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Sep 23, 2013
09/13

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Holger F. Hofmann

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Recently, weak measurements have attracted a lot of interest as an experimental method for the investigation of non-classical correlations between observables that cannot be measured jointly. Here, I explain how the complex valued statistics observed in weak measurements relate to the operator algebra of the conventional Hilbert space formalism and show that the algebra of operators originates from more fundamental relations between the physical properties of a quantum system that can be...

Source: http://arxiv.org/abs/1305.0053v1

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Sep 19, 2013
09/13

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Holger F. Hofmann

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The effects of any quantum measurement can be described by a collection of measurement operators {M_m} acting on the quantum state of the measured system. However, the Hilbert space formalism tends to obscure the relationship between the measurement results and the physical properties of the measured system. In this paper, a characterization of measurement operators in terms of measurement resolution and disturbance is developed. It is then possible to formulate uncertainty relations for the...

Source: http://arxiv.org/abs/quant-ph/0209162v2

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Sep 21, 2013
09/13

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Holger F. Hofmann

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Quantum teleportation is possible because entanglement allows a definition of precise correlations between the non-commuting properties of a local system and corresponding non-commuting properties of a remote system. In this paper, the exact causality achieved by maximal entanglement is analyzed and the results are applied to the transfer of effects acting on the entanglement distribution channels to the teleported output state. In particular, it is shown how measurements performed on the...

Source: http://arxiv.org/abs/quant-ph/0203128v2

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Sep 21, 2013
09/13

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Holger F. Hofmann

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It is shown that a quantum controlled-NOT gate simultaneously performs the logical functions of three distinct conditional local operations. Each of these local operations can be verified by measuring a corresponding truth table of four local inputs and four local outputs. The quantum parallelism of the gate can then be observed directly in a set of three simple experimental tests, each of which has a clear intuitive interpretation in terms of classical logical operations. Specifically, quantum...

Source: http://arxiv.org/abs/quant-ph/0407165v3

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Sep 23, 2013
09/13

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Holger F. Hofmann

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Experimentally, the imaginary parts of complex weak values are obtained from the response of the system to small unitary phase shifts generated by the target observable. The complex conditional probabilities obtained from weak measurements can therefore be explained in terms of transformation dynamics. Specifically, the complex phase of weak conditional probabilities provides a complete description of the transformation dynamics between the initial and the final state generated by the...

Source: http://arxiv.org/abs/1105.0224v1

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Jul 19, 2013
07/13

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Holger F. Hofmann

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Quantum metrology uses small changes in the output probabilities of a quantum measurement to estimate the magnitude of a weak interaction with the system. The sensitivity of this procedure depends on the relation between the input state, the measurement results, and the generator observable describing the effect of the weak interaction on the system. This is similar to the situation in weak measurements, where the weak value of an observable exhibits a symmetric dependence on initial and final...

Source: http://arxiv.org/abs/1005.4741v3

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Sep 24, 2013
09/13

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Holger F. Hofmann

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In a recent paper (arXiv:1111.3328), Pusey, Barrett and Rudolph claim to prove that statistical interpretations of quantum mechanics do not work. In fact, their proof assumes that all statistical interpretations must be based on hidden variable realism. Effectively, the authors demand from the start that reality must be decided by mathematics, and not by measurements. If this unjustified assumption is dropped, the quantum formalism has a natural statistical interpretation that fully explains...

Source: http://arxiv.org/abs/1112.2446v2

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Jun 30, 2018
06/18

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Holger F. Hofmann

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Quantum paradoxes show that quantum statistics can exceed the limits of positive joint probabilities for physical properties that cannot be measured jointly. It is therefore impossible to describe the relations between the different physical properties of a quantum system by assigning joint realities to their observable values. Instead, recent experimental results obtained by weak measurements suggest that non-classical correlations could be expressed by complex valued quasi-probabilities,...

Topic: Quantum Physics

Source: http://arxiv.org/abs/1406.3085

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Jun 29, 2018
06/18

by
Holger F. Hofmann

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Physics explains the laws of motion that govern the time evolution of observable properties and the dynamical response of systems to various interactions. However, quantum theory separates the observable part of physics from the unobservable time evolution by introducing mathematical objects that are only loosely connected to the actual physics by statistical concepts and cannot be explained by any conventional sets of events. Here, I examine the relation between statistics and dynamics in...

