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When estimating the phase of a single mode, the quantum Fisher information for a pure probe state is proportional to the photon number variance of the probe state. In this work, we point out particular states that offer photon number distributions exhibiting a large variance, which would help to improve the local estimation precision. These theoretical examples are expected to stimulate the community to put more attention to those states that we found, and to work towards their experimental realization and usage in quantum metrology., Comment: 7 pages, 1 figure

We investigate an optimal distance of two components in an entangled coherent state for quantum phase estimation in lossy interferometry. The optimal distance is obtained by an economical point, representing the quantum Fisher information that we can extract per input energy. Maximizing the formula of the quantum Fisher information over an input mean photon number, we show that, as the losses of the interferometer increase, it can be more beneficial to prepare an initially entangled coherent state that is less entangled. This represents that the optimal distance of the two-mode components decreases with more loss in the interferometry. Under the constraint of the input mean photon number, we obtain that the optimal entangled coherent state is more robust than a separable coherent state, even in a high photon loss rate. The optimal entangled coherent state preserves quantum advantage over the standard interferometric limit of the separable coherent state. We also show that the corresponding optimal measurement requires correlation measurement bases., Comment: 8 pages, 12 figures, close to published version

We present a method to extract M-partie bosonic correlations from an N-partite maximally symmetric state (M < N) with the help of successive applications of single-boson subtractions. We also propose an experimental photonic setup to implement it that can be done with the present technologies., Comment: 7 pages, 2 figures

Quantum fidelity is a measure to quantify the closeness of two quantum states. In an operational sense, it is defined as the minimal overlap between the probability distributions of measurement outcomes and the minimum is taken over all possible positive-operator valued measures (POVMs). Quantum fidelity has been investigated in various scientific fields, but the identification of associated optimal measurements has often been overlooked despite its great importance for practical purposes. We find here the optimal POVMs for quantum fidelity between multi-mode Gaussian states in a closed analytical form. Our general finding is specified for selected single-mode Gaussian states of particular interest and we identify three types of optimal measurements: a number-resolving detection, a projection on the eigenbasis of operator $\hat{x}\hat{p}+\hat{p}\hat{x}$, and a quadrature detection, each of which is applied to distinct types of single-mode Gaussian states. We also show the equivalence between optimal measurements for quantum fidelity and those for quantum parameter estimation, enabling one to easily find the optimal measurements for displacement, phase, squeezing, and loss parameter estimations using Gaussian states., Comment: 11 pages, 2 figures

We consider an evolution of two elementary quantum particles and ask the question: under what conditions such a system behaves as a single object? It is obvious that if the attraction between the particles is stronger than any other force acting on them the whole system behaves as one. However, recent insight from the quantum information theory suggests that in bipartite systems it is not attraction per se that is responsible for the composite nature, but the entanglement between the parts. Since entanglement can be present between the subsystems that interacted in the past, but do not interact anymore, it is natural to ask when such an entangled pair behaves as a single object. We show that there are situations when entanglement is enough to observe single-particle behaviour. However, due to the no-signalling condition, in general an interaction, or a post-selective measurement, is necessary for a complex collective behaviour., Comment: 12 pages, 8 figures

The central issue in quantum parameter estimation is to find out the optimal measurement setup that leads to the ultimate lower bound of an estimation error. We address here a question of whether a Gaussian measurement scheme can achieve the ultimate bound for phase estimation in single-mode Gaussian metrology that exploits single-mode Gaussian probe states in a Gaussian environment. We identify three types of optimal Gaussian measurement setups yielding the maximal Fisher information depending on displacement, squeezing, and thermalization of the probe state. We show that the homodyne measurement attains the ultimate bound for both displaced thermal probe states and squeezed vacuum probe states, whereas for the other single-mode Gaussian probe states, the optimized Gaussian measurement cannot be the optimal setup, although they are sometimes nearly optimal. We then demonstrate that the measurement on the basis of the product quadrature operators XP+PX, i.e., a non-Gaussian measurement, is required to be fully optimal., Comment: 13 pages, 6 figures

Non-commutativity is one of the most elementary non-classical features of quantum observables. Here we propose a method to detect non-commutativity of interaction Hamiltonians of two probe objects coupled via a mediator. If these objects are open to their local environments, our method reveals non-decomposability of temporal evolution into a sequence of interactions between each probe and the mediator. The Hamiltonians or Lindblad operators can remain unknown throughout the assessment, we only require knowledge of the dimension of the mediator. Furthermore, no operations on the mediator are necessary. Technically, under the assumption of decomposable evolution, we derive upper bounds on correlations between the probes and then demonstrate that these bounds can be violated with correlation dynamics generated by non-commuting Hamiltonians, e.g., Jaynes-Cummings coupling. An intuitive explanation is provided in terms of multiple exchanges of a virtual particle which lead to the excessive accumulation of correlations. A plethora of correlation quantifiers are helpful in our method, e.g., quantum entanglement, discord, mutual information, and even classical correlation. Finally, we discuss exemplary applications of the method in quantum information: the distribution of correlations and witnessing dimension of an object., Comment: 7 pages, 2 figures

We present a study on two-particle indistinguishability and particle-species identification by introducing a Fisher-information (FI) approach---in which two particles pass through a two-wave mixing operation and the number of particles is counted in one of the output modes. In our study, we first show that FI can reproduce the Hong-Ou-Mandel (HOM) effect with two bosons or two fermions. In particular, it is found that even though bosons and fermions exhibit different physical behavior (i.e., "bunching" or "anti-bunching") due to their indistinguishability, the aspects of HOM-like dip are quantitatively same. We then provide a simple method for estimating the degree of two-particle indistinguishability in a Mach-Zehnder interferometer-type setup. The presented method also enables us to identify whether the particles are bosons or fermions. Our study will provide useful primitives for various study of boson and fermion characteristics., Comment: 11+1 pages, 6 figures. Corrected typos in page 6