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arXiv:1511.09447

Towards an experimental demonstration of some novel qubit behavior

Scott Roger Shepard

Published Nov 30, 2015• 0 citations
arXivHTMLPDF

Abstract

We show that the quantum angle measurement for x-polarized photon number states results in an angle which will never correspond to the y-axis for an odd number of photons; yet for an even number of photons it always can. The analogy of this surprising effect for other particles or ions (qubits in their spin up state) is presented and we show why such an effect cannot be observed in a standard SU(2) interferometer. The quantum phase representation of such an interferometer provides clues as to how its apparatus might be modified in order to demonstrate these phenomena. The same representation is then used to provide insight on the range and sensitivity that one can expect from quantum phase statistical inference algorithms which can surpass the Heisenberg limit.

DOI
10.48550/arxiv.1511.09447

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We show that the quantum angle measurement for x-polarized photon number states results in an angle which will never correspond to the y-axis for an odd number of photons; yet for an even number of photons it always can. The analogy of this surprising effect for other particles or ions (qubits in their spin up state) is presented and we show why such an effect cannot be observed in a standard SU(2) interferometer. The quantum phase representation of such an interferometer provides clues as to how its apparatus might be modified in order to demonstrate these phenomena. The same representation is then used to provide insight on the range and sensitivity that one can expect from quantum phase statistical inference algorithms which can surpass the Heisenberg limit.
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We investigate phase estimation in an SU(1,1) interferometer employing mmm-photon-added even and odd coherent states as nonclassical input resources. The phase sensitivity is evaluated through intensity detection and the error propagation method, while the ultimate precision limit is determined from the quantum Cramér-Rao bound with the quantum Fisher information serving as the relevant metrological quantity. Our results demonstrate that photon addition significantly enhances the phase sensitivity, increases the quantum Fisher information, and reduces the quantum Cramér-Rao bound, leading to a clear improvement over the corresponding even and odd coherent states. Furthermore, the achievable sensitivity exceeds the standard quantum limit and gradually approaches the Heisenberg scaling with increasing photon-addition number. We also find that the mmm-photon-added even coherent states exhibit a modest advantage over their odd counterparts. As mmm increases, however, this distinction becomes progressively weaker, suggesting that photon addition diminishes the role of the initial parity of the coherent state in determining the interferometric performance.
Photon number states are assigned a parity of +1 if their photon number is even and a parity of −1 if odd. The parity operator, which is minus one to the power of the photon number operator, is a Hermitian operator and thus a quantum mechanical observable although it has no classical analogue, the concept being meaningless in the context of classical light waves. In this paper we review work on the application of the parity operator to the problem of quantum metrology for the detection of small phase shifts with quantum optical interferometry using highly entangled field states such as the so-called N00N states, and states obtained by injecting twin Fock states into a beam splitter. With such states and with the performance of parity measurements on one of the output beams of the interferometer, one can breach the standard quantum limit, or shot-noise limit, of sensitivity down to the Heisenberg limit, the greatest degree of phase sensitivity allowed by quantum mechanics for linear phase shifts. Heisenberg limit sensitivities are expected to eventually play an important role in attempts to detect gravitational waves in interferometric detection systems such as LIGO and VIRGO.
Abstract The SU(1,1) interferometer, a nonlinear analog of the traditional Mach–Zehnder interferometer, has emerged as a powerful tool for achieving phase sensitivity beyond the standard quantum limit. In this work, we propose the use of a superposition of even and odd coherent states as input state to enhance the phase sensitivity of an SU(1,1) interferometer. These non-classical states exhibit unique properties such as squeezing, entanglement, and quantum interference, which can be harnessed to improve metrological precision. Phase sensitivity is analyzed using single-intensity detection and homodyne detection schemes under both ideal and photon loss cases, which demonstrates significant improvements over classical and squeezed-vacuum inputs. In addition, we evaluate the quantum Cramér-Rao lower bound by employing the quantum Fisher information formalism, showing that it surpasses the standard quantum limit and approaches the Heisenberg limit under optimal conditions. Our results highlight the potential of the even and odd coherent states superposition in quantum metrology and provide a pathway for achieving ultra-precise phase measurements in SU(1,1) interferometers for applications in optical sensing, and quantum information processing.
We report an experimental observation of correlated-photon statistics using a single detector. The usual coincidence dip in a two-photon polarization interferometer is accompanied by a dip in single-photon detection rates. Surprisingly, a dip in the singles rate is also observed when the interferometer is aligned for a coincidence peak, or anti-dip. This effect is explained by taking into account all possible photon number states that reach the detector, rather than considering just the state post-selected by the coincidence measurement.