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We optimize two-mode, entangled, number states of light in the presence of loss in order to maximize the extraction of the available phase information in an interferometer. Our approach optimizes over the entire available input Hilbert space with no constraints, other than fixed total initial photon number. We optimize to maximize the Fisher information, which is equivalent to minimizing the phase uncertainty. We find that in the limit of zero loss the optimal state is the so-called N00N state, for small loss, the optimal state gradually deviates from the N00N state, and in the limit of large loss the optimal state converges to a generalized two-mode coherent state, with a finite total number of photons. The results provide a general protocol for optimizing the performance of a quantum optical interferometer in the presence of photon loss, with applications to quantum imaging, metrology, sensing, and information processing.
We analyze the optimal state, as given by Berry and Wiseman [Phys. Rev. Lett {bf 85}, 5098, (2000)], under the canonical phase measurement in the presence of photon loss. The model of photon loss is a generic fictitious beam splitter, and we present
Electromagnetically induced transparency (EIT) has been often proposed for generating nonlinear optical effects at the single photon level; in particular, as a means to effect a quantum non-demolition measurement of a single photon field. Previous tr
Precise measurement is crucial to science and technology. However, the rule of nature imposes various restrictions on the precision that can be achieved depending on specific methods of measurement. In particular, quantum mechanics poses the ultimate
Fragile quantum features such as entanglement are employed to improve the precision of parameter estimation and as a consequence the quantum gain becomes vulnerable to noise. As an established tool to subdue noise, quantum error correction is unfortu
A significant obstacle for practical quantum computation is the loss of physical qubits in quantum computers, a decoherence mechanism most notably in optical systems. Here we experimentally demonstrate, both in the quantum circuit model and in the on