Topic: Quantum Physics

Source: http://arxiv.org/abs/1606.00108

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Jul 20, 2013
07/13

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Holger F. Hofmann

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The density operator of a quantum state can be represented as a complex joint probability of any two observables whose eigenstates have non-zero mutual overlap. Transformations to a new basis set are then expressed in terms of complex conditional probabilities that describe the fundamental relation between precise statements about the three different observables. Since such transformations merely change the representation of the quantum state, these conditional probabilities provide a...

Source: http://arxiv.org/abs/1107.0536v2

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Sep 20, 2013
09/13

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Holger F. Hofmann

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Since quantum feedback is based on classically accessible measurement results, it can provide fundamental insights into the dynamics of quantum systems by making available classical information on the evolution of system properties and on the conditional forces acting on the system. In this paper, the feedback-induced interaction dynamics between a pair of quantum systems is analyzed. It is pointed out that any interaction Hamiltonian can be simulated by local feedback if the levels of...

Source: http://arxiv.org/abs/quant-ph/0506002v1

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Sep 19, 2013
09/13

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Holger F. Hofmann

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By using finite resolution measurements it is possible to simultaneously obtain noisy information on two non-commuting polarization components of a single photon. This method can be applied to a pair of entangled photons with polarization statistics that violate Bell's inequalities. The theoretically predicted results show that the non-classical nature of entanglement arises from negative joint probabilities for the non-commuting polarization components. These negative probabilities allow a...

Source: http://arxiv.org/abs/quant-ph/0010022v1

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Sep 23, 2013
09/13

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Holger F. Hofmann

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Since weak measurements are known to produce measurement values that can be much larger than the maximal eigenvalues of the measured observable, it is an interesting question how this enhancement of the measurement signal relates to the sensitivity of quantum measurements as investigated in the field of quantum metrology. In this presentation, it is pointed out that the estimation of a small interaction parameter using weak measurements actually corresponds to standard quantum metrology, where...

Source: http://arxiv.org/abs/1012.0071v1

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Jun 27, 2018
06/18

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Holger F. Hofmann

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Quantum statistics originate from the physics of state preparation. It is therefore wrong to think of quantum states as fundamental. In fact, quantum states are merely summaries of dynamical processes that randomize the properties of the system by drawing on the inexhaustible reservoir of quantum fluctuations provided by the physical tools used to control the quantum system. The mathematical form of the "state vector" is actually an expression of the laws of causality which describe...

Topic: Quantum Physics

Source: http://arxiv.org/abs/1505.02464

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Sep 23, 2013
09/13

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Holger F. Hofmann

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A statistical analysis of optimal universal cloning shows that it is possible to identify an ideal (but non-positive) copying process that faithfully maps all properties of the original Hilbert space onto two separate quantum systems. The joint probabilities for non-commuting measurements on separate clones then correspond to the real parts of the complex joint probabilities observed in weak measurements on a single system, where the measurements on the two clones replace the corresponding...

Source: http://arxiv.org/abs/1111.5910v3

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Sep 22, 2013
09/13

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Holger F. Hofmann

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Finite resolution quantum nondemolition (QND) measurements allow a determination of light field properties while preserving some of the original quantum coherence of the input state. It is thus possible to measure correlations between the photon number and a quadrature component of the same light field mode. Nonclassical features emerge as photon number quantization is resolved. In particular, a strong anti-correlation of quantization and coherence is observable in QND measurements of photon...

Source: http://arxiv.org/abs/quant-ph/0004073v1

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Sep 23, 2013
09/13

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Holger F. Hofmann

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Quantum mechanics does not permit joint measurements of non-commuting observables. However, it is possible to measure the weak value of a projection operator, followed by the precise measurement of a different property. The results can be interpreted as complex joint probabilities of the two non-commuting measurement outcomes. Significantly, it is possible to predict the outcome of completely different measurements by combining the joint probabilities of the initial state with complex...

