Quantum measurements constrained by the third law of thermodynamics
arXiv:2209.06024 · doi:10.1103/PhysRevA.107.022406
Abstract
In the quantum regime, the third law of thermodynamics implies the unattainability of pure states. As shown recently, such unattainability implies that a unitary interaction between the measured system and a measuring apparatus can never implement an ideal projective measurement. In this paper, we introduce an operational formulation of the third law for the most general class of physical transformations, the violation of which is both necessary and sufficient for the preparation of pure states. Subsequently, we investigate how such a law constrains measurements of general observables, or positive operator valued measures. We identify several desirable properties of measurements which are simultaneously enjoyed by ideal projective measurements -- and are hence all ruled out by the third law in such a case -- and determine if the third law allows for these properties to obtain for general measurements of general observables and, if so, under what conditions. It is shown that while the third law rules out some of these properties for all observables, others may be enjoyed by observables that are sufficiently "unsharp".
References in corpus (39)
- Minimal Energy Cost for Thermodynamic Information Processing: Measurement and Information Erasure
- Operational Quantum Mechanics, Quantum Axiomatics and Quantum Structures
- An improved Landauer Principle with finite-size corrections
- An Invitation to Quantum Incompatibility
- A derivation (and quantification) of the third law of thermodynamics
- Ideal Projective Measurements Have Infinite Resource Costs
- The WAY theorem and the quantum resource theory of asymmetry
- Quantum measurement and the first law of thermodynamics: the energy cost of measurement is the work value of the acquired information
- Non-disturbing quantum measurements
- Thermodynamic limits of dynamic cooling
- Integral Quantum Fluctuation Theorems under Measurement and Feedback control
- Unifying paradigms of quantum refrigeration: A universal and attainable bound on cooling
- Lüders Theorem for Unsharp Quantum Measurements
- Conservation laws, uncertainty relations, and quantum limits of measurements
- Third Law of Thermodynamics as a Single Inequality
- Unsharp Quantum Reality
- Quantum resources for purification and cooling: fundamental limits and opportunities
- Energetics of a Single Qubit Gate
- How energy conservation limits our measurements
- Measurement-based Formulation of Quantum Heat Engine
- 'Measurement of Quantum Mechanical Operators' Revisited
- Quantum Horn's lemma, finite heat baths, and the third law of thermodynamics
- Heisenberg's uncertainty principle for simultaneous measurement of positive-operator-valued measures
- Operations, Disturbance, and Simultaneous Measurability
- Maximal energy extraction via quantum measurement
- Completely positive maps on modules, instruments, extremality problems, and applications to physics
- Extremal quantum protocols
- Wigner-Araki-Yanase theorem on Distinguishability
- Joint measurability in nonequilibrium quantum thermodynamics
- Thermodynamic work cost of quantum estimation protocols
- Thermodynamic Constraints on Quantum Information Gain and Error Correction: A Triple Trade-Off
- A relational perspective on the Wigner-Araki-Yanase theorem
- Correlation properties of quantum measurements
- Energy-Time Uncertainty Relations in Quantum Measurements
- Complete measurements of quantum observables
- Thermodynamically free quantum measurements
- Channels, measurements and post-selection in quantum thermodynamics
- Extreme commutative quantum observables are sharp
- Relation between strength of interaction and accuracy of measurement for a quantum measurement
Cited by in corpus (7)
- Universal validity of the second law of information thermodynamics
- Limits on quantum measurement engines
- Competition of decoherence and quantum speed limits for quantum-gate fidelity in the Jaynes-Cummings model
- Information geometry of nonmonotonic quantum natural gradient
- Can we accurately read or write quantum data?
- Thermodynamic Constraints on the Emergence of Intersubjectivity in Quantum Systems
- Time-cost-error trade-off relation in thermodynamics: The third law and beyond