, depolarizing and amplitude damping. We illustrate how well a physically…
Optical systems are a main platform for quantum information processing. A main challenge is information loss due to scattering in unmonitored modes. These losses are modeled as state-independent beam-splitter interactions, with a thermal…
We analyze how an action of a qubit channel (map) can be estimated from the measured data that are incomplete or even inconsistent. That is, we consider situations when measurement statistics is insufficient to determine consistent…
A central theme in classical algorithms for the reconstruction of discontinuous functions from observational data is perimeter regularization via the use of the total variation. On the other hand, sparse or noisy data often demands a…
Reversible computation is an unconventional form of computing where any executed sequence of operations can be executed in reverse at any point during computation. It has recently been attracting increasing attention in various research…
The conventional postulate for the probabilistic interpretation of quantum mechanics is asymmetric in preparation and measurement, making retrodiction reliant on inference by use of Bayes' theorem. Here, a more fundamental symmetric…
Quantum supermaps are a higher-order generalization of quantum maps, taking quantum maps to quantum maps. It is known that any completely positive, trace non-increasing (CPTNI) map can be performed as part of a quantum measurement. By…
We introduce the framework of Bayesian relative belief that directly evaluates whether or not the experimental data at hand supports a given hypothesis regarding a quantum system by directly comparing the prior and posterior probabilities…
Given a tripartite quantum state on $A,B,C$ and the erasure channel on $C$, the rotated Petz map is a recovery channel that acts on $B$ to recover the erased quantum information. The infidelity of the best recovery is upper-bounded by the…
In general, a quantum measurement yields an undetermined answer and alters the system to be consistent with the measurement result. This process maps multiple initial states into a single state and thus cannot be reversed. This has…
Lieb and Ruskai's strong subadditivity theorem, which shows that the conditional mutual information must be nonnegative, is fundamental in quantum theory. It has numerous applications, such as in quantum error correction. When the mutual…