Measurements take a singular role in quantum theory. While they are often idealized as an instantaneous process, this is in conflict with all other physical processes in nature. In this Letter, we adopt a standpoint where the interaction with an environment is a crucial ingredient for the occurrence of a measurement. Within this framework, we derive lower bounds on the time needed for a measurement to occur. Our bound scales proportionally to the change in entropy of the measured system, and decreases as the number of of possible measurement outcomes or the interaction strength driving the measurement increases. We evaluate our bound in two examples where the environment is modelled by bosonic modes and the measurement apparatus is modelled by spins or bosons.
Measurements take a singular role in quantum theory. While they are often idealized as an instantaneous process, this is in conflict with all other physical processes in nature. In this Letter, we adopt a standpoint where the interaction with an environment is a crucial ingredient for the occurrence of a measurement. Within this framework, we derive lower bounds on the time needed for a measurement to occur. Our bound scales proportionally to the change in entropy of the measured system, and decreases as the number of of possible measurement outcomes or the interaction strength driving the measurement increases. We evaluate our bound in two examples where the environment is modelled by bosonic modes and the measurement apparatus is modelled by spins or bosons.
The quantum measurement problem the tension between unitary Schrödinger evolution and the projection postulate has been with us since the early days of quantum theory. Here we derive a lower bound on the time required for any quantum measurement, treating the measurement as quantum channel discrimination carried out by the environment. The resulting bound, \tau_{\mathcal{M}} \ge \frac{\ln N}{2\pi\gamma}, relates the measurement time \tau_{\mathcal{M}} to the number of distinguishable outcomes N and the system-environment coupling strength \gamma. It follows from combining a finite channel-capacity limit on information transfer with the thermodynamic cost of erasing information, as set by Landauer's principle. The bound explains why measurements look instantaneous at macroscopic scales while still being bounded away from zero, gives a timescale for the onset of classical objectivity under quantum Darwinism, and yields concrete, testable predictions for weak-measurement experiments in cavity quantum electrodynamics and superconducting circuits.
The measurement postulate of quantum theory stands in conflict with the laws of thermodynamics and has evoked debate regarding what actually constitutes a measurement. With the help of modern quantum statistical mechanics, we take the first step in formalizing the hypothesis that quantum measurements are driven by the natural tendency of closed systems to maximize entropy, a notion that we call the measurement-equilibration hypothesis. In this paradigm, we investigate how classical measurement outcomes can emerge within a purely unitary framework, and find that (1) the interactions used in standard measurement models fail to spontaneously encode information classically and (2) while ideal projective measurements are impossible, one can (for a given form of Hamiltonian) approximate them exponentially well as more physical systems are collected together into an “observer” system. We thus lay the groundwork for self-contained models of quantum measurement, proposing improvements to our simple scheme.
The quantum measurement problem persists because physics has never provided an operational definition of "observer" specifying which physical interactions constitute observations. We apply a thermodynamic operational definition developed from a prior observer framework: an observer is any self-maintaining bounded system that reduces entropy through differential environmental processing, where the system's persistence depends on the character of that processing. We distinguish between measurement (any interaction satisfying the definition's first two conditions, producing decoherence that suppresses quantum interference) and observation (an interaction involving a system satisfying all three conditions, producing autonomous, feedback-sustained decoherence). This distinction resolves the observer ambiguity in the canonical measurement-problem thought experiments: it specifies which systems observe, where in any causal chain observation occurs, and why the intuitive placement of the Heisenberg cut at the apparatus is practically correct. The Frauchiger-Renner inconsistency becomes identifiable and addressable once observer status is operationally assigned, because the definition identifies where the domain of unrestricted unitary description must be constrained. The nature of that constraint (collapse, irreversible branching, transaction completion) is interpretation-dependent; the criterion for where it applies is not, though the strength of the resulting resolution varies across interpretations. The definition does not resolve the problem of definite outcomes, derive the Born rule, or select the preferred basis. It resolves the component of the measurement problem that has blocked progress on those questions: the absence of any criterion for which systems perform observations.