Source: http://arxiv.org/abs/1303.0078v1

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Sep 18, 2013
09/13

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Holger F. Hofmann

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By limiting the resolution of quantum measurements, the measurement induced changes of the quantum state can be reduced, permitting subsequent measurements of variables that do not commute with the initially measured property. It is then possible to experimentally determine correlations between non-commuting variables. The application of this method to the polarization statistics of entangled photon pairs reveals that negative conditional probabilities between non-orthogonal polarization...

Source: http://arxiv.org/abs/quant-ph/0008122v2

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Sep 21, 2013
09/13

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Holger F. Hofmann

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It is shown that coherent superpositions of two oppositely polarized n-photon states can be created by post-selecting the transmission of n independently generated photons into a single mode transmission line. It is thus possible to generate highly non-classical n-photon polarization states using only the bunching effects associated with the bosonic nature of photons. The effects of mode-matching errors are discussed and the possibility of creating n-photon entanglement by redistributing the...

Source: http://arxiv.org/abs/quant-ph/0311198v2

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Sep 23, 2013
09/13

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Holger F. Hofmann

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The continuous transition from a low resolution quantum nondemolition measurement of light field intensity to a precise measurement of photon number is described using a generalized measurement postulate. In the intermediate regime, quantization appears as a weak modulation of measurement probability. In this regime, the measurement result is strongly correlated with the amount of phase decoherence introduced by the measurement interaction. In particular, the accidental observation of half...

Source: http://arxiv.org/abs/quant-ph/9909013v2

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Sep 21, 2013
09/13

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Holger F. Hofmann

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Weak measurements performed between quantum state preparation and post-selection result in complex values for self-adjoint operators, corresponding to complex conditional probabilities for the projections on specific eigenstates. In this paper, it is shown that the complex phases of these weak conditional probabilities describe the dynamic response of the system to unitary transformations. Quantum mechanics thus unifies the statistical overlap of different states with the dynamical structure of...

Source: http://arxiv.org/abs/1104.0062v2

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Sep 22, 2013
09/13

by
Holger F. Hofmann

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The concept of negative probabilities can be used to decompose the interaction of two qubits mediated by a quantum controlled-NOT into three operations that require only classical interactions (that is, local operations and classical communication) between the qubits. For a single gate, the probabilities of the three operations are 1, 1, and -1. This decomposition can be applied in a probabilistic simulation of quantum computation by randomly choosing one of the three operations for each gate...

Source: http://arxiv.org/abs/0805.0029v2

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Sep 23, 2013
09/13

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Holger F. Hofmann

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The origin of non-classical correlations is difficult to identify since the uncertainty principle requires that information obtained about one observable invariably results in the disturbance of any other non-commuting observable. Here, this problem is addressed by investigating the uncertainty trade-off between measurement errors and disturbance for measurement interactions controlled by the state of a single qubit, where the measurement is described by a quantum coherent superposition of a...

Source: http://arxiv.org/abs/1212.2683v2

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Sep 22, 2013
09/13

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Holger F. Hofmann

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It is shown that the condition for achieving the quantum Cramer-Rao bound of phase estimation in conventional two-path interferometers is that the state is symmetric with regard to an (unphysical) exchange of the two paths. Since path symmetry is conserved under phase shifts, the maximal phase sensitivity can be achieved at arbitrary bias phases, indicating that path symmetric states can achieve their quantum Cramer-Rao bound in Bayesian estimates of a completely unknown phase.

Source: http://arxiv.org/abs/0812.0044v1

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Sep 22, 2013
09/13

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Holger F. Hofmann

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It is shown that a good estimate of the fidelity of an experimentally realized quantum process can be obtained by measuring the outputs for only two complementary sets of input states. The number of measurements required to test a quantum network operation is therefore only twice as high as the number of measurements required to test a corresponding classical system.

