Global InformationMonogamy of entanglement information
| Part of a series of articles about |
| Quantum mechanics |
|---|
|
In quantum physics, the "monogamy" of quantum entanglement refers to the fundamental property that it cannot be freely shared between arbitrarily many parties.
In order for two qubits A and B to be maximally entangled, they must not be entangled with any third qubit C whatsoever. Even if A and B are not maximally entangled, the degree of entanglement between them constrains the degree to which either can be entangled with C. In full generality, for qubits , monogamy is characterized by the Coffman–Kundu–Wootters (CKW) inequality, which states that
where is the density matrix of the substate consisting of qubits and and is the "tangle," a quantification of bipartite entanglement equal to the square of the concurrence.[1][2]
Monogamy, which is closely related to the no-cloning property,[3][4] is purely a feature of quantum correlations, and has no classical analogue. Supposing that two classical random variables X and Y are correlated, we can copy, or "clone," X to create arbitrarily many random variables that all share precisely the same correlation with Y. If we let X and Y be entangled quantum states instead, then X cannot be cloned, and this sort of "polygamous" outcome is impossible.
The monogamy of entanglement has broad implications for applications of quantum mechanics ranging from black hole physics to quantum cryptography, where it plays a pivotal role in the security of quantum key distribution.[5]
- ^ Coffman, Valerie; Kundu, Joydip; Wootters, William (2000). "Distributed entanglement". Physical Review A. 61 (5): 052306. arXiv:quant-ph/9907047. Bibcode:2000PhRvA..61e2306C. doi:10.1103/physreva.61.052306. S2CID 1781516.
- ^ Osborne, Tobias J.; Verstraete, Frank (2006). "General Monogamy Inequality for Bipartite Qubit Entanglement". Physical Review Letters. 96 (22): 220503. arXiv:quant-ph/0502176. Bibcode:2006PhRvL..96v0503O. doi:10.1103/PhysRevLett.96.220503. hdl:1854/LU-8588637. PMID 16803293. S2CID 14366769.
- ^ Seevnick, Michael (2010). "Monogamy of correlations versus monogamy of entanglement". Quantum Information Processing. 9 (2): 273–294. arXiv:0908.1867. doi:10.1007/s11128-009-0161-6.
- ^ Pawłowski, Jan Martin (2006). "Quantum dynamics as an analog of conditional probability". Physical Review A. 74 (4): 042310. arXiv:quant-ph/0606022. Bibcode:2006PhRvA..74d2310L. doi:10.1103/PhysRevA.74.042310. S2CID 56054135.
- ^ Leifer, Matthew (2010). "Security proof for cryptographic protocols based only on the monogamy of Bell's inequality violations". Physical Review A. 82 (3): 032313. arXiv:0907.3778. Bibcode:2010PhRvA..82c2313P. doi:10.1103/PhysRevA.82.032313. S2CID 119078270.