Changepoint Problem in Quantumn Setting

In the changepoint problem, we determine when the distribution observed has changed to another one. We expand this problem to the quantum case where copies of an unknown pure state are being distributed. We study the fundamental case, which has only two candidates to choose. This problem is equal to identifying a given state with one of the two unknown states when multiple copies of the states are provided. In this paper, we assume that two candidate states are distributed independently and uniformly in the space of the whole pure states. The minimum of the averaged error probability is given and the optimal POVM is defined as to obtain it. Using this POVM, we also compute the error probability which depends on the inner product. These analytical results allow us to calculate the value in the asymptotic case, where this problem approaches to the usual discrimination problem

Information-disturbance tradeoff in quantum measurements

We present a simple information-disturbance tradeoff relation valid for any general measurement apparatus: The disturbance between input and output states is lower bounded by the information the apparatus provides in distinguishing these two states.Comment: 4 Pages, 1 Figure. Published version (reference added and minor changes performed

Correlation analysis of stochastic gravitational wave background around 0.1-1Hz

We discuss prospects for direct measurement of stochastic gravitational wave background around 0.1-1Hz with future space missions. It is assumed to use correlation analysis technique with the optimal TDI variables for two sets of LISA-type interferometers. The signal to noise for detection of the background and the estimation errors for its basic parameters (amplitude, spectral index) are evaluated for proposed missions.Comment: 11 pages, 7 figures, revised version, to appear in PR

Sub-Heisenberg estimation strategies are ineffective

In interferometry, sub-Heisenberg strategies claim to achieve a phase estimation error smaller than the inverse of the mean number of photons employed (Heisenberg bound). Here we show that one can achieve a comparable precision without performing any measurement, just using the large prior information that sub-Heisenberg strategies require. For uniform prior (i.e. no prior information), we prove that these strategies cannot achieve more than a fixed gain of about 1.73 over Heisenberg-limited interferometry. Analogous results hold for arbitrary single-mode prior distributions. These results extend also beyond interferometry: the effective error in estimating any parameter is lower bounded by a quantity proportional to the inverse expectation value (above a ground state) of the generator of translations of the parameter.Comment: 4 pages, 2 figures, revised version that was publishe

Discrimination of the binary coherent signal: Gaussian-operation limit and simple non-Gaussian near-optimal receivers

We address the limit of the Gaussian operations and classical communication in the problem of quantum state discrimination. We show that the optimal Gaussian strategy for the discrimination of the binary phase shift keyed (BPSK) coherent signal is a simple homodyne detection. We also propose practical near-optimal quantum receivers that beat the BPSK homodyne limit in all areas of the signal power. Our scheme is simple and does not require realtime electrical feedback.Comment: 7 pages, 4 figures, published versio

Quantum criticality as a resource for quantum estimation

We address quantum critical systems as a resource in quantum estimation and derive the ultimate quantum limits to the precision of any estimator of the coupling parameters. In particular, if L denotes the size of a system and \lambda is the relevant coupling parameters driving a quantum phase transition, we show that a precision improvement of order 1/L may be achieved in the estimation of \lambda at the critical point compared to the non-critical case. We show that analogue results hold for temperature estimation in classical phase transitions. Results are illustrated by means of a specific example involving a fermion tight-binding model with pair creation (BCS model).Comment: 7 pages. Revised and extended version. Gained one author and a specific exampl

Optimal minimum-cost quantum measurements for imperfect detection

Knowledge of optimal quantum measurements is important for a wide range of situations, including quantum communication and quantum metrology. Quantum measurements are usually optimised with an ideal experimental realisation in mind. Real devices and detectors are, however, imperfect. This has to be taken into account when optimising quantum measurements. In this paper, we derive the optimal minimum-cost and minimum-error measurements for a general model of imperfect detection.Comment: 5 page

Optimum unambiguous discrimination of two mixed states and application to a class of similar states

We study the measurement for the unambiguous discrimination of two mixed quantum states that are described by density operators $\rho_1$ and $\rho_2$ of rank d, the supports of which jointly span a 2d-dimensional Hilbert space. Based on two conditions for the optimum measurement operators, and on a canonical representation for the density operators of the states, two equations are derived that allow the explicit construction of the optimum measurement, provided that the expression for the fidelity of the states has a specific simple form. For this case the problem is mathematically equivalent to distinguishing pairs of pure states, even when the density operators are not diagonal in the canonical representation. The equations are applied to the optimum unambiguous discrimination of two mixed states that are similar states, given by $\rho_2= U\rho_1 U^{\dag}$, and that belong to the class where the unitary operator U can be decomposed into multiple rotations in the d mutually orthogonal two-dimensional subspaces determined by the canonical representation.Comment: 8 pages, changes in title and presentatio

Discrimination of two mixed quantum states with maximum confidence and minimum probability of inconclusive results

We study an optimized measurement that discriminates two mixed quantum states with maximum confidence for each conclusive result, thereby keeping the overall probability of inconclusive results as small as possible. When the rank of the detection operators associated with the two different conclusive outcomes does not exceed unity we obtain a general solution. As an application, we consider the discrimination of two mixed qubit states. Moreover, for the case of higher-rank detection operators we give a solution for particular states. The relation of the optimized measurement to other discrimination schemes is also discussed.Comment: 7 pages, 1 figure, accepted for publication in Phys. Rev.

Optimal estimation of entanglement

Entanglement does not correspond to any observable and its evaluation always corresponds to an estimation procedure where the amount of entanglement is inferred from the measurements of one or more proper observables. Here we address optimal estimation of entanglement in the framework of local quantum estimation theory and derive the optimal observable in terms of the symmetric logarithmic derivative. We evaluate the quantum Fisher information and, in turn, the ultimate bound to precision for several families of bipartite states, either for qubits or continuous variable systems, and for different measures of entanglement. We found that for discrete variables, entanglement may be efficiently estimated when it is large, whereas the estimation of weakly entangled states is an inherently inefficient procedure. For continuous variable Gaussian systems the effectiveness of entanglement estimation strongly depends on the chosen entanglement measure. Our analysis makes an important point of principle and may be relevant in the design of quantum information protocols based on the entanglement content of quantum states.Comment: 9 pages, 2 figures, v2: minor correction