Quantum discord is said to involve correlations between two quantum systems; but with a clause that it won't necessarily be quantum entanglement correlations. Then mathematically ; whats the criteria of such a condition between two systems? I mean; separability of density matrix was guaranteeing me the fact that two subsystems are not entangled; until i came to the fact of discord. But now if mathematically I have a density matrix that can't be separated; how can i say its entangled when i know the possibility of this new phenomenon? Because no no entanglement implying classical relations is not a full picture. In quantum entanglement; when the states are maximally entangled' we say that we can teleport, so we have a physical application of the phenomenon. what is the case with this quantum discord; can it be extracted and put to use somewhere; or where has it been put to use?
The concept of quantumness as measured by quantum discord can be essentially explained as the impossibility of measuring a quantum state without disturbing it. For a bipartite system composed by subsystems A and B, a fully classical state (i.e., a state with vanishing quantum discord with respect to either A or B) is described by a density operator given by \rho_c = \sum_{i} p_i \Pi_i^{A} \otimes \Pi_i^{B}, where {p_i} is a probability distribution and {\Pi_i^{A}} and {\Pi_i^{B}} are complete sets of orthogonal projectors (which ensure the possibility of non-selectively measuring subsystems A or B of \rho_c without disturbance). Notice that classical density operators exhibit a more restrictive structure than separable (unentangled) density operators, which can be written for bipartite systems as \rho_s = \sum_{i} p_i \rho_i^{A} \otimes \rho_i^{B}, with {p_i} a probability distribution and the sets {\rho_i^{A}} and {\rho_i^{B}} given by arbitrary reduced density operators for subsystems A and B (NOT necessarily given by orthogonal projectors). Hence, the set of separable states contains the set of classical states as a subset.
Hello Hrushikesh,
Quantum discord is a measure of non-classical correlations that includes entanglement as a subset. It may be extracted and put to use. Look at these two papers, they are very well written:
http://www.nature.com/nphys/journal/v8/n9/full/nphys2377.html
http://www.nature.com/nphys/journal/v8/n9/full/nphys2376.html
Hi,
You may also have a look at a very recent PRL:
Quantum Discord Determines the Interferometric Power of Quantum States
Phys. Rev. Lett. 112, 210401 (2014)
a copy of which may be found on arXiv.
Hope this helps.
Cheers,
Hallo Hrushikesh,
Take a look on this paper (a copy of it in Researchgate)
Asymptotic dynamics of quantum discord in open quantum systems
J. Phys. B: At. Mol. Opt. Phys. 44, 145503 (2011)
@Alexander, Henni Ouerdane and Hichem Eleuch; I am thankful to you people for providing these useful links.
I am now trying to understand the mathematics of density matrices in these context and also investigate the entropy of such correlations .
The concept of quantumness as measured by quantum discord can be essentially explained as the impossibility of measuring a quantum state without disturbing it. For a bipartite system composed by subsystems A and B, a fully classical state (i.e., a state with vanishing quantum discord with respect to either A or B) is described by a density operator given by \rho_c = \sum_{i} p_i \Pi_i^{A} \otimes \Pi_i^{B}, where {p_i} is a probability distribution and {\Pi_i^{A}} and {\Pi_i^{B}} are complete sets of orthogonal projectors (which ensure the possibility of non-selectively measuring subsystems A or B of \rho_c without disturbance). Notice that classical density operators exhibit a more restrictive structure than separable (unentangled) density operators, which can be written for bipartite systems as \rho_s = \sum_{i} p_i \rho_i^{A} \otimes \rho_i^{B}, with {p_i} a probability distribution and the sets {\rho_i^{A}} and {\rho_i^{B}} given by arbitrary reduced density operators for subsystems A and B (NOT necessarily given by orthogonal projectors). Hence, the set of separable states contains the set of classical states as a subset.
In my opinion, the discord is just the manifestation of the non-commutativity of quantum theory. That is, you cannot measure something without disturbing. You can even "simulate" discord using a classical source affected by noise, see https://scirate.com/arxiv/1407.5507 . The operational interpretations of quantum discord are very few (most notable being quantum state merging). On the other hand, quantum entanglement proved to be an essential resource in various quantum information processing tasks, such as teleportation, dense coding, quantum speedup, error correction etc. And, most notably, CANNOT be classically simulateable (that is, violates Bell's inequality). So I agree completely with Marcelo S. Sarandy, and I also believe that a vast majority of recent papers on quantum discord are (excuse my expression) complete junk (basically, computing discord in various un-physical systems with no real operational interpretation).
I think a good way to understand answer of this question is the paper
""
The classical-quantum boundary for correlations: Discord and related measures
Rev. Mod. Phys. 84, 1655 – Published 26 November 2012
Kavan Modi, Aharon Brodutch, Hugo Cable, Tomasz Paterek, and Vlatko Vedral
""BEST
quantum discord and quantum entanlglement are proportional to each other by reason of its geometric measure, AND non zero quantum discord can outperform quantum entanglement. THE Hilbert-Schmidt distance,which obeys a factorization law,can be put in relation to von Neumann measurements and EQUALS THE ENTROPY OF ENTANGLEMENT IN PURE STATES (STATE VECTOR IN HILBERT SPACE).
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Quantum Physics
- Quantum Mechanics