We derive how the energy extractable from a quantum system through local operations depends on measurement-induced correlations with the apparatus. Starting from two-path wave–particle–entanglement (concurrence) triality relations of the form D² + V² + C² = 1, and the theory of quantum ergotropy, we prove that for a two-level system measured under the unambiguous quantum state discrimination (UQSD) protocol, the locally extractable energy satisfies E_loc = E₀√(1 − C²), where E₀ is the qubit excitation energy and C quantifies system–apparatus correlation. The total energy of the system–apparatus composite is conserved—what varies with measurement strength is access, not existence. At maximum correlation (λ = 0.25), only 70.7% of the system's energy is locally extractable; the remaining 29.3% requires joint operations on system and apparatus. We present experimental protocols to test these predictions using existing weak measurement technology.
We derive how the energy extractable from a quantum system through local operations depends on measurement-induced correlations with the apparatus. Starting from two-path wave–particle–entanglement (concurrence) triality relations of the form D² + V² + C² = 1, and the theory of quantum ergotropy, we prove that for a two-level system measured under the unambiguous quantum state discrimination (UQSD) protocol, the locally extractable energy satisfies E_loc = E₀√(1 − C²), where E₀ is the qubit excitation energy and C quantifies system–apparatus correlation. The total energy of the system–apparatus composite is conserved—what varies with measurement strength is access, not existence. At maximum correlation (λ = 0.25), only 70.7% of the system's energy is locally extractable; the remaining 29.3% requires joint operations on system and apparatus. We present experimental protocols to test these predictions using existing weak measurement technology.
We present a unified energy-ontological interpretation of non-relativistic quantum mechanics within the framework of Energy-Efficiency Theory (EET). Starting from three physically grounded axioms, we define the constrained potential U(r,t) as the spatial density of localized bound-state energy, and derive the continuity equation for the normalized constrained potential ρ(r,t)=U(r,t)/E_c. We prove that ρ(r,t) satisfies the quantum probability continuity equation, establishing the exact correspondence ρ(r,t)=|ψ|^2. We introduce the dimensionless energy ratio η = Ė_resp / Ė_main, which quantifies the balance between energy allocated to spatial exploration (response) and constraint maintenance. From first principles, we derive a modified Schrödinger equation with a real effective potential that preserves probability conservation for all values of η. Using an exact analytical solution for Gaussian wave packets, we derive the scaling relations Δx ∝ η^{-1/2} and Δp ∝ η^{1/2}, which imply the Heisenberg uncertainty principle ΔxΔp ≥ ħ/2 independent of η. Wave-particle duality is interpreted as the continuous sliding of η between exploration-dominated (wave-like, η>1) and maintenance-dominated (particle-like, η<1) regimes. We extend the framework to quantum measurement, deriving the scaling of η from first-principles system-apparatus energy coupling, and unify projective measurements, weak measurements, the quantum eraser, and decoherence within a single framework. We present four experimentally falsifiable predictions with strict statistical criteria, along with a protocol for independent experimental control of η. This work provides a self-consistent energy-ontological foundation for non-relativistic quantum mechanics, unifying probability density, wave-particle duality, the uncertainty principle, and quantum measurement under a single energy allocation framework.
The concept of ergotropy was previously introduced as the maximum extractable work from a quantum state. Its enhancement, which is induced by quantum correlation via projective measurement, was formulated as the daemonic ergotropy. In this work, we investigate the ergotropy in the presence of quantum correlation via weak measurement because of its elegant effects on the measured system. By considering a bipartite correlated quantum system consisting of main and ancillary systems, we demonstrate that the extractable work by the non-selective weak measurement on the ancilla is always equal to the situation captured by the strong measurement. However, the selective weak measurement interestingly reveals more work than the daemonic ergotropy and the ergotropy of the total system is greater than or equal to the daemonic ergotropy. Moreover, it is shown that for Bell diagonal states, at the cost of losing quantum correlation, the total extractable and thus non-local extractable works can be increased by using measurement. Also, we find that there is no direct relationship between quantum correlation and non-local extractable work for these cases.
In this paper, a protocol is proposed in which energy extraction from local vacuum states is possible by using quantum measurement information for the vacuum state of quantum fields. In the protocol, Alice, who stays at a spatial point, excites the ground state of the fields by a local measurement. Consequently, wave packets generated by Alice's measurement propagate the vacuum to spatial infinity. Let us assume that Bob stays away from Alice and fails to catch the excitation energy when the wave packets pass in front of him. Next Alice announces her local measurement result to Bob by classical communication. Bob performs a local unitary operation depending on the measurement result. In this process, positive energy is released from the fields to Bob's apparatus of the unitary operation. In the field systems, wave packets are generated with negative energy around Bob's location. Soon afterwards, the negative-energy wave packets begin to chase after the positive-energy wave packets generated by Alice and form loosely bound states.
Weak measurement is a new technique which allows one to describe the evolution of postselected quantum systems. It appears to be useful for resolving a variety of thorny quantum paradoxes, particularly when used to study properties of pairs of particles. Unfortunately, such nonlocal or joint observables often prove difficult to measure directly in practice (for instance, in optics-a common testing ground for this technique-strong photon-photon interactions would be needed to implement an appropriate von Neumann interaction). Here we derive a general, experimentally feasible, method for extracting these joint weak values from correlations between single-particle observables.
Weak measurement is a potentially powerful tool for studying post-selected quantum systems. The original approach to weak measurement requires a different von Neumann interaction between the quantum system and measurement pointer for weak values of every different observable. When studying weak values of properties of more than one particle, which is necessary for studying entanglement, these interactions can range from difficult to impossible to implement experimentally. For example, the measurement of properties on a pair of optical photons requires a strong Kerr-like nonlinearity at the two-photon level. In a recent work, we described a new method for extracting weak values of operators that can be expressed as products of two local, single-particle operators by studying the correlations in experimentally feasible local, single-particle measurements. In the present work, that theoretical approach is generalized so that weak values of products of N local, single-particle operators can be extracted from the correlations in N single-particle measurements.
Within the framework of microscopic thermodynamics, correlations can play a crucial role in energy extraction. We experimentally investigated the link between information encoded in tunable correlations and its utility for feedback-assisted energy transfer. We realized an agent-demon protocol involving two trapped-ion qubits and show that an appropriate feedback policy increases the average energy stored in the demon qubit by capitalizing on correlations between the constituents. For the chosen family of nearly pure resource states, we quantify both the concurrence and the feedback-assisted energy gain and observe the predicted relation between them. We also show theoretically that the same fixed protocol yields the same gain after complete dephasing in the local energy basis. The experiment establishes a concurrence-gain relation within the investigated pure-state family.