Extrapolated quantum states, void states and a huge novel class of distillable entangled states
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A nice and interesting property of any pure tensor product state is that each such state has distillable entangled states at an arbitrarily small distance \(\epsilon \) in its neighborhood. We say that such nearby states are \(\epsilon \)-entangled, and we call the tensor product state in that case, a “boundary separable state,” as there is entanglement at any distance from this “boundary.” Here we find a huge class of separable states that also share the property mentioned above—they all have \(\epsilon \)-entangled states at any small distance in their neighborhood. Furthermore, the entanglement they have is proved to be distillable. We then extend this result to the discordant/classical cut and show that all classical states (correlated and uncorrelated) have discordant states at distance \(\epsilon \), and provide a constructive method for finding \(\epsilon \)-discordant states.
KeywordsQuantum computing and quantum information Entanglement Distillability Discord
We thank Lin Chen for helpful comments on the pre-print. MB was partly supported by NSERC and FCAR through INTRIQ. AB was partly supported by NSERC, Industry Canada and CIFAR. TM was partly supported by the Israeli MOD. AB and TM were partly supported The Gerald Schwartz and Heather Reisman Foundation. AB is currently at the Center for Quantum Information and Quantum Control at the University of Toronto.
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Conflict of interest
The a authors declare that they have no conflict of interest.
- Boyer M, Brodutch A, Mor T (2017) Entanglement and deterministic quantum computing with one qubit. Phys Rev A (2017, to appear). arXiv:1606.05283
- Boyer M, Mor T (2014) Extrapolated states, void states, and a huge novel class of distillable entangled states. In: Dediu AH, Lozano M, Martín-Vide C (eds) Theory and practice of natural computing. Lecture notes in computer science, vol 8890. Springer, Berlin, pp 107–118. doi:10.1007/978-3-319-13749-0_10 Google Scholar
- Chen L, Djokovic DZ (2011) Distillability and PPT entanglement of low-rank quantum states. J Phys A: Math Theor 44:285303. doi:10.1088/1751-8113/44/28/285303
- Groisman B, Kenigsberg D, Mor T (2007) “Quantumness” versus “classicality” of quantum states. arXiv:quant-ph/0703103
- Gurvits L (2003) Classical deterministic complexity of Edmonds’ problem and quantum entanglement. In: Proceedings of the thirty-fifth annual ACM symposium on theory of computing, ACM, New York, NY, USA, STOC ’03, pp 10–19. doi:10.1145/780542.780545
- Henderson L, Vedral V (2001) Classical, quantum and total correlations. J Phys A Math Gen 34(35):6899. doi:10.1088/0305-4470/34/35/315