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We report a theoretical and experimental study on the role of indistinguishability in the estimation of an interferometric phase. In particular, we show that the quantum Fisher information, which limits the maximum precision achievable in the parameter estimation, increases linearly with respect to the degree of indistinguishability between the input photons in a two-port interferometer, in the ideal case of a pure probe state. We experimentally address the role played by the indistinguishability for the case of two photons entering a polarization-based interferometer, where the degree of indistinguishability is characterized by the overlap between two spatial modes. The experimental results support the fact that, even in the presence of white noise, a quantum enhancement in the interferometric phase estimation can be obtained from a minimum degree of indistinguishability.
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We derive the form of the quantum filter equation describing the continuous observation of the phase of a quantum system in an arm of an interferometer via non-demolition measurements when the statistics of an input field used for the indirect measurement are in a general coherent state. Both quadrature homodyne detection and photon-counting dection schemes are covered, and we solve the linearized filter for a specific application.
Quantum coherence, a basic feature of quantum mechanics residing in superpositions of quantum states, is a resource for quantum information processing. Coherence emerges in a fundamentally different way for nonidentical and identical particles, in that for the latter a unique contribution exists linked to indistinguishability which cannot occur for nonidentical particles. We experimentally demonstrate by an optical setup this additional contribution to quantum coherence, showing that its amount directly depends on the degree of indistinguishability and exploiting it to run a quantum phase discrimination protocol. Furthermore, the designed setup allows for simulating Fermionic particles with photons, thus assessing the role of particle statistics (Bosons or Fermions) in coherence generation and utilization. Our experiment proves that independent indistinguishable particles can supply a controllable resource of coherence for quantum metrology.
We observe that quantum indistinguishability is a dynamical effect dependent on measurement duration. We propose a quantitative criterion for observing indistinguishability in quantum fluids and its implications including quantum statistics and derive a viscoelastic function capable of describing both long-time and short-time regimes where indistinguishability and its implications are operative and inactive, respectively. On the basis of this discussion, we propose an experiment to observe a transition between two states where the implications of indistinguishability become inoperative, including a transition between statistics-active and statistics-inactive states.
The indistinguishability of independent single photons is presented by decomposing the single photon pulse into the mixed state of different transform limited pulses. The entanglement between single photons and outer environment or other photons induces the distribution of the center frequencies of those transform limited pulses and makes photons distinguishable. Only the single photons with the same transform limited form are indistinguishable. In details, the indistinguishability of single photons from the solid-state quantum emitter and spontaneous parametric down conversion is examined with two-photon Hong-Ou-Mandel interferometer. Moreover, experimental methods to enhance the indistinguishability are discussed, where the usage of spectral filter is highlighted.
This paper focuses on the quantum amplitude estimation algorithm, which is a core subroutine in quantum computation for various applications. The conventional approach for amplitude estimation is to use the phase estimation algorithm, which consists of many controlled amplification operations followed by a quantum Fourier transform. However, the whole procedure is hard to implement with current and near-term quantum computers. In this paper, we propose a quantum amplitude estimation algorithm without the use of expensive controlled operations; the key idea is to utilize the maximum likelihood estimation based on the combined measurement data produced from quantum circuits with different numbers of amplitude amplification operations. Numerical simulations we conducted demonstrate that our algorithm asymptotically achieves nearly the optimal quantum speedup with a reasonable circuit length.
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