arXiv subjects

Clive Cenxin Aw

Publications and source records attributed to Clive Cenxin Aw.

8 recordsLinked to original sources

arXiv2026

Tomographic Limits of the Petz Recovery Map

The Petz recovery map is considered one of the key candidates for the quantum analogue of Bayesian inference and Jeffrey's conditionalization. Since, there seems to be a natural connection between Bayesian inference and the notion of state tomography, it is natural to ask if the Petz recovery can be used for this latter task. In this paper, we discuss such recent results on iterated Petz recovery and relate them to Bayesian approaches to quantum state tomography. We highlight the limitations of direct Petz iteration and show how an extended Petz construction, by lifting the inference problem to a classical distribution over candidate quantum states, recovers the structure of Bayesian and maximum likelihood tomography. This provides perspective on the modifications or nuances required for a Petz approach to quantum retrodiction to perform quantum state tomography.

quant-ph↗

arXiv2026

Schr\"odinger Bridges via the Hacking of Bayesian Priors in Classical and Quantum Regimes

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 reference prior distribution such that, for a fixed channel and evidence, the update matches a chosen target distribution. We prove that this is generically possible in both classical and quantum settings whenever Bayesian inversions are well-defined (with the Petz recovery map as the quantum analogue to Bayes' rule), and provide constructive algorithms for doing so. We further establish a duality between prior hacking and Schr\"odinger bridge problems (a key object in statistical physics with applications in generative modelling), yielding in the quantum setting a unique, inference-consistent selection among candidate bridges. This formally establishes the Bayes-like updating that Schr\"odinger bridges are performing with respect to the process as opposed to the reference prior, both in classical and quantum settings.

quant-ph↗

arXiv2025

Quantifying Irreversibility via Bayesian Subjectivity for Classical & Quantum Linear Maps

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 inference, loss of information results in the retrodiction for the initial state becoming increasingly influenced by the choice of reference prior. In this paper, we import this latter perspective into physics, by quantifying the irreversibility of any process with its Bayesian subjectivity -- that is, the sensitivity of its retrodiction to one's prior. From this perspective, we review analytical and numerical results that highlight both intuitive and subtle insights that this measure sheds on irreversible processes.

quant-ph↗

arXiv2024

Emergence of Fluctuation Relations in UNO

In the last two decades, fluctuation theorems have been proved formally and demonstrated experimentally for several variables (such as entropy production, work, or flux) and different noises causing the fluctuations (of either thermal or other origin; Markovian or non-Markovian). Here we report the observation of a detailed fluctuation relation in a statistical process outside thermodynamics and physics: the card game UNO. As the fluctuating variable, we consider the number of steps $W$ needed for one player's deck to change from $x$ to $y$ number of cards. The other players and the remaining cards play the role of a finite non-Markovian bath. Numerical simulations of runs of the game show that $W$ obeys a fluctuation relation analogous to Crooks' theorem. While the observed behavior shares some common features with infinite random walks, it also exhibits deviations that are clear signatures of non-Markovianity and the finiteness of the bath: Notably, the parameter corresponding to temperature depends strongly on the transition $x\rightarrow y$. Our paper contributes to extending the scope of fluctuation theorems beyond their usual thermodynamic setting.

physics.soc-ph↗

arXiv2024

Role of Dilations in Reversing Physical Processes: Tabletop Reversibility and Generalized Thermal Operations

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 reverse channel. Using logical inference, the reverse channel is the Bayesian retrodiction (the Petz recovery map in the quantum formalism) of the original one. Alternatively, we know from physics that every irreversible process can be modeled as an open system: one can then define the corresponding closed system by adding a bath ("dilation"), trivially reverse the global reversible process, and finally remove the bath again. We prove that the two recipes are strictly identical, both in the classical and in the quantum formalism, once one accounts for correlations formed between system and the bath. Having established this, we define and study special classes of maps: product-preserving maps (including generalized thermal maps), for which no such system-bath correlations are formed for some states; and tabletop time-reversible maps, when the reverse channel can be implemented with the same devices as the original one. We establish several general results connecting these classes, and a very detailed characterization when both the system and the bath are one qubit. In particular, we show that when reverse channels are well-defined, product-preservation is a sufficient but not necessary condition for tabletop reversibility; and that the preservation of local energy spectra is a necessary and sufficient condition to generalized thermal operations.

quant-ph↗

arXiv2023

Quantum Bayesian Inference in Quasiprobability Representations

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 in the language of Hilbert spaces. In this paper, we derive the expression of the Petz recovery map within any quasiprobability representation, with explicit formulas for the two canonical choices of normal quasiprobability representations (which include Discrete Wigner representations) and of representations based on symmetric, informationally complete positive operator-valued measures (SIC-POVMs). By using the same mathematical syntax of (quasi-)stochastic matrices acting on (quasi-)stochastic vectors, the core difference in logical inference between classical and quantum theory is found in the manipulation of the reference prior rather than in the representation of the channel.

quant-ph↗

arXiv2022

Detecting quantumness in uniform precessions

Building on work by Tsirelson, we present a family of protocols that detect the nonclassicality of suitable states of a single quantum system, under the sole assumption that the measured dynamical observable undergoes a uniform precession. The case of the harmonic oscillator was anticipated in the work by Tsirelson, which we extend. We then apply the protocols to finite-dimensional spins that undergo uniform precession in real space and find a gap between the classical and the quantum expectations for every $j\geq \frac{3}{2}$ (excluding $j=2$).

quant-ph↗

arXiv2021

Fluctuation Theorems with Retrodiction rather than Reverse Processes

Irreversibility is usually captured by a comparison between the process that happens and a corresponding "reverse process". In the last decades, this comparison has been extensively studied through fluctuation relations. Here we revisit fluctuation relations from the standpoint, suggested decades ago by Watanabe, that the comparison should involve the prediction and the retrodiction on the unique process, rather than two processes. We identify a necessary and sufficient condition for a retrodictive reading of a fluctuation relation. The retrodictive narrative also brings to the fore the possibility of deriving fluctuation relations based on various statistical divergences, and clarifies some of the traditional assumptions as arising from the choice of a reference prior.

cond-mat.stat-mech↗