Source: http://arxiv.org/abs/quant-ph/0409083v3

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Jun 28, 2018
06/18

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Holger F. Hofmann

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Quantum theory expresses the observable relations between physical properties in terms of probabilities that depend on the specific context described by the "state" of a system. However, the laws of physics that emerge at the macroscopic level are fully deterministic. Here, it is shown that the relation between quantum statistics and deterministic dynamics can be explained in terms of ergodic averages over complex valued probabilities, where the fundamental causality of motion is...

Topic: Quantum Physics

Source: http://arxiv.org/abs/1508.02779

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Sep 21, 2013
09/13

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Holger F. Hofmann

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Even though measurement results obtained in the real world are generally both noisy and continuous, quantum measurement theory tends to emphasize the ideal limit of perfect precision and quantized measurement results. In this article, a more general concept of noisy measurements is applied to investigate the role of quantum noise in the measurement process. In particular, it is shown that the effects of quantum noise can be separated from the effects of information obtained in the measurement....

Source: http://arxiv.org/abs/quant-ph/9907018v4

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Jun 30, 2018
06/18

by
Holger F. Hofmann

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In the operator formalism of quantum mechanics, the density operator describes the complete statistics of a quantum state in terms of d^2 independent elements, where d is the number of possible outcomes for a precise measurement of an observable. In principle, it is therefore possible to express the density operator by a joint probability of two observables that cannot actually be measured jointly because they do not have any common eigenstates. However, such joint probabilities do not refer to...

Topic: Quantum Physics

Source: http://arxiv.org/abs/1404.6327

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Sep 22, 2013
09/13

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Holger F. Hofmann

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A new approach to chemical bonding is introduced in order to provide an improved understanding of the connection between basic quantum mechanics and the covalent pair bond. It's focus is on the fact that the energy of the bond is largely given by the kinetic energy of the electrons, while the Coulomb forces are only comparable to the kinetic energy terms close to the atomic nuclei, where they define the shape and the size of the atomic orbitals. If atomic orbitals are used as a starting point,...

Source: http://arxiv.org/abs/physics/9612007v3

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Sep 23, 2013
09/13

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Holger F. Hofmann

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It is shown that a highly phase sensitive polarization squeezed (2n-1)-photon state can be generated by subtracting a diagonally polarized photon from the 2n photon component generated in collinear type II downconversion. This polarization wedge state has the interesting property that its photon number distribution in the horizontal and vertical polarizations remains sharply defined for phase shifts of up to 1/n between the circularly polarized components. Phase shifts at the Heisenberg limit...

Source: http://arxiv.org/abs/quant-ph/0510005v3

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Sep 23, 2013
09/13

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Holger F. Hofmann

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Realistic quantum gates operate at non-vanishing noise levels. Therefore, it is necessary to evaluate the performance of each device according to some experimentally observable criteria of device performance. In this presentation, the characteristic properties of quantum operations are discussed and efficient measurement strategies are proposed.

Source: http://arxiv.org/abs/quant-ph/0411011v1

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Sep 20, 2013
09/13

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Holger F. Hofmann

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The evaluation of uncertainties in quantum measurements is problematic since the correct value of an observable between state preparation and measurement is experimentally inaccessible. In Ozawa's formulation of uncertainty relations for quantum measurements, the correct value of an observable is represented by the operator of that observable. Here, I consider the implications of this operator-based assignment of values to individual systems and discuss the relation with weak values and weak...

Source: http://arxiv.org/abs/1205.0073v1

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Jun 30, 2018
06/18

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Holger F. Hofmann

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It is possible to completely explain all aspects of quantum mechanics by expressing the relations between physical properties in terms of complex conditional probabilities (Phys. Rev. A 89, 042115(2014)). These fully deterministic probabilities replace the classical notions of phase space geometries and continuous trajectories with a more accurate description that takes into account the role of dynamics in the emergence of reality. We can then understand why so many previous attempts to find a...

Topics: Quantum Physics, General Relativity and Quantum Cosmology

Source: http://arxiv.org/abs/1405.0053

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Sep 17, 2013
09/13

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Holger F. Hofmann

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As a consequence of having a positive partial transpose, bound entangled states lack many of the properties otherwise associated with entanglement. It is therefore interesting to identify properties that distinguish bound entangled states from separable states. In this paper, it is shown that some bound entangled states violate a non-symmetric class of local uncertainty relations (quant-ph/0212090). This result indicates that the asymmetry of non-classical correlations may be a characteristic...

