Simulating quantum instruments with projective measurements and quantum post-processing
arXiv:2503.00956 · doi:10.1103/bhr5-g71p
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 -dimensional Lüders instruments that correspond to weak versions of standard basis measurements and show that for large these can permit scalable noise-advantages over projective implementations.
6+13 pages
References in corpus (31)
- Separability of Mixed States: Necessary and Sufficient Conditions
- Quantum Resource Theories
- Symmetric Informationally Complete Quantum Measurements
- A Schmidt number for density matrices
- Quantum State Disturbance vs. Information Gain: Uncertainty Relations for Quantum Information
- Multiple Observers Can Share the Nonlocality of Half of an Entangled Pair by Using Optimal Weak Measurements
- Simulating positive-operator-valued measures with projective measurements
- Sequential random access codes and self-testing of quantum measurement instruments
- Self-testing non-projective quantum measurements in prepare-and-measure experiments
- Three-observer Bell inequality violation on a two-qubit entangled state
- Operational framework for quantum measurement simulability
- Experimental characterisation of unsharp qubit observables and sequential measurement incompatibility via quantum random access codes
- Enabling computation of correlation bounds for finite-dimensional quantum systems via symmetrisation
- Semidefinite programming relaxations for quantum correlations
- Device-Independent Certification of a Nonprojective Qubit Measurement
- Entanglement Detection Beyond Measuring Fidelities
- Determination of the Schmidt number
- Experimental Demonstration of Sequential Quantum Random Access Codes
- Experimental demonstration of coherent state estimation with minimal disturbance
- Experimental certification of an informationally complete quantum measurement in a device-independent protocol
- Bounding sets of sequential quantum correlations and device-independent randomness certification
- Noise-robust preparation contextuality shared between any number of observers via unsharp measurements
- Structural Quantification of Entanglement
- Information-Disturbance Tradeoff in Quantum State Discrimination
- Projective measurements are sufficient for recycling nonlocality
- Semi-device-independent certification of independent quantum state and measurement devices
- Resource-efficient high-dimensional entanglement detection via symmetric projections
- Certification of a Nonprojective Qudit Measurement using Multiport Beamsplitters
- Quantum Correlation Sharing: A Review On Recent Progress From Nonlocality To Other Non-Classical Correlations
- Enhanced Schmidt number criteria based on correlation trace norms
- Detecting the dimensionality of genuine multi-particle entanglement