Conservation relation of nonclassicality and entanglement for Gaussian states in a beam-splitter

We study the relation between single-mode nonclassicality and two-mode entanglement in a beam-splitter. We show that not all of the nonclassicality (entanglement potential) is transformed into two-mode entanglement for an incident single-mode light. Some of the entanglement potential remains as single-mode nonclassicality in the two entangled output modes. Two-mode entanglement generated in the process can be equivalently quantified as the increase in the minimum uncertainty widths (or decrease in the squeezing) of the output states compared to the input states. We use the nonclassical depth and logarithmic negativity as single-mode nonclassicality and entanglement measures, respectively. We realize that a conservation relation between the two quantities can be adopted for Gaussian states, if one works in terms of uncertainty width. This conservation relation is extended to many sets of beam-splitters.Comment: 10 pages, 8 figure

Quantum States Preparation in Cavity Optomechanics

Quantum entanglement and quantum superposition are fundamental properties of quantum mechanics, which underline quantum information and quantum computation. Preparing quantum states in the macroscopic level is both conceptually interesting for extending quantum physics to a broader sense and fundamentally important for testing the validity of quantum mechanics. In this dissertation, schemes of preparing macroscopic entanglement and macroscopic superposition states in cavity optomechanics are studied using the unitary evolution method in the nonlinear regime or Lyapunov equation in the linearized regime. Quantum entanglement and quantum superposition states can be realized using experimentally feasible parameters with the proposals in this dissertation. Firstly, a scheme of entangling two movable end mirrors in a Fabry-Perot cavity that are coupled to a common single photon superposition state is studied. It is shown that strong entanglement can be obtained either in the single-photon strong coupling regime deterministically or in the single-photon weak coupling regime conditionally. Secondly, a scheme of entangling two movable end mirrors, that are coupled to two-mode entangled fields generated from a correlated-emission laser is investigated. By tuning the input driving laser frequencies at the Stokes sidebands of the cavity, the radiation-pressure coupling can be linearized as an effective beam-splitter-like interaction. Hence entanglement can be transferred from the two-mode fields to the two mechanical mirrors. Macroscopic entanglement between macroscopic mirrors persists at temperature ~ 1K. Thirdly, a scheme of creating macroscopic quantum superpositions of a mechanical mirror via periodically flipping a photonic qubit is proposed. Quantum superposition states of a mechanical mirror can be obtained via the nonlinear radiation coupling with a single-photon superposition state. However, the difference between two superposed mechanical states is very small due to the weak single-photon coupling rate available in experiment. By periodically flipping the photonic qubit state, the difference can be magnified. It is shown in detail that this scheme is experimentally feasible under current technology

Classical-Nonclassical Polarity of Gaussian States

Gaussian states with nonclassical properties such as squeezing and entanglement serve as crucial resources for quantum information processing. Accurately quantifying these properties within multi-mode Gaussian states has posed some challenges. To address this, we introduce a unified quantification: the 'classical-nonclassical polarity', represented by $\mathcal{P}$. For a single mode, a positive value of $\mathcal{P}$ captures the reduced minimum quadrature uncertainty below the vacuum noise, while a negative value represents an enlarged uncertainty due to classical mixtures. For multi-mode systems, a positive $\mathcal{P}$ indicates bipartite quantum entanglement. We show that the sum of the total classical-nonclassical polarity is conserved under arbitrary linear optical transformations for any two-mode and three-mode Gaussian states. For any pure multi-mode Gaussian state, the total classical-nonclassical polarity equals the sum of the mean photon number from single-mode squeezing and two-mode squeezing. Our results provide a new perspective on the quantitative relation between single-mode nonclassicality and entanglement, which may find applications in a unified resource theory of nonclassical features

The Metrological Power of Nonclassical Single-Mode States

Nonclassical states enable metrology with a precision beyond that possible with classical physics. Both for practical applications and to understand non-classicality as a resource, it is useful to know the maximum quantum advantage that can be provided by a nonclassical state when it is combined with arbitrary classical states. This advantage has been termed the "metrological power" of a quantum state. A key open question is whether the metrological powers for the metrology of different quantities are related, especially metrology of force (acceleration) and phase shifts (time). Here we answer this question for all single-mode states, both for local and distributed metrology, by obtaining complete expressions for the metrological powers for the metrology of essentialy any quantity (any single-mode unitary transformation), as well as the linear networks that achieve this maximal precision. This shows that the metrological powers for all quantities are proportional to a single property of the state, which for pure states is the quadrature variance, maximized over all quadratures.Comment: 5 pages main text, 2 figures, 3 pages supplemental material