J. Calsamiglia

Discriminating States: The Quantum Chernoff Bound

We consider the problem of discriminating two different quantum states in the setting of asymptotically many copies, and determine the minimal probability of error. This leads to the identification of the quantum Chernoff bound, thereby solving a long-standing open problem. The bound reduces to the classical Chernoff bound when the quantum states under consideration commute. The quantum Chernoff bound is the natural symmetric distance measure between quantum states because of its clear operational meaning and because it does not seem to share some of the undesirable features of other distance measures.

All nonclassical correlations can be activated into distillable entanglement.

We devise a protocol in which general nonclassical multipartite correlations produce a physically relevant effect, leading to the creation of bipartite entanglement. In particular, we show that the relative entropy of quantumness, which measures all nonclassical correlations among subsystems of a quantum system, is equivalent to and can be operationally interpreted as the minimum distillable entanglement generated between the system and local ancillae in our protocol. We emphasize the key role of state mixedness in maximizing nonclassicality: Mixed entangled states can be arbitrarily more nonclassical than separable and pure entangled states.

Computable Measure of Nonclassicality for Light

We propose the entanglement potential (EP) as a measure of nonclassicality for quantum states of a single-mode electromagnetic field. It is the amount of two-mode entanglement that can be generated from the field using linear optics, auxiliary classical states, and ideal photodetectors. The EP detects nonclassicality, has a direct physical interpretation, and can be computed efficiently. These three properties together make it stand out from previously proposed nonclassicality measures. We derive closed expressions for the EP of important classes of states and analyze as an example of the degradation of nonclassicality in lossy channels.

Maximum efficiency of a linear-optical Bell-state analyzer

Abstract.In a photonic realization of qubits the implementation of quantum logic is rather difficult due to the extremely weak interaction on the few photon level. On the other hand, in these systems interference is available to process the quantum states. We formalize the use of interference by the definition of a simple class of operations which include linear-optical elements, auxiliary states and conditional operations.We investigate an important subclass of these tools, namely linear-optical elements and auxiliary modes in the vacuum state. For these tools, we are able to extend a previous qualitative result, a no-go theorem for perfect Bell-state analyzer on two qubits in polarization entanglement, by a quantitative statement. We show that within this subclass it is not possible to discriminate unambiguously four equiprobable Bell states with a probability higher than 50%.

Generalized measurements by linear elements

I give a first characterization of the class of generalized measurements that can be exactly realized on a pair of qudits encoded in indistinguishable particles, by using only linear elements and particle detectors. Two immediate results follow from this characterization. (i) The Schmidt number of each element in the positive operator valued measure cannot exceed the number of initial particles. This rules out any possibility of performing perfect Bell measurements for qudits. (ii) The maximum probability of performing a generalized incomplete Bell measurement is one-half.

Quantum Chernoff bound as a measure of distinguishability between density matrices: Application to qubit and Gaussian states

Hypothesis testing is a fundamental issue in statistical inference and has been a crucial element in the development of information sciences. The Chernoff bound gives the minimal Bayesian error probability when discriminating two hypotheses given a large number of observations. Recently the combined work of Audenaert et al. Phys. Rev. Lett. 98, 160501 2007 and Nussbaum and Szkola e-print arXiv:quant-ph/0607216 has proved the quantum analog of this bound, which applies when the hypotheses correspond to two quantum states. Based on this quantum Chernoff bound, we define a physically meaningful distinguishability measure and its corresponding metric in the space of states; the latter is shown to coincide with the Wigner-Yanase metric. Along the same lines, we define a second, more easily implementable, distinguishability measure based on the error probability of discrimination when the same local measurement is performed on every copy. We study some general properties of these measures, including the probability distribution of density matrices, defined via the volume element induced by the metric. It is shown that the Bures and the local-measurement based metrics are always proportional. Finally, we illustrate their use in the paradigmatic cases of qubits and Gaussian infinite-dimensional states. DOI: 10.1103/PhysRevA.77.032311

Phase estimation for thermal Gaussian states

We give the optimal bounds on the phase-estimation precision for mixed Gaussian states in the single-copy and many-copy regimes. Specifically, we focus on displaced thermal and squeezed thermal states. We find that while for displaced thermal states an increase in temperature reduces the estimation fidelity, for squeezed thermal states a larger temperature can enhance the estimation fidelity. The many-copy optimal bounds are compared with the minimum variance achieved by three important single-shot measurement strategies. We show that the single-copy canonical phase measurement does not always attain the optimal bounds in the many-copy scenario. Adaptive homodyning schemes do attain the bounds for displaced thermal states, but for squeezed states they yield fidelities that are insensitive to temperature variations and are, therefore, suboptimal. Finally, we find that heterodyne measurements perform very poorly for pure states but can attain the optimal bounds for sufficiently mixed states. We apply our results to investigate the influence of losses in an optical metrology experiment. In the presence of losses squeezed states cease to provide the Heisenberg limited precision, and their performance is close to that of coherent states with the same mean photon number.

Anomalous Frictional Behavior in Collisions of Thin Disks

We report on two-dimensional collision experiments with nine thin Delrin disks with variable axisymmetric mass distributions. The disks floated on an air table, and collided at speeds of about 0.5 to 1.0 m/s with a flat-walled stationary thick steel plate clamped to the table. The collision angle was varied. The observed normal restitution was roughly independent of angle, consistent with other studies. The frictional interaction differed from that reported for spheres and thick disks, and from predictions of most standard rigid-body collision models. For sliding two-dimensional collisions, most authors assume the ratio of tangential to normal impulse equals μ (friction coefficient). The observed impulse ratio was appreciably lower: roughly 0.5 μ slightly into the sliding regime, approaching μ only for nearly grazing collisions. Separate experiments were conducted to estimate μ; check its invariance with force magnitude; and check that the anomalies observed are not strongly dependent on velocity magnitude. We speculate that these slightly anomalous findings are related to the two-dimensional deformation fields in thin disks, and with the disks being only impulse-response rigid and not force-response rigid.

Entanglement percolation in quantum complex networks.

Quantum networks are essential to quantum information distributed applications, and communicating over them is a key challenge. Complex networks have rich and intriguing properties, which are as yet unexplored in the quantum setting. Here, we study the effect of entanglement percolation as a means to establish long-distance entanglement between arbitrary nodes of quantum complex networks. We develop a theory to analytically study random graphs with arbitrary degree distribution and give exact results for some models. Our findings are in good agreement with numerical simulations and show that the proposed quantum strategies enhance the percolation threshold substantially. Simulations also show a clear enhancement in small-world and other real-world networks.

Optimal signal states for quantum detectors

Quantum detectors provide information about the microscopic properties of quantum systems by establishing correlations between those properties and a set of macroscopically distinct events that we observe. The question of how much information a quantum detector can extract from a system is therefore of fundamental significance. In this paper, we address this question within a precise framework: given a measurement apparatus implementing a specific POVM measurement, what is the optimal performance achievable with it for a specific information readout task and what is the optimal way to encode information in the quantum system in order to achieve this performance? We consider some of the most common information transmission tasks—the Bayes cost problem, unambiguous message discrimination and the maximal mutual information. We provide general solutions to the Bayesian and unambiguous discrimination problems. We also show that the maximal mutual information is equal to the classical capacity of the quantum-to-classical channel describing the measurement, and study its properties in certain special cases. For a group covariant measurement, we show that the problem is equivalent to the problem of accessible information of a group covariant ensemble of states. We give analytical proofs of optimality in some relevant cases. The framework presented here provides a natural way to characterize generalized quantum measurements in terms of their information readout capabilities.