Operationally Invariant Measure of the Distance between Quantum States by Complementary Measurements
arXiv:quant-ph/0303111 · doi:10.1103/PhysRevLett.91.087902
Abstract
We propose an operational measure of distance of two quantum states, which conversely tells us their closeness. This is defined as a sum of differences in partial knowledge over a complete set of mutually complementary measurements for the two states. It is shown that the measure is operationally invariant and it is equivalent to the Hilbert-Schmidt distance. The operational measure of distance provides a remarkable interpretation of the information distance between quantum states.
arXiv comment4 pages
References in corpus (8)
- On the Measurement of Qubits
- Quantifying Entanglement
- Quantum Copying: Beyond the No-Cloning Theorem
- Operationally Invariant Information in Quantum Measurements
- Entanglement Teleportation via Werner States
- Conceptual Inadequacy of the Shannon Information in Quantum Measurements
- A device for feasible fidelity, purity, Hilbert-Schmidt distance and entanglement witness measurements
- Invariant information and quantum state estimation
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