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 rel
ations 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.
Retrieving classical information encoded in optical modes is at the heart of many quantum information processing tasks, especially in the field of quantum communication and sensing. Yet, despite its importance, the fundamental limits of optical mode
discrimination have been studied only in few specific examples. Here we present a toolbox to find the optimal discrimination of any set of optical modes. The toolbox uses linear and semi-definite programming techniques, which provide rigorous (not heuristic) bounds, and which can be efficiently solved on standard computers. We study both probabilistic and unambiguous single-shot discrimination in two scenarios: the channel-discrimination scenario, typical of metrology, in which the verifier holds the light source and can set up a reference frame for the phase; and the source-discrimination scenario, more frequent in cryptography, in which the verifier only sees states that are diagonal in the photon-number basis. Our techniques are illustrated with several examples. Among the results, we find that, for many sets of modes, the optimal state for mode discrimination is a superposition or mixture of at most two number states; but this is not general, and we also exhibit counter-examples.
Quantitative studies of irreversibility in statistical mechanics often involve the consideration of a reverse process, whose definition has been the object of many discussions, in particular for quantum mechanical systems. Here we show that the rever
se channel very naturally arises from Bayesian retrodiction, both in classical and quantum theories. Previous paradigmatic results, such as Jarzynskis equality, Crooks fluctuation theorem, and Tasakis two-measurement fluctuation theorem for closed driven quantum systems, are all shown to be consistent with retrodictive arguments. Also, various corrections that were introduced to deal with nonequilibrium steady states or open quantum systems are justified on general grounds as remnants of Bayesian retrodiction. More generally, with the reverse process constructed on consistent logical inference, fluctuation relations acquire a much broader form and scope.
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 id
entically prepared (i.i.d.) ancillas in some specific states [Seah et al., Phys. Rev. Lett., 180602 (2019)]. Here we refine the analysis of this metrological advantage by optimising 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 Cramer-Rao bound can be beaten, and when a collective measurement of $N>1$ ancilla may return advantages over single-copy measurements.
Under the assumption that every material object can ultimately be described by quantum theory, we ask how a probe system evolves in a device prepared and kept in a superposition state of values of its classical parameter. We find that, under ideal co
nditions, the evolution of the system would be unitary, generated by an effective Hamiltonian. We describe also an incoherent use of the device that achieves the same effective evolution on an ensemble. The effective Hamiltonian thus generated may have qualitatively different features from that associated to a classical value of the parameter.
For any pair of quantum states (the hypotheses), the task of binary quantum hypotheses testing is to derive the tradeoff relation between the probability $p_{01}$ of rejecting the null hypothesis and $p_{10}$ of accepting the alternative hypothesis.
The case when both hypotheses are explicitly given was solved in the pioneering work by Helstrom. Here, instead, for any given null hypothesis as a pure state, we consider the worst-case alternative hypothesis that maximizes $p_{10}$ under a constraint on the distinguishability of such hypotheses. Additionally, we restrict the optimization to separable measurements, in order to describe tests that are performed locally. The case $p_{01}=0$ has been recently studied under the name of quantum state verification. We show that the problem can be cast as a semi-definite program (SDP). Then we study in detail the two-qubit case. A comprehensive study in parameter space is done by solving the SDP numerically. We also obtain analytical solutions in the case of commuting hypotheses, and in the case where the two hypotheses can be orthogonal (in the latter case, we prove that the restriction to separable measurements generically prevents perfect distinguishability). In regards to quantum state verification, our work shows the existence of more efficient strategies for noisy measurement scenarios.
The Alberti-Ulhmann criterion states that any given qubit dichotomy can be transformed into any other given qubit dichotomy by a quantum channel if and only if the testing region of the former dichotomy includes the testing region of the latter dicho
tomy. Here, we generalize the Alberti-Ulhmann criterion to the case of arbitrary number of qubit or qutrit states. We also derive an analogous result for the case of qubit or qutrit measurements with arbitrary number of elements. We demonstrate the possibility of applying our criterion in a semi-device independent way.
We discuss a self-contained spin-boson model for a measurement-driven engine, in which a demon generates work from thermal excitations of a quantum spin via measurement and feedback control. Instead of granting it full direct access to the spin state
and to Landauers erasure strokes for optimal performance, we restrict this demons action to pointer measurements, i.e. random or continuous interrogations of a damped mechanical oscillator that assumes macroscopically distinct positions depending on the spin state. The engine can reach simultaneously the power and efficiency benchmarks and operate in temperature regimes where quantum Otto engines would fail.
If Alice and Bob start out with an entangled state $|Psi_{AB}rangle$, Bob may update his state to $|varphi_Brangle$ either by performing a suitable measurement himself, or by receiving the information that a measurement by Alice has steered that stat
e. While Bobs update on his state is identical, his update on Alices state differs: if Bob has performed the measurement, he has steered the state $|chi_{leftarrow}(varphi)rangle_A$ of Alice; if Alice has made the measurement, to steer $|varphirangle_B$ on Bob she must have found a different state $|chi_{rightarrow}(varphi)rangle_A$. Based on this observation, a consequence of the well-known `Hardys ladder, we show that information from direct measurement must trump inference from steering. The erroneous belief that both paths should lead to identical conclusions can be traced to the usual prejudice that measurements should reveal a pre-existing state of affairs. We also prove a technical result on Hardys ladder: the minimum overlap between the steered and the steering state is $2sqrt{p_{0}p_{n-1}}/(p_0+p_{n-1})$, where $p_0$ and $p_{n-1}$ are the smallest (non-zero) and the largest Schmidt coefficients of $|Psirangle_{AB}$.
We investigate the performance of a three-spin quantum absorption refrigerator using a refined open quantum system model valid across all inter-spin coupling strengths. It describes the transition between previous approximate models for the weak and
the ultrastrong coupling limit, and it predicts optimal refrigeration for moderately strong coupling, where both approximations are inaccurate. Two effects impede a more effective cooling: the coupling between the spins no longer reduces to a simple resonant energy exchange (the rotating wave approximation fails), and the interactions with the thermal baths become sensitive to the level splitting, thus opening additional heat channels between the reservoirs. We identify the modified conditions of refrigeration as a function of the inter-spin coupling strength, and we show that, contrary to intuition, a high-temperature work reservoir thwarts refrigeration in the strong coupling regime.
