The pretty bad measurement
arXiv:2403.17252 · doi:10.1103/PhysRevA.110.042211
Abstract
The quantum state discrimination problem has Alice sending a quantum state to Bob who wins if he correctly identifies the state. The pretty good measurement, also known as the square root measurement, performs pretty well at this task. We study the version of this problem where Bob tries to lose with the greatest probability possible (which is harder than it sounds). We define the pretty bad measurement which performs pretty well at this task, or in other words, pretty poorly for the original task. We show that both the pretty good measurement and the pretty bad measurement are always no worse than blind guessing at their respective tasks. As an application, we apply the pretty bad measurement to the quantum state anomaly detection problem and show how to avoid pretty bad qubits.
8 pages, 7 figures. Published under the title "Quantum state exclusion through offset measurement" in Physical Review A. Version 2: Updated references and theorems
References in corpus (26)
- Quantum state tomography via compressed sensing
- On the reality of the quantum state
- Efficient quantum state tomography
- Quantum state discrimination and its applications
- Reliable Quantum State Tomography
- Quantum state tomography of an itinerant squeezed microwave field
- Quantum State Tomography via Linear Regression Estimation
- Adaptive quantum state tomography improves accuracy quadratically
- Systematic errors in current quantum state tomography tools
- Minimum-error discrimination between three mirror-symmetric states
- Experimental quantum state tomography of a solid state qubit
- Experimental single-setting quantum state tomography
- Robust and Efficient High-dimensional Quantum State Tomography
- Conclusive Exclusion of Quantum States
- Unambiguous State Discrimination of Coherent States with Linear Optics: Application to Quantum Cryptography
- All quantum resources provide an advantage in exclusion tasks
- Exact Identification of a Quantum Change Point
- Qubit State Discrimination
- A necessary condition for incompatibility of observables in general probabilistic theories
- Optimal measurements for the dihedral hidden subgroup problem
- Noncontextuality Inequalities from Antidistinguishability
- Simple Communication Complexity Separation from Quantum State Antidistinguishability
- Optimality of the pretty good measurement for port-based teleportation
- On the optimal error exponents for classical and quantum antidistinguishability
- A note on the inner products of pure states and their antidistinguishability
- Quantum multi-anomaly detection