Source: http://arxiv.org/abs/quant-ph/0305003v1

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Sep 19, 2013
09/13

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Holger F. Hofmann

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The spatiotemporal dynamics of photon emission into a non-local farfield channel and two local nearfield channels from a pair of coupled two level systems is analysed using a model for emission based on Wigner-Weisskopf theory. The local quantum beats can be observed in the two nearfield channels. However, the presence of the farfield causes decoherence in the quantum beats even if only photon emissions into the near field channels are considered.

Source: http://arxiv.org/abs/quant-ph/9709017v1

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Jul 19, 2013
07/13

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Holger F. Hofmann

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Weak measurements can provide a complete characterization of post-selected ensembles, including the uncertainties of observables. Interestingly, the average uncertainties for pure initial and final states are always zero, suggesting the kind of complete knowledge that would allow a knowledge of past, presence and future in the sense of Laplace's demon. However, the quantum version actually describes cancellations of positive and negative uncertainties made possible by the strangeness of weak...

Source: http://arxiv.org/abs/1005.0654v1

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Sep 21, 2013
09/13

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F. Hofmann; H. Lenske

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The density matrix expansion is used to derive a local energy density functional for finite range interactions with a realistic meson exchange structure. Exchange contributions are treated in a local momentum approximation. A generalized Slater approximation is used for the density matrix where an effective local Fermi momentum is chosen such that the next to leading order off-diagonal term is canceled. Hartree-Fock equations are derived incorporating the momentum structure of the underlying...

Source: http://arxiv.org/abs/nucl-th/9705049v1

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Sep 23, 2013
09/13

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Masanori Hiroishi; Holger F. Hofmann

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We explore the mechanism of quantum teleportation by analyzing the weak measurement statistics post-selected by the result of the Bell measurement for the joint system composed of the input A and the spatially separated output B. It is shown that the weak measurement statistics observed before the Bell measurement includes correlations which relate every physical property in the input A to a corresponding physical property in the output B. The Bell measurement thus identifies the accidental...

Source: http://arxiv.org/abs/1303.3637v2

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Sep 21, 2013
09/13

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Changliang Ren; Holger F. Hofmann

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To fully utilize the energy-time degree of freedom of photons for optical quantum information processes, it is necessary to control and characterize the quantum states of the photons at extremely short time scales. For measurements beyond the time resolution of available detectors, two-photon interference with a photon in a short time reference pulse may be a viable alternative. In this paper, we derive the temporal measurement operators for the bunching statistics of a single photon input...

Source: http://arxiv.org/abs/1106.0071v1

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Sep 19, 2013
09/13

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Holger F. Hofmann; Ortwin Hess

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It is shown that the interference between spontaneous emission into the non-lasing supermode and the laser field of a semiconductor laser array causes spatial holeburning which couples the dynamics of the spontaneous emission with the laser field. In particular, phase locking between the spontaneous emission and the lasing mode leads to the formation of a spectral triplet composed of in-phase relaxation oscillation sidebands and an out-of-phase line at the lasing frequency.

Source: http://arxiv.org/abs/physics/9709040v1

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Sep 22, 2013
09/13

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Holger F. Hofmann; Shigeki Takeuchi

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We show that the density matrix of a spin-l system can be described entirely in terms of the measurement statistics of projective spin measurements along a minimum of 4l+1 different spin directions. It is thus possible to represent the complete quantum statistics of any N-level system within the spherically symmetric three dimensional space defined by the spin vector. An explicit method for reconstructing the density matrix of a spin-1 system from the measurement statistics of five...

Source: http://arxiv.org/abs/quant-ph/0310003v3

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Sep 22, 2013
09/13

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Holger F. Hofmann; Changliang Ren

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We show that a weak projective measurement of photon arrival time can be realized by controllable two photon interferences with photons from short-time reference pulses at a polarization beam splitter. The weak value of the projector on the arrival time defined by the reference pulse can be obtained from the coincidence rates conditioned by a specific output measurement. If the weak measurement is followed by a measurement of frequency, the coincidence counts reveal the complete temporal...

