Simulating quantum instruments with projective measurements and quantum post-processing

• URL: http://arxiv.org/abs/2503.00956v1
• Date: Sun, 02 Mar 2025 16:31:03 GMT
• Title: Simulating quantum instruments with projective measurements and quantum post-processing
• Authors: Shishir Khandelwal, Armin Tavakoli,
• Abstract summary: We show that the simulability of instruments can be connected to an entanglement classification problem.<n>This leads to a computationally efficient necessary condition for simulation of generic instruments and to a complete characterisation for qubits.
• Score: 12.084121187559864
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum instruments describe both the classical outcome and the updated state associated with a quantum measurement. We ask whether these processes can be simulated using only a natural subset of resources, namely projective measurements on the system and quantum processing of the post-measurement states. We show that the simulability of instruments can be connected to an entanglement classification problem. This leads to a computationally efficient necessary condition for simulation of generic instruments and to a complete characterisation for qubits. We use this to address relevant quantum information tasks, namely (i) the noise-tolerance of standard qubit unsharp measurements, (ii) non-projective advantages in information-disturbance trade-offs, and (iii) increased sequential Bell inequality violations under projective measurements. Moreover, we consider also $d$-dimensional L\"uders instruments that correspond to weak versions of standard basis measurements and show that for large $d$ these can permit scalable noise-advantages over projective implementations.

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