Work cost of quantum measurements
Work cost of quantum measurements Kais Abdelkhalek, David Reeb, Yoshifumi Nakata Institute for Theoretical Physics Leibniz Universität Hannover 24.04.15 QIG@ITP Hannover Work cost of quantum measurements Why are measurements important? 1. Non-unitary state transformation Zeno stabilisation Quantum error correction 2. Feedback: action based on measurement outcome Szilard engine QIG@ITP Hannover Work cost of quantum measurements „Didn‘t Charlie Bennett solve this problem already?“ measurements can be implemented reversibly only true for classical systems Szilard engine Important: Do not forget any system that is involved in the process QIG@ITP Hannover Work cost of quantum measurements Recent work by Kammerlander/Anders (2015): possible clear axiomatic framework only projective measurements dephasing only required for particular measurement outcome is not stored Work cost of quantum measurements QIG@ITP Hannover Goal: describe general measurements Inefficiency of measurement with a microscopic model that incorporates a memory projections describe the erasure process to allow for repetitive use of memory Quantify work cost in terms of Work cost of quantum measurements Measurement model for: QIG@ITP Hannover Work cost of quantum measurements Measurement model for: QIG@ITP Hannover QIG@ITP Hannover Work cost of quantum measurements Measurement model for: specifies a measurement device QIG@ITP Hannover Work cost of quantum measurements Measurement model for: specifies a measurement device QIG@ITP Hannover Work cost of quantum measurements Measurement model for: specifies a measurement device For all measurements such a device exists! Outcome is now stored in Work cost: Note: . QIG@ITP Hannover Work cost of quantum measurements Measurement model for: specifies a measurement device For all measurements such a device exists! Outcome is now stored in Work cost: Note: . QIG@ITP Hannover Work cost of quantum measurements Erasure model: Landauer erasure Work cost: Total work cost: “work cost for operating the measurement device“ QIG@ITP Hannover Work cost of quantum measurements Same microscopic model: Additional assumption by Sagawa/Ueda: no entanglement only efficient measurements QIG@ITP Hannover Work cost of quantum measurements arbitrary efficient + no entanglement Sagawa/Ueda projective QIG@ITP Hannover Work cost of quantum measurements arbitrary efficient + no entanglement Sagawa/Ueda projective Our main result: Work cost of operating a measurement device rank-1 QIG@ITP Hannover Work cost of quantum measurements arbitrary efficient + no entanglement Sagawa/Ueda projective Our main result: Work cost of operating a measurement device Work cost of quantum measurements Properties of our bound: • for efficient measurements: Correct generalisation of previous bound! • for arbitrary measurements: can construct equality! Inefficient measurements can yield work! QIG@ITP Hannover QIG@ITP Hannover Work cost of quantum measurements arbitrary Work cost can be negative! efficient + no entanglement Sagawa/Ueda projective Work cost of quantum measurements Precise knowledge over the gap terms: Even better bound for projective measurements: Equality result for the work cost of projective measurements: Projective measurements always cost work! QIG@ITP Hannover QIG@ITP Hannover Work cost of quantum measurements arbitrary Work cost can be negative! efficient + no entanglement Sagawa/Ueda projective Thank you for your attention!
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