The role of system-meter entanglement in controlling the resolution and decoherence of quantum measurements

Abstract

Measurement processes can be separated into an entangling interaction between the system and a meter and a subsequent read-out of the meter state that does not involve any further interactions with the system. In the interval between these two stages, the system and the meter are in an entangled state that encodes all possible effects of the read-out in the form of non-local quantum correlations between the system and the meter. Here, we show that the entanglement generated in the system-meter interaction expresses a fundamental relation between the amount of decoherence and the conditional probabilities that describe the resolution of the measurement. Specifically, the entanglement generated by the measurement interaction correlates both the target observable and the back-action effects on the system with sets of non-commuting physical properties in the meter. The choice of read-out in the meter determines the trade-off between irreversible decoherence and measurement information by steering the system into a corresponding set of conditional output states. The Hilbert space algebra of entanglement ensures that the irreversible part of the decoherence is exactly equal to the Hellinger distance describing the resolution achieved in the measurement. We can thus demonstrate that the trade-off between measurement resolution and back-action is a fundamental property of the entanglement generated in measurement interactions.

arXiv comment12 pages, including 1 figure. The title was changed to be more specific. References and clarifications have been added. The conclusions have been modified to explain the main results in more detail

References in corpus (18)

• Quantifying Coherence
• Steering, Entanglement, Nonlocality, and the EPR Paradox
• A Delayed Choice Quantum Eraser
• Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement
• The uncertainty principle determines the non-locality of quantum mechanics
• Quantum State Disturbance vs. Information Gain: Uncertainty Relations for Quantum Information
• Violation of the Leggett-Garg inequality with weak measurements of photons
• Proof of Heisenberg's error-disturbance relation
• Quantum root-mean-square error and measurement uncertainty relations
• Noise and disturbance in quantum measurements: an information-theoretic approach
• Violation of Leggett-Garg inequalities in quantum measurements with variable resolution and back-action
• Uncertainty Relation Revisited from Quantum Estimation Theory
• Degree of Complementarity Determines the Nonlocality in Quantum Mechanics
• Certainty in Heisenberg's uncertainty principle: Revisiting definitions for estimation errors and disturbance
• Information-disturbance tradeoff in quantum measurements
• Error-Disturbance Trade-off in Sequential Quantum Measurements
• Local measurement uncertainties impose a limit on non-local quantum correlations
• Measurement uncertainty from no-signaling and non-locality

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• Origin of meter fluctuations in weak measurement interactions
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