Weak measurements with a qubit meter

We derive schemes to measure the so-called weak values of quantum system observables by coupling of the system to a qubit meter system. We highlight, in particular, the meaning of the imaginary part of the weak values, and show how it can be measured directly on equal footing with the real part of the weak value. We present compact expressions for the weak value of single qubit observables and of product observables on qubit pairs. Experimental studies of the results are suggested with cold trapped ions.     

Weak density of states

Let L be a quantum logic, here an orthoalgebra, and let be a convex set of states on L. Then generates a base-normed space, and the dual-order unit-normed space contains a canonically constructed homomorphic copy of L, denoted by e(L). A convex set of states on L is said to be ample provided that every state on L is obtained by restricting an element of the base of the bi-dual order unit-normed space to e(L). For a quantum logic L we show that a convex set of states is ample if and only if is weakly dense in the convex set of all states on L. The notion of ampleness is then discussed in the context of Gleason-type theorems for W^* algebras and JBW algebras and also in the context of classical logics.Dedicated to Prof. Peter Mittelstaedt on the occasion of his sixtieth birthday. Research supported by the Swiss National Science Foundation.     

Controlled quantum state sharing of arbitrary two-qubit states with five-qubit cluster states

In this paper, we propose a controlled quantum state sharing scheme to share an arbitrary two-qubit state using a five-qubit cluster state and the Bell state measurement. In this scheme, the five-qubit cluster state is shared by a sender (Alice), a controller (Charlie), and a receiver (Bob), and the sender only needs to perform the Bell-state measurements on her particles during the quantum state sharing process, the controller performs a single-qubit projective measurement on his particles, then the receiver can reconstruct the arbitrary two-qubit state by performing some appropriate unitary transformations on his particles after he has known the measured results of the sender and the controller.     

Weak measurements are universal

It is well known that any projective measurement can be decomposed into a sequence of weak measurements, which cause only small changes to the state. Similar constructions for generalized measurements, however, have relied on the use of an ancilla system. We show that any generalized measurement can be decomposed into a sequence of weak measurements without the use of an ancilla, and give an explicit construction for these weak measurements. The measurement procedure has the structure of a random walk along a curve in state space, with the measurement ending when one of the end points is reached. This shows that any measurement can be generated by weak measurements, and hence that weak measurements are universal. This may have important applications to the theory of entanglement.     

Coherent states for arbitrary Lie group

The concept of coherent states originally closely related to the nilpotent group of Weyl is generalized to arbitrary Lie group. For the simplest Lie groups the system of coherent states is constructed and its features are investigated.     

Quantum mechanics of successive measurements with arbitrary meter coupling

We study successive measurements of two observables using von Neumann's measurement model. The two-pointer correlation for arbitrary coupling strength allows retrieving the initial system state. We recover Lüders rule, the Wigner formula and the Kirkwood-Dirac distribution in the appropriate limits of the coupling strength.     

Weak measurements as an instance of non-ideal measurements

We introduce weak measurements (WM) as a type of non-ideal measurement (NIM) coupling the system and the measuring device in a specific manner involving a weak interaction followed by post-selection. For the particular case of a WM measurement of spin, we solve the quantum dynamics for the coupled system-meter ensemble exactly for any type of non-ideal measurement. The standard WM regime is obtained as a limiting case; eccentric ??semi-weak?? values not only appear in other cases of NIM, but can also have a larger magnitude than the usual weak values. A couple of examples comparing the merits of the WM regime and of the exact treatment in situations of potential interest to quantum information applications are considered.     

Transient photodecay measurements as a probe of the density of localized states in amorphous semiconductors

We show that structure in the density of localized states of an amorphous semiconductor beyond the apparently ubiquitous exponential band tails yield deviations from the usual power-law decay of the photocurrent, i(t) ∝ t^α?1, which can be described analytically. With our expression, dispersive-transport results can be deconvoluted to provide a spectroscopy of the localized-state distribution when well-defined defect centers and band tails are simultaneously present.     

Experimental quantum teleportation of arbitrary quantum states

Received: 1 July 1998/Revised version: 2 October 1998     

Concurrence of arbitrary dimensional bipartite quantum states

We derive an analytical lower bound for the concurrence of a bipartite quantum state in arbitrary dimension. A functional relation is established relating concurrence, the Peres-Horodecki criterion, and the realignment criterion. We demonstrate that our bound is exact for some mixed quantum states. The significance of our method is illustrated by giving a quantitative evaluation of entanglement for many bound entangled states, some of which fail to be identified by the usual concurrence estimation method.     

Generation of arbitrary four-atom entangled decoherence-free states

This paper proposes a scheme to generate arbitrary four-atom entangled decoherence-free states by using simple linear optical elements, four one-sided cavities in which four atoms are confined respectively. By conveniently tuning the titled angle of one half-wave plate, it can obtain arbitrary four-atom entangled decoherence-free states with a successful probability of 1 as long as there is no photon loss.     

The NMR reciprocity theorem for arbitrary probe geometry

It is shown that the NMR reciprocity theorem is a variant of a problem considered by Lorentz in 1895. This formulation is quite general and applies to electric-dipole-based as well as coil-based or resonator-based magnetic resonance probes. The reasoning is related to, but different from, the proof of the reciprocity theorem for radiofrequency networks and for transmit/receive antenna systems in telecommunications. The signal-to-noise ratio of the NMR experiment is also discussed in very general terms.     

Exact hole-bound states for semiconductor quantum wells with arbitrary potential profiles

An efficient numerical-analytical method for finding confined and continuum states in quantum-well systems with arbitrary potential profiles, described by coupled Schrödinger equations, is presented. The method is based on the analytical properties of the wave functions, in particular, the power series representation of solutions of the corresponding coupled differential equations. Using only the general properties of the coefficients of a system of an arbitrary number of coupled Schrödinger equations, and imposing for definiteness the simplest boundary conditions, we derive exact expressions for the wave functions and present methods for accurate calculations of the energies and wave functions of confined states and of the wave functions of continuum states in quantum wells. The method is applied to the calculation of the dispersion of hole bound states in a single GaAs quantum well with truncated parabolic confining potentials of different strengths. The results are compared with data available from previous calculations.     

Symmetric informationally complete measurements of arbitrary rank

There has been much interest in so-called SIC-POVMs, i.e., rank 1 symmetric informationally complete positive operator valued measures. In this paper we discuss the larger class of POVMs that are symmetric and informationally complete, but not necessarily rank 1. This class of POVMs is of some independent interest. In particular it includes a POVM that is closely related to the discrete Wigner function. However, it is interesting mainly because of the light it casts on the problem of constructing rank 1, symmetric, informationally complete POVMs. In this connection we derive an extremal condition alternative to the one derived by Renes et al. The text was submitted by the author in English.     

Deterministic joint remote preparation of arbitrary multi-qudit states

In this Letter, we put forward a new nontrivial three-step strategy for joint remote preparation of arbitrary two-qudit states (JRSP) in a deterministic manner from a spatially separated multi-sender to one receiver. The scheme is then extended to the arbