Robust strategies for lossy quantum interferometry

Abstract

We give a simple multiround strategy that permits to beat the shot noise limit when performing interferometric measurements even in the presence of loss. In terms of the average photon number employed, our procedure can achieve twice the sensitivity of conventional interferometric ones in the noiseless case. In addition, it is more precise than the (recently proposed) optimal two-mode strategy even in the presence of loss.PACS numbers: 03.65. Ta,06.20.Dk,42.50.St The shot noise limit is the minimum noise level that the Heisenberg uncertainty relations permit to achieve when classical states are employed in the apparatuses. Many quantum strategies have been proposed to beat the shot noise [1,2] and to achieve the ultimate Heisenberg limit [12], but virtually all of them are very sensitive to noise and loss of photons [3]. Only very recently some interferometric strategies were presented that can beat the shot noise even in the presence of relevant losses of photons [4,5]. These are all instances of parallel strategies [2], where both arms of the interferometer are sampled at the same time using a mode-entangled quantum state of the light (see Fig. 1a). In addition to the parallel strategies, in quantum metrology it is also possible to achieve the Heisenberg limit using multiround (or sequential) strategies [6,7] which, in the noiseless case, are equivalent in terms of resources and of achievable precision [2]. Both arms of the interferometer are sampled at the same time using a two-mode entangled state. The phase factor ϕ is imprinted in the state as a phase difference between the two modes. b) Sequential strategy proposed here. A loss-resistant single mode state is sent through the first interferometer arm, sampling the phase ϕ. Then a unitary transformation is applied and the state is sent back through the other interferometer arm. This is needed so that the final phase shift experienced by the state is only the relative phase in the interferometer. The state is measured after one (or more) round trips.Here we detail how multiround strategies can be used to perform interferometry-see Fig. 1b. An appropriate input state is prepared (we will analyze two examples below). This state is fed into the first interferometer arm. It picks up a phase ϕ + ϑ, where ϕ is the interferometric phase we want to estimate, and ϑ is the absolute phase picked up by the free evolution in the arm (which is equal to the phase which would be picked up also in the reference arm). The main trick of multiround interferometry is the use of the unitarywhere |n is the Fock basis and M is the largest nonzero component of the initial input state. The purpose of this unitary is to permute the first M components of the Fock state expansion of a state in such a way that, when the state is sent back through the reference arm, the absolute phase ϑ is removed from the state (only an irrelevant global phase factor e iMϑ persists). Thus, at the end of the round trip of Fig. 1b (multiple round trips are also possible), only the relative phase ϕ is im...

Robust quantum metrological schemes based on protection of quantum Fisher information

“…This is a considerable improvement over the standard quantum limit 1/ √ N . Nevertheless, those entanglement-enhanced strategies that are optimal for the noiseless systems easily lose the quantum gain for the noisy systems [9,11,12,[14][15][16][17][18][19][20][21][22][23][24][25][26].…”

“…In quantum metrology, delicate and fragile quantum features are being used to enhance the sensitivity of experimental apparatus, e.g., non-classical probe states were used for the high sensitivity of optical interferometer and atomic spectroscopy [1][2][3][4][5][6][7][8]. However the quantum enhancement for the sensitivity may be subdued by the presence of ubiquitous and inevitable noise [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. Therefore it is of utmost significance to investigate the robustness of the optimal strategies for the high sensitivity against noise.…”

Advances in quantum metrology

“…However, as an alternative to the fragile two-mode states, some more robust single mode states were also analyzed, e.g. pure Gaussian states in the presence of phase diffusion [108], mixed Gaussian states in the presence of loss [109], or single mode variants of the two mode states [110]. In contrast to the two mode case (where the phase is the relative one between the two modes) here the phase is measured relative to a strong classical signal (using heterodyne or homodyne measurements) or similar strategies.…”

Supersensitive ancilla-based adaptive quantum phase estimation

“…Correlations are further tuned by placing a second HWP with an optic axis at an angle α 2 in the upper arm, after the PBS, as shown in Fig 2. The states created by this process are states that, in general, are not optimal when p = 0. This may not be surprising; for a large number of estimation tasks, the optimal quantum probe states are rarely optimal once decoherence is introduced to the system [26][27][28][29]. The input state after preparation is given by Now, the calculation of the optimal Fisher information for a given value of φ, F…”