Distinguishing mixed quantum states: Minimum-error discrimination versus optimum unambiguous discrimination

We consider two different optimized measurement strategies for the discrimination of nonorthogonal quantum states. The first is conclusive discrimination with a minimum probability of inferring an erroneous result, and the second is unambiguous, i. e. error-free, discrimination with a minimum probability of getting an inconclusive outcome, where the measurement fails to give a definite answer. For distinguishing between two mixed quantum states, we investigate the relation between the minimum error probability achievable in conclusive discrimination, and the minimum failure probability that can be reached in unambiguous discrimination of the same two states. The latter turns out to be at least twice as large as the former for any two given states. As an example, we treat the case that the state of the quantum system is known to be, with arbitrary prior probability, either a given pure state, or a uniform statistical mixture of any number of mutually orthogonal states. For this case we derive an analytical result for the minimum probability of error and perform a quantitative comparison to the minimum failure probability.Comment: Replaced by final version, accepted for publication in Phys. Rev. A. Revtex4, 6 pages, 3 figure

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.

Programmable quantum state discriminators with simple programs

We describe a class of programmable devices that can discriminate between two quantum states. We consider two cases. In the first, both states are unknown. One copy of each of the unknown states is provided as input, or program, for the two program registers, and the data state, which is guaranteed to be prepared in one of the program states, is fed into the data register of the device. This device will then tell us, in an optimal way, which of the templates stored in the program registers the data state matches. In the second case, we know one of the states while the other is unknown. One copy of the unknown state is fed into the single program register, and the data state which is guaranteed to be prepared in either the program state or the known state, is fed into the data register. The device will then tell us, again optimally, whether the data state matches the template or is the known state. We determine two types of optimal devices. The first performs discrimination with minimum error, the second performs optimal unambiguous discrimination. In all cases we first treat the simpler problem of only one copy of the data state and then generalize the treatment to n copies. In comparison to other works we find that providing n > 1 copies of the data state yields higher success probabilities than providing n > 1 copies of the program states.Comment: 17 pages, 5 figure

Temperature- and Magnetic-Field-Dependent Optical Properties of Heavy Quasiparticles in YbIr2Si2

We report the temperature- and magnetic-field-dependent optical conductivity spectra of the heavy electron metal YbIr$_2$Si$_2$. Upon cooling below the Kondo temperature ($T_{\rm K}$), we observed a typical charge dynamics that is expected for a formation of a coherent heavy quasiparticle state. We obtained a good fitting of the Drude weight of the heavy quasiparticles by applying a modified Drude formula with a photon energy dependence of the quasiparticle scattering rate that shows a similar power-law behavior as the temperature dependence of the electrical resistivity. By applying a magnetic field of 6T below $T_{\rm K}$, we found a weakening of the effective dynamical mass enhancement by about 12% in agreement with the expected decrease of the $4f$-conduction electron hybridization on magnetic field.Comment: 5 pages, 4 figures. to be published in Journal of the Physical Society of Japan Vol. 79 (2010) No. 1

Cosmogenic nuclides in cometary materials: Implications for rate of mass loss and exposure history

As planned, the Rosetta mission will return to earth with a 10-kg core and a 1-kg surface sample from a comet. The selection of a comet with low current activity will maximize the chance of obtaining material altered as little as possible. Current temperature and level of activity, however, may not reliably indicate previous values. Fortunately, from measurements of the cosmogenic nuclide contents of cometary material, one may estimate a rate of mass loss in the past and perhaps learn something about the exposure history of the comet. Perhaps the simplest way to estimate the rate of mass loss is to compare the total inventories of several long-lived cosmogenic radionuclides with the values expected on the basis of model calculations. Although model calculations have become steadily more reliable, application to bodies with the composition of comets will require some extension beyond the normal range of use. In particular, the influence of light elements on the secondary particle cascade will need study, in part through laboratory irradiations of volatile-rich materials. In the analysis of cometary data, it would be valuable to test calculations against measurements of short-lived isotopes

Eccentric Taylor-Couette Flow with orbital motion of the inner cylinder

This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.The flow in a Taylor-Couette system is one of the most explored flows today. The behaviour of the flow is characterized by Reynolds number, radii and aspect ratio. By reducing the gap width the Taylor-Couette system can be used as a simplified bearing model which has one additional feature. To cover flow effects of a real bearing the rotating inner cylinder moves on an offset track. Thus the system is also characterized by a varying annulus. That changes the eccentricity which is also related to the critical Reynolds number for the system. There is a higher Reynolds number for a higher eccentricity. This is used as a benchmark to validate the code. Depending on the eccentric position of the rotating inner cylinder one can notice either Taylor Vortex flow or Couette Flow. After testing the code the gap width will be adjusted to realistic bearing geometries. This second part refers to bearing simulations where the gap width is adjusted to real bearing conditions. In Fact the present system is a simplified bearing, which covers not all details of a real one. It becomes more complex in later stages of the project, where oil feedings and notches are implemented as well as the occurrence of cavitation. Furthermore the offset tracks will be much more complex. The final goal is to develop a 3D simulation tool for hydrodynamic journal bearings that resolves effects like cross flow from the oil feedings and also cavitation. Known methods based on the Reynolds equations fail to predict important flow characteristics in complex bearing geometries due to their two dimensional nature. If sufficiently low local pressure areas occur, cavitation- related damages may appear. So the pressure distribution of the flow is of interest

Powers of componentwise linear ideals

We give criteria for graded ideals to have the property that all their powers are componentwise linear. Typical examples to which our criteria can be applied include the vertex cover ideals of certain finite graphs

Optimum measurement for unambiguously discriminating two mixed states: General considerations and special cases

Based on our previous publication [U. Herzog and J. A. Bergou, Phys.Rev. A 71, 050301(R) (2005)] we investigate the optimum measurement for the unambiguous discrimination of two mixed quantum states that occur with given prior probabilities. Unambiguous discrimination of nonorthogonal states is possible in a probabilistic way, at the expense of a nonzero probability of inconclusive results, where the measurement fails. Along with a discussion of the general problem, we give an example illustrating our method of solution. We also provide general inequalities for the minimum achievable failure probability and discuss in more detail the necessary conditions that must be fulfilled when its absolute lower bound, proportional to the fidelity of the states, can be reached.Comment: Submitted to Journal of Physics:Conference Series (Proceedings of the 12th Central European Workshop on Quantum Optics, Ankara, June 2005