Quantum, classical, and total amount of correlations in a quantum state
By Berry Groisman, Sandu Popescu, Andreas J. Winter. 2004
513 citations recorded by the source corpus.
We give an operational definition of the quantum, classical, and total amounts of correlations in a bipartite quantum state. We argue that these quantities can be defined via the amount of work (noise) that is required to erase (destroy) the correlations: for the total correlation, we have to erase completely, for the quantum correlation we have to erase until a separable state is obtained, and the classical correlation is the maximal correlation left after erasing the quantum correlations. In particular, we show that the total amount of correlations is equal to the quantum mutual information, thus providing it with a direct operational interpretation. As a by-product, we obtain a direct, operational, and elementary proof of strong subadditivity of quantum entropy.
View Paper: https://www.semanticscholar.org/paper/0723e6d996d726e2cedd669be6bd6ef40bfd8b2c
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Citations in the corpus
- Area laws in quantum systems: mutual information and correlations. (2007, background): “It quantifies the information aboutB which can be obtained fromA and vice versa.”
- Entanglement in many-body systems (2007, background): “Also the quantum mutual information (Groisman et al., 2005), see Eq.”
- The classical-quantum boundary for correlations: Discord and related measures (2011, methodology): “(Groisman et al., 2005) use a similar idea to define quantum, classical and total correlations through the amount of work required to delete each.”
- Holographic mutual information is monogamous (2011, background): “where ABdenotes A[B) is nite and regulator-independent. This quantity is known as the mutual information. It measures the total amount of correlation (both classical and quantum) between Aand B. (See [5], for example, for an operational justication of that statement.) Consistent with this interpreta”
- Partial quantum information (2005, unknown): “Secondly, the measurement of Alice makes her state completely product with R , thus reinforcing the interpretation of quantum mutual information as the minimum entropy production of any local decorrelating process 14,15 .”