We show that the readout analysis in Phys. Rev. A 113, 012420 (2026) does not establish the claimed resource accounting of one thermal query followed by many statistically useful probe samples. A CNOT fanout of a diagonal post-query probe broadcasts its one-qubit marginal but produces perfectly correlated registers rather than independent copies. Consequently, neither the trace distance nor the relative entropy between the balanced and constant hypotheses increases, and repeated measurements of the ancillas provide only one Bernoulli observation. Independent samples instead require repeated preparation and heat exchange, which are repeated queries under the definition adopted in the original paper. We also show that the sample lower bound stated there does not follow from Pinsker's inequality: the inequality gives the opposite ordering for the reciprocal relative entropy. The thermal-kickback mechanism may still encode the decision in the probe temperature, but the one-query readout claim and the quoted necessity of approximately 116 samples require correction.
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Comment on https://doi.org/10.1103/qky6-2bfs (arXiv:2505.15887)
We show that the readout analysis in Phys. Rev. A 113, 012420 (2026) does not establish the claimed resource accounting of one thermal query followed by many statistically useful probe samples. A CNOT fanout of a diagonal post-query probe broadcasts its one-qubit marginal but produces perfectly correlated registers rather than independent copies. Consequently, neither the trace distance nor the relative entropy between the balanced and constant hypotheses increases, and repeated measurements of the ancillas provide only one Bernoulli observation. Independent samples instead require repeated preparation and heat exchange, which are repeated queries under the definition adopted in the original paper. We also show that the sample lower bound stated there does not follow from Pinsker's inequality: the inequality gives the opposite ordering for the reciprocal relative entropy. The thermal-kickback mechanism may still encode the decision in the probe temperature, but the one-query readout claim and the quoted necessity of approximately 116 samples require correction.
In collisional thermometry, a system in contact with the thermal bath is probed by a stream of ancillas. Coherences and collective measurements were shown to improve the Fisher information in some parameter regimes, for a stream of independent and identically prepared (i.i.d.) ancillas in some specific states [Seah et al., Phys. Rev. Lett. 123, 180602 (2019)]. Here we refine the analysis of this metrological advantage by optimizing over the possible input ancilla states, also for block-i.i.d. states of block size b=2. For both an indirect measurement interaction and a coherent energy exchange channel, we show when the thermal Cram\'er-Rao bound can be beaten, and when a collective measurement of N>1 ancilla may return advantages over single-copy measurements.
Ojha, Sardana, and Ghosh [Phys. Rev. A 113, 042221 (2026)] propose that tracing environmental records of particle permutations produces an entropy kB ln N!, thereby explaining the Gibbs factor, and use the same construction to multiply the Saha equilibrium relation by 1/(Ne!Np!). We show that these conclusions do not follow. The reduced density matrix printed in their Eq. (32) is not a partial trace, and even under the natural corrected interpretation the entropy equals kB ln N! only when the system branch states are mutually orthogonal. That condition is not generally satisfied and, when imposed on labeled permutation branches, does not by itself restrict the particle state to one bosonic or fermionic symmetry sector. A two-particle calculation makes the contradiction explicit. Their Gibbs-paradox calculation also starts from a distinguishable-particle entropy while calling it the Sackur-Tetrode entropy. In the Saha section, the state in Eq. (52), as written, factorizes and has zero system-environment entanglement. The proposed factorial does not approach unity in the claimed dilute-gas limit, does not yield a finite nonzero intensive thermodynamic limit, and counts indistinguishability twice. We give the corrected canonical and fugacity-based formulations and identify which standard results of the paper remain unaffected.
Measuring the temperature of a quantum system is an essential task in almost all aspects of quantum technologies. Theoretically, an optimal strategy for thermometry often requires measuring energy, which demands full accessibility over the entire system as well as a complex entangled measurement basis. In this paper, we take a different approach and show that single-qubit sequential measurements in the computational basis not only allow for precise thermometry of a many-body system, but may also achieve precision beyond the thermometry capacity of the probe at equilibrium, given by the Cram\'er-Rao bound. Thus, using consecutive single-qubit measurements of the probe out of equilibrium is, in most cases, very beneficial, as it achieves lower-temperature uncertainties and avoids demanding energy measurements when compared with probes at thermal equilibrium. To obtain such precision, the time between the two subsequent measurements should be smaller than the thermalization time so that the probe never thermalizes. Therefore, the nonequilibrium dynamics of the system continuously imprint information about temperature in the state of the probe. To demonstrate the generality of our findings, we consider thermometry in both spin chains and the Jaynes-Cummings model.
Preparing quantum samples (QSAMPLES), coherent encodings of stationary distributions of reversible Markov chains, is a fundamental primitive in quantum sampling, particularly for quantum simulated annealing. A central limitation of existing phase-estimation-based frameworks is the ancilla qubit overhead. In this work, we present a new end-to-end framework requiring only one ancilla qubit in the working register. The key technical ingredient is a selective phase compiler circuit using one ancilla qubit, built from a generalized quantum signal processing (GQSP)-based projector onto the 1-eigenspace of the qubitized Szegedy walk. Embedding these selective phase compilers into the fixed-point amplitude amplification (FPAA) procedure and iterating yields a quantum algorithm that, given an initial state, oracle access, lower bounds on the overlaps between adjacent states, and lower bounds on the phase gaps, outputs a QSAMPLE within any desired trace distance and thus total variation distance. The query complexity scales inversely with the square roots of both the minimum overlap and the minimum spectral gap of the Markov chains across the cooling schedule, up to polylogarithmic factors. We also perform simulations to verify how our qubit and query complexity evolve with the trace distance, and how this work compares to the previous framework. These results establish two improvements over the previous framework by Wocjan and Abeyesinghe. First, the working-register ancilla cost is reduced to one. Second, by inserting our GQSP-based selective phase compiler into the FPAA procedure, we improve the QSAMPLE transport overlap dependence from inverse minimum overlap to inverse square-root minimum overlap, relative to their Grover pi-over-three fixed-point method. Finally, as a direct application, we apply the quantum algorithm to prepare a Gibbs QSAMPLE and obtain a rigorous complexity analysis.
We demonstrate how a single heat exchange between a probe thermal qubit and multiqubit thermal machine encoding a Boolean function can determine whether the function is balanced or constant, thus providing a thermodynamic solution to the Deutsch-Jozsa problem. We introduce a thermodynamic model of quantum query complexity, showing how qubit thermal machines can act as oracles, queried via heat exchange with a probe. While the Deutsch-Jozsa problem requires an exponential encoding in the number of oracle bits, we also explore a restricted Bernstein-Vazirani problem, which admits a linear thermal oracle and a single thermal query solution. We establish bounds on the number of samples needed to determine the probe temperature encoding the solution for the Deutsch-Jozsa problem, showing that it remains constant with problem size. Additionally, we propose a proof-of-principle experimental implementation to solve the three-bit Bernstein-Vazirani problem via thermal kickback. This work bridges thermodynamics and complexity theory, suggesting that quantum thermodynamics could provide an unconventional route to computing beyond classical computation.