Quantum fluctuations are fundamental to quantum technologies, affecting quantum computing, sensing, cryptography, and thermodynamics. A paradigmatic example is quantum work, which, for a thermally isolated driven system, is identified with the variation of its energy. Although quantum mechanics provides precise rules for measuring energy and other observables at individual instants of time, it does not provide a standard framework for characterizing the statistics of their variations between two times. This ambiguity has led to competing protocols that can assign different work distributions--and, more generally, different fluctuation statistics--to the same physical process, with consequences for both foundational physics and quantum technologies. In this work, we propose four fundamental criteria that any consistent protocol for measuring energy variations must satisfy, grounded in conservation laws, state independence of the measurement apparatus, the no-signaling principle, and constraints on physical reality. We prove that these criteria uniquely select the two-time quantum observable protocol. We then show that this conclusion extends beyond work and energy to the variation of arbitrary physical observables, including charge, particle number, and momentum. This result has the potential to establish the foundations for measurements of quantum processes, possibly resolving ambiguities in quantum fluctuation measurements. Moreover, it enables the extension of quantum information concepts, such as entanglement and Bell's inequalities, to processes rather than instantaneous observables.
Quantum fluctuations are fundamental to quantum technologies, affecting quantum computing, sensing, cryptography, and thermodynamics. A paradigmatic example is quantum work, which, for a thermally isolated driven system, is identified with the variation of its energy. Although quantum mechanics provides precise rules for measuring energy and other observables at individual instants of time, it does not provide a standard framework for characterizing the statistics of their variations between two times. This ambiguity has led to competing protocols that can assign different work distributions--and, more generally, different fluctuation statistics--to the same physical process, with consequences for both foundational physics and quantum technologies. In this work, we propose four fundamental criteria that any consistent protocol for measuring energy variations must satisfy, grounded in conservation laws, state independence of the measurement apparatus, the no-signaling principle, and constraints on physical reality. We prove that these criteria uniquely select the two-time quantum observable protocol. We then show that this conclusion extends beyond work and energy to the variation of arbitrary physical observables, including charge, particle number, and momentum. This result has the potential to establish the foundations for measurements of quantum processes, possibly resolving ambiguities in quantum fluctuation measurements. Moreover, it enables the extension of quantum information concepts, such as entanglement and Bell's inequalities, to processes rather than instantaneous observables.
Technological advances over the past few decades have made it possible to address quantum systems down to individual quanta of energy. Artificial atoms are now routinely fabricated and manipulated using solid-state technology. Exciting new applications are now within grasp, such as quantum heat engines, which have been theorised to achieve energy efficiencies not possible for their classical counterparts. Energy fluctuations are an inherent part of these devices and a detailed understanding of them is required. However, the proper theoretical framework under which such fluctuations are to be understood is still debated. In this thesis, we study energy fluctuations in open quantum systems at the level of individual runs of an experimental protocol. This work has been carried out in two parts. In the first part, we focus on calorimetric measurements – a promising new experimental protocol to continuously measure energy fluctuations of a qubit interacting with a thermal environment. Applying the protocol to more complex systems is not straightforward. Using a simple two-level approximation, we show that for some experimental parameters this protocol can be extended to a driven harmonic oscillator. Another aspect of the calorimetric protocol is that it can induce non-Markovian effects which affect how work and heat are defined. We quantify the degree of non-Markovianity induced by this measurement protocol, when applied to a qubit, based on a previously developed theoretical model. Importantly, we show that non-Markovianity does not necessarily decrease monotonically with the environment size. The attempt to extend the calorimetric protocol to general systems has led to the second part of this thesis. The calorimetric detection is a particular case of a continuously monitored system. However, other schemes exist that lead to different definitions of work and heat. Reconciling these approaches is not straightforward, as evidenced by the many work definitions present in the literature. The difficulty is centred at the fact that, in the orthodox interpretation of quantum mechanics, energy is not always a well-defined quantity. Here, based on the Bohmian interpretation of quantum mechanics, we put forward a general framework to remove this problem in a clear conceptual manner. In particular, we show that the classical definition of work for closed systems can be straightforwardly generalised to the quantum case. For an open system, we used the Bohmian conditional wave function which provides a stochastic state evolution for the open system. We show that this approach can lead to new insights regarding the role of entanglement in energy fluctuations and has the potential to provide a general and observer-independent framework of energy fluctuations in open quantum systems. The results presented in this thesis give a small contribution to the developing field of quantum thermodynamics.