The thesis of this paper is that quantum measurement can be analyzed and understood within quantum mechanics itself. The statistics of the measurement process comes from the unknown details of the macroscopic measurement device. Quantum measurement is analyzed within the framework of scattering theory of quantum field theory with the aim of finding a physical rather than a metaphysical understanding. The measurement interaction is treated together with the quantum process to be measured. The evaluation of a Feynman diagram for the total process leads to one factor from the measurement interaction for each channel multiplying the basic scattering amplitudes. With increasing entanglement taken into account, these factors compete for dominance. They depend on unknown details of the measurement apparatus. The statistics of this competition is studied under the assumption that the measurement interaction does not introduce any bias. A binary quantum system is analyzed and after that the n-channel case. As a background, a couple of classical examples are shown, leading to the same selective mechanisms. The result of this analysis is that the quantum measurement process can be understood, whether a single measurement or an ensemble of measurements, as a result of an ordinary unitary time development, based on the interaction beteen the system subjet to measurement and the measurement apparatus. This result makes it possible to view the quantum-mechanical state as describing reality rather than merely a potentiality. This opens again for an ontology of physics, and hence for science in general.
The uncertainty principle limits the ability for observer to precisely measure two incompatible observables, and plays a crucial role in quantum precision measurement in the quantum information science. When quantum systems interact with their surroundings, they inevitably result in decoherence, which increases the uncertainty of the system. In the process of quantum information processing, the effective regulation of uncertainty becomes a key problem that needs to be solved. In this work, we investigate the quantum-memory-assisted entropic uncertainty relation of a two-qubit system under correlated channels with dephasing colored noise. We demonstrate that it is possible to control the entropic uncertainty, U, and its lower bound, Ub, by combining correlations between successive uses of channels and the non-Markovianity of the dynamical evolution. Firstly, the evolutionary characteristics of the trace distance are employed to distinguish between Markovianity and non-Markovianity of the channel. Subsequently, the system is selected to be either a maximally entangled state or separated state initially. By adjusting the strength η of the correlations, we find that with the increase of η, the entropic uncertainty and its lower bound decrease. Especially, if the channel is fully correlated (η = 1), the entropic uncertainty and its lower bound remain constant under the channel, indicating that decoherence is completely suppressed. A comparison of Markovian channel with non-Markovian channel reveals that the entropic uncertainty and its lower bound exhibit oscillatory behaviour under non-Markovian channels. The combination of correlations and non-Markovianity of the channel demonstrates that the entropic uncertainty and its lower bound can be reduced under fully correlated channels where the non-Markovianity has no effect. This is because fully correlated channels suppress decoherence to a greatest extent. Under partially correlated channels, the combination of correlations and non-Markovianity can more effectively reduce the entropic uncertainty and its lower bound. Under such channels, correlations of the channel reduce the entropic uncertainty and its lower bound during the whole evolution, while the non-Markovianity contributes to their oscillations and reduce them in some specific time. Furthermore, the results show that the entropic uncertainty and its lower bound reach steady values that depend only on the strength of the correlations after long-time evolution. In other words, the stronger the correlations, the lower the entropy uncertainty and its lower bound of steady states will be. Finally, we analyse the physical nature of the decrease of the entropic uncertainty and its lower bound, and it is found that the decrease of the entropic uncertainty and its lower bound originate from the increase of the quantum correlations in the system.
The measurement process of observables in a quantum system comes out to be an unsovable problem which started in the early times of the development of the theory. In the present note we consider the measured system part of an open system interacting with the measuring device and show under which ideal conditions the measure process may ideally work. Our procedure leads to the conclusion that there is no hope that any experimental procedure will be able to lead to a clean solution of the process, except maybe in very specific cases. The reasons for this situation are deeply rooted in the fundamental properties of quantum theory.