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Transcript

Entanglement and Distinguishability of Quantum States Augusto Smerzi INO-CNR, BEC Center and Department of Physics Via Sommarive 14, 38123 Povo, Trento, Italy e-mail: smerzi@science.unitn.it Abstract Entanglement is an algebraic property of quantum states. Its physical interpretation is typically related to non-locality. In our talk we will show that entanglement is physically related also with the concept of distinguishability of quantum states. Lets consider two systems differing by a unitary transformation. Can we decide if the two corresponding states are different with a finite number of measurements? This would be possible only if the difference between the state probabilities is smaller than the fluctuations of the results of the measurements [1]. It is therefore possible to define a statistical distance which is the number of distinguishable states along a certain path in the Hilbert space. We demonstrate that quantum mechanics put an upper bound on the minimal statistical distance among two classically correlated states of N q-bits. However, if the q-bits √ are entangled, the statistical distance can be reduced up to a factor N . In other words, entangled states can evolve faster under unitary transformations than classical states. This has important implications in the theory of quantum Zeno dynamics [2] as well as in interferometry and, quite generally, in the theory of a parameter estimation [3]. In particular, we will show that entanglement is a necessary resource to overcome the shot noise limit and saturate the Heisenberg limit, the highest sensitivity allowed by quantum mechanics. Keywords: Entanglement, quantum interferometry, quantum Zeno dynamics References [1] W.K. Wooters, Phys. Rev D23, 357 (1981) [2] A. Smerzi, arXiv:1002.2760 [3] L. Pezzè and A. Smerzi Phys. Rev. Lett. 102, 100401 (2009); P. Hyllus, L. Pezzè and A. Smerzi, arXiv:1003.0649