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Let two coordinate systems, in possession of Alice and Bob, be related to each other by an unknown rotation R∈ SO (3). Alice is to send identical states | ψ⟩ to Bob who will make measurements on the received state and will determine the rotation R. The task of Bob is to estimate these parameters of the rotation R by the best possible measurements. Based on the quantum Fisher information, we show that Greenberger–Horne–Zeilinger (GHZ) states are near optimal states for this task. We show concrete measurements which will allow Bob to determine the rotation R. This shows that GHZ states, as superposition of macroscopically distinct states, are useful in yet another context in quantum... 

We prove an extended convexity for quantum Fisher information of a mixed state with a given convex decomposition. This convexity introduces a bound which has two parts: (i) The classical part associated with the Fisher information of the probability distribution of the states contributing to the decomposition, and (ii) the quantum part given by the average quantum Fisher information of the states in this decomposition. Next we use a non-Hermitian extension of a symmetric logarithmic derivative in order to obtain another upper bound on quantum Fisher information, which helps to derive a closed form for the bound in evolutions having the semigroup property. We enhance the extended convexity... 

Quantum metrology calculates the ultimate precision of all estimation strategies, measuring what is their root-mean-square error (RMSE) and their Fisher information. Here, instead, we ask how many bits of the parameter we can recover; namely, we derive an information-theoretic quantum metrology. In this setting, we redefine "Heisenberg bound" and "standard quantum limit" (the usual benchmarks in the quantum estimation theory) and show that the former can be attained only by sequential strategies or parallel strategies that employ entanglement among probes, whereas parallel-separable strategies are limited by the latter. We highlight the differences between this setting and the RMSE-based... 

In estimating an unknown parameter of a quantum state the quantum Fisher information (QFI) is a pivotal quantity, which depends on the state and its derivate with respect to the unknown parameter. We prove the continuity property for the QFI in the sense that two close states with close first derivatives have close QFIs. This property is completely general and irrespective of dynamics or how states acquire their parameter dependence and also the form of parameter dependence-indeed this continuity is basically a feature of the classical Fisher information that in the case of the QFI naturally carries over from the manifold of probability distributions onto the manifold of density matrices. We... 

While recent supervised dictionary learning methods have attained promising results on the classification tasks, their performance depends on the availability of the large labeled datasets. However, in many real world applications, accessing to sufficient labeled data may be expensive and/or time consuming, but its relatively easy to acquire a large amount of unlabeled data. In this paper, we propose a probabilistic framework for discriminative dictionary learning which uses both the labeled and unlabeled data. Experimental results demonstrate that the performance of the proposed method is significantly better than the state of the art dictionary based classification methods  

Similarity measure is an important part of image registration. The main challenge of similarity measure is lack of robustness to different distortions. A well-known distortion is spatially-varying intensity distortion. Its main characteristic is correlation among pixels. Most traditional intensity based similarity measures (e.g., SSD, MI) assume stationary image and pixel to pixel independence. Hence, these similarity measures are not robust against spatially-varying intensity distortion. Here, we suppose that non-stationary intensity distortion has a sparse representation in transform domain, i.e. its distribution has high peak at origin and a long tail. We use two viewpoints of Maximum... 

In this paper, we address theoretical limitations in estimating the mixing matrix in noisy Sparse Component Analysis (SCA) in the two-sensor case. We obtain the Cramér-Rao Bound (CRB) error estimation of the mixing matrix based on the observation vector x=(x1,x2)T. Using the Bernoulli-Gaussian (BG) sparse distribution for sources, and some reasonable approximations, the Fisher Information Matrix (FIM) is approximated by a diagonal matrix. Then, the effect of off-diagonal terms in computing the CRB is investigated. Moreover, we compute an oracle CRB versus the blind uniform CRB and show that this is only 3 dB better than the blind uniform CRB. Finally, the CRB, the approximated CRB, the... 

In this study, the optimal sensor placement problem for multi-source angle of arrival localisation is investigated. The authors adopt the A-optimality criterion, maximising the trace of Fisher information matrix, to determine the optimal sensor-target geometry under distance-dependent Gaussian noise model. A recursive representation of the Cramer-Rao lower bound is derived to recast the sensor placement problem into a sequential method, obtaining the optimal sensor geometries in a step by step manner. Note that the state-of-the-art methods are highly sensitive to the source location changes such that they should be relocated by any later changes in target geometries, which is practically... 

In this study, the optimal sensor placement problem for multi-source angle of arrival localisation is investigated. The authors adopt the A-optimality criterion, maximising the trace of Fisher information matrix, to determine the optimal sensor-target geometry under distance-dependent Gaussian noise model. A recursive representation of the Cramer-Rao lower bound is derived to recast the sensor placement problem into a sequential method, obtaining the optimal sensor geometries in a step by step manner. Note that the state-of-the-art methods are highly sensitive to the source location changes such that they should be relocated by any later changes in target geometries, which is practically... 

In this letter, we address the theoretical limitations in estimating the mixing matrix in noisy sparse component analysis (SCA) for the two-sensor case. We obtain the Cramer-Rao lower bound (CRLB) error estimation of the mixing matrix. Using the Bernouli-Gaussian (BG) sparse distribution, and some simple assumptions, an approximation of the Fisher information matrix (FIM) is calculated. Moreover, this CRLB is compared to some of the main methods of mixing matrix estimation in the literature. © 2008 IEEE  

Localization of an emitting or reflecting target is one of the most important issues in a wide range of applications including radar, sonar, wireless communication and sensor networks. Due to significant effect on the positioning accuracy, designing the optimal sensor-target geometry has been considered as an important problem in the localization literature. The existing sensor placement methods mainly solve the problem in the cases without any constraints on the sensors locations. In the realistic scenarios, however, the sensors cannot be placed simply in arbitrary locations due to such constraints as the geographical limitations, communication problems between the sensor pairs and the... 

The sensor-source geometry has a significant effect on accuracy of source localization problems. In a sensor placement problem, one attempts to optimally place the sensors in the surveillance area so as to optimize a performance criterion. Sensor placement methods mainly solve the associated problems without taking any specific constraint on permissible location of sensors into account. In practical applications, however, possible location for deployment of the sensors are subject to such limitations as environmental, industrial, and communication constraints, which affects the optimal sensor-source geometry. In this article, we consider the problem of optimal sensor placement, based on time... 

In this paper, we analyze the accuracy of target localization in multiple-input multiple-output (MIMO) radars with widely-separated antennas. The relative target-antennas geometry plays an important role in target localization. We investigate the optimal placement of transmit and receive antennas for coherent and non-coherent processing, based on maximizing the determinant of the Fisher information matrix (FIM), which is equivalent to minimizing the error ellipse area. The square root of the average determinant of the FIM can be expressed as a product of three parameters, namely the equivalent single radar gain, coherency gain and geometry gain. It is shown that the coherency gain of...