Full characterization of modular values for finite-dimensional systems. (English) Zbl 1360.81107
Summary: In [“Modular values and weak values of quantum observables”, Phys. Rev. Lett. 105, No. 23 (2010; doi:10.1103/physrevlett.105.230401)], Y. Kedem and L. Vaidman obtained a relationship between the spin-operator modular value and its weak value for specific coupling strengths. Here we give a general expression for the modular value in the \(n\)-dimensional Hilbert space using the weak values up to \((n - 1)\)th order of an arbitrary observable for any coupling strength, assuming non-degenerated eigenvalues. For the two-dimensional case, it shows a linear relationship between the weak value and the modular value. We also relate the modular value of the sum of observables to the weak value of their product.
MSC:
| 81P50 | Quantum state estimation, approximate cloning |
| 81P40 | Quantum coherence, entanglement, quantum correlations |
| 81P45 | Quantum information, communication, networks (quantum-theoretic aspects) |
| 81P15 | Quantum measurement theory, state operations, state preparations |
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