Mini Workshop on Quantum Metrology

Event date: 
2016-02-03 (All day)
GIQ Seminar room

Schedule: 2:30 - 3:10 pm : Janek Kolodynski, “The asymptotic role of entanglement in quantum metrology”. Abstract: Quantum systems allow one to sense physical parameters beyond the reach of classical statistics---with resolutions greater than 1/N, where $N$ is the number of constituent particles independently probing a parameter. In the canonical phase estimation scenario the Heisenberg Limit 1/N^2 may be reached, which requires, as we show, both the relative size of the largest entangled block and the geometric measure of entanglement to be nonvanishing as N diverges. Yet, we also demonstrate that in the asymptotic N limit any precision scaling arbitrarily close to the Heisenberg Limit (1/N^(2-epsilon) with epsilon>0) may be attained, even though the system gradually becomes noisier and separable, so that both the above entanglement quantifiers asymptotically vanish. Our work shows that sufficiently large quantum systems achieve nearly optimal resolutions despite their relative amount of entanglement being arbitrarily small. In deriving our results, we establish the continuity relation of the Quantum Fisher Information evaluated for a phase-like parameter, which lets us link the QFI directly to the geometry of quantum states, and hence naturally to the geometric measure of entanglement. 3:10 - 3:50 pm :  Michal Oszmaniec,  “Random symmetric states for robust quantum metrology”. Abstract: We systematically study how useful random states are for quantum metrology, i.e., surpass the classical limits imposed on precision in the canonical phase estimation scenario. First, we prove that random pure states drawn from the Hilbert space of distinguishable particles typically do not lead to super-classical scaling of precision even when allowing for local unitary optimization. Conversely, we show that random states from the symmetric subspace typically achieve the optimal Heisenberg scaling without the need for local unitary optimization. Surprisingly, this occurs irrespectively of their purity and, in contrast to GHZ states, the Heisenberg scaling is preserved under finite particle losses. Moreover, we prove that for such states a standard photon-counting interferometric measurement suffices to typically achieve the Heisenberg scaling of precision for all possible values of the phase at the same time. Finally, we demonstrate that metrologically useful states can be prepared with short random optical circuits generated from three types of beam-splitters and a non-linear (Kerr-like) transformation. Coffee break
4:05 - 4:45 pm : Michail Skotiniotis, “Quantum Metrology with full and fast control”. Abstract: We consider ultimate limits on how precise a parameter, such as frequency or magnetic field strength, can be estimated in the presence of general noise.  We show that the usage of full quantum control, in particular of auxiliary systems and fast continuous quantum error correction, allows one to improve the achievable accuracy. When an overall Hamiltonian description is appropriate, we find that a quadratic improvement (Heisenberg scaling) is achievable for all kinds of noise except noise generated by the Hamiltonian to be estimated. For generic incoherent noise processes we show that Heisenberg scaling can be restored for all rank-one Pauli noise processes; all other noise processes ultimately limit us to  the standard quantum limit despite full quantum control.  However, a significant improvement is still possible for limited resources. We introduce a simple experimentally accessible sequential scheme, making use of a single sensing system plus one auxiliary system, that outperforms entanglement-based schemes without error correction operating with a finite number of parallel systems. 

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