Considering a general microscopic model for a quantum measuring apparatus comprising a quantum probe coupled to a thermal bath, we analyze the energetic resources necessary for the realization of a quantum measurement, which includes the creation of system-apparatus correlations, the irreversible transition to a statistical mixture of definite outcomes, and the apparatus resetting. Crucially, we do not resort to another quantum measurement to capture the emergence of objective measurement results, but rather exploit the properties of the thermal bath which redundantly records the measurement result in its degrees of freedom, naturally implementing the paradigm of quantum Darwinism. In practice, this model allows us to perform a quantitative thermodynamic analysis of the measurement process. From the expression of the second law, we show how the minimal required work depends on the energy variation of the system being measured plus information-theoretic quantities characterizing the performance of the measurement – efficiency and completeness. Additionally, we show that it is possible to perform a thermodynamically reversible measurement, thus reaching the minimal work expenditure, and provide the corresponding protocol. Finally, for finite-time measurement protocols, we illustrate the increasing work cost induced by rising entropy production inherent in finite-time thermodynamic processes. This highlights an emerging trade-off between velocity of the measurement and work cost, on top of a trade-off between efficiency of the measurement and work cost. We apply those findings to bring new insights in the thermodynamic balance of the measurement-powered quantum engines.
Characterizing fluctuations of work in coherent quantum systems is notoriously problematic. Here we reveal the ultimate source of the problem by proving that ( A ) energy conservation and ( B ) the Jarzynski fluctuation theorem cannot be observed at the same time. Condition A stipulates that, for any initial state of the system, the measured average work must be equal to the difference of initial and final average energies, and that untouched systems must exchange deterministically zero work. Condition B is only for thermal initial states and encapsulates the second law of thermodynamics. We prove that A and B are incompatible for work measurement schemes that are differentiable functions of the state and satisfy two mild structural constraints. This covers all existing schemes and leaves the theoretical possibility of jointly observing A and B open only for a narrow class of exotic schemes. For the special but important case of state-independent schemes, the situation is much more rigid: we prove that, essentially, only the two-point measurement scheme is compatible with B .
In the paradigmatic example of quantum measurements, whenever one measures a system which starts in a superposition of two states of a conserved quantity, it jumps to one of the two states, implying different final values for the quantity that should have been conserved. The standard law of conservation for quantum mechanics handles this jump by stating only that the total distribution of the conserved quantity over repeated measurements is unchanged, but states nothing about individual cases. Here however we show that one can go beyond this and have conservation in each individual instance. We made our arguments in the case of angular momentum of a particle on a circle, where many technicalities simplify, and bring arguments to show that this holds in full generality. Hence we argue that the conservation law in quantum mechanics should be rewritten, to go beyond its hitherto statistical formulation, to state that the total of a conserved quantity is unchanged in every individual measurement outcome. As a further crucial element, we show that conservation can be localised at the level of the system of interest and its relevant frame of reference, and is independent on any assumptions on the distribution of the conserved quantity over the entire universe.
Regarded as one of the most fundamental concepts of classical mechanics and thermodynamics, work has received well-grounded definitions within the quantum framework since the 1970s, having being successfully applied to many contexts. Recent developments in the concept have taken place in the emergent field of quantum thermodynamics, where work is frequently characterized as a stochastic variable. Notwithstanding this remarkable progress, it is still debatable whether some sensible notion of work can be posed for a strictly quantum instance involving a few-particle system prepared in a pure state and abandoned to its closed autonomous dynamics. By treating work as a quantum mechanical observable with a well-defined classical limit, here we show that this scenario can be satisfactorily materialized. We prove, by explicit examples, that one can indeed assign eigensystems to work operators. This paves the way for frameworks involving quantum superposition and nonlocal steering of work. We also show that two-point measurement protocols can be inappropriate to describe work (and other two-time physical quantities), especially in the semiclassical regime. However subtle it may be, our quantum mechanical notion of work is experimentally testable and requires an updating of our intuition regarding the concept of two-time elements of reality. In this context, we derive a work-energy uncertainty relation, and we illustrate how energy conservation emerges as an element of physical reality.
This record presents Execution-Based Quantum Theory of Measurement: A Thermodynamic Completion Framework, a theoretical framework addressing the unresolved question of how and when quantum possibilities become executed physical outcomes. Standard quantum mechanics accurately predicts probability distributions but does not specify the physical conditions under which a potential outcome becomes an irreversible fact. This work proposes a completion rule, not an interpretation, grounded in continuous time evolution, irreversible dissipation, and global informational consistency. The framework introduces: Execution as a time-extended, physical process distinct from decoherence A minimum irreversible energy dissipation condition required for outcome realization A measurable execution timescale (τₑₓₑc), distinct from decoherence time A Wait State regime where interference may be suppressed while execution remains incomplete Conditional, sequential extension of reality through successive executions, without invoking observer causation, instantaneous collapse, or parallel universes The theory preserves all established first principles, including unitary quantum dynamics prior to execution, thermodynamics, and a single continuous spacetime. Observers and measurements are treated as physical record-holders that arise after execution, not as causal agents. Four falsifiable experimental tests are proposed across independent platforms: Tunable dissipation in superconducting circuit QED Photonic which-path storage with dissipation gating Mesoscopic pointer systems with controlled environmental damping Matter-wave interferometry under adjustable thermal load Each experiment provides explicit scaling laws and failure criteria to test the separation between decoherence and execution. This framework is derived from, but does not redefine, the Resonance Trinity Law (RTL), which serves as the parent substrate-level principle. No experimental validation is claimed in this record; the purpose is to define a clear, testable theoretical structure and safeguard authorship prior to experimental investigation.