Source: http://arxiv.org/abs/1210.4212v3

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Sep 22, 2013
09/13

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Toshiki Ide; Holger F. Hofmann

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The information encoded in the polarization of a single photon can be transferred to a remote location by two-channel continuous-variable quantum teleportation. However, the finite entanglement used in the teleportation causes random changes in photon number. If more than one photon appears in the output, the continuous-variable teleportation accidentally produces clones of the original input photon. In this paper, we derive the polarization statistics of the $N$-photon output components and...

Source: http://arxiv.org/abs/quant-ph/0702204v2

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Sep 22, 2013
09/13

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Holger F. Hofmann; Shigeki Takeuchi

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We present an optical filter that transmits photon pairs only if they share the same horizontal or vertical polarization, without decreasing the quantum coherence between these two possibilities. Various applications for entanglement manipulations and multi-photon qubits are discussed.

Source: http://arxiv.org/abs/quant-ph/0111001v2

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Sep 19, 2013
09/13

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Holger F. Hofmann; Ortwin Hess

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We investigate the polarization fluctuations caused by quantum noise in quantum well vertical cavity surface emitting lasers (VCSELs). Langevin equations are derived on the basis of a generalized rate equation model in which the influence of competing gain-loss and frequency anisotropies is included. This reveals how the anisotropies and the quantum well confinement effects shape the correlations and the magnitude of fluctuations in ellipticity and in polarization direction. According to our...

Source: http://arxiv.org/abs/quant-ph/9703034v1

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Sep 22, 2013
09/13

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Holger F. Hofmann; O. Hess

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We present quantum Maxwell-Bloch equations (QMBE) for spatially inhomogeneous semiconductor laser devices. The QMBE are derived from fully quantum mechanical operator dynamics describing the interaction of the light field with the quantum states of the electrons and the holes near the band gap. By taking into account field-field correlations and field-dipole correlations, the QMBE include quantum noise effects which cause spontaneous emission and amplified spontaneous emission. In particular,...

Source: http://arxiv.org/abs/physics/9807011v2

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Sep 23, 2013
09/13

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Toshiki Ide; Holger F. Hofmann

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Superpositions of two orthogonal single-photon polarization states are commonly used as optical qubits. If such qubits are sent by continuous variable quantum teleportation, the modifications of the qubit states due to imperfect entanglement cause an increase in the average photon number of the output state. This effect can be interpreted as an accidental quantum cloning of the single photon input. We analyze the output statistics of the single photon teleportation and derive the transfer and...

Source: http://arxiv.org/abs/quant-ph/0511220v1

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Sep 18, 2013
09/13

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Holger F. Hofmann; Takafumi Ono

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We show that the quantum interference between downconverted photon pairs and photons from coherent laser light can produce a maximally path entangled N-photon output component with a fidelity greater than 90% for arbitrarily high photon numbers. A simple beam splitter operation can thus transform the 2-photon coherence of down-converted light into an almost optimal N-photon coherence.

Source: http://arxiv.org/abs/0705.0047v2

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Sep 18, 2013
09/13

by
Holger F. Hofmann; Shigeki Takeuchi

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Entangled states represent correlations between two separate systems that are too precise to be represented by products of local quantum states. We show that this limit of precision for the local quantum states of a pair of N-level systems can be defined by an appropriate class of uncertainty relations. The violation of such local uncertainty relations may be used as an experimental test of entanglement generation.

Source: http://arxiv.org/abs/quant-ph/0212090v3

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Sep 17, 2013
09/13

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Holger F. Hofmann; Shigeki Takeuchi

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The efficient experimental verification of entanglement requires an identification of the essential physical properties that distinguish entangled states from non-entangled states. Since the most characteristic feature of entanglement is the extreme precision of correlations between spatially separated systems, we propose a quantitative criterion based on local uncertainty relations (quant-ph/0212090). Some basic sum uncertainty relations for N-level systems are introduced and the amount of...

Source: http://arxiv.org/abs/quant-ph/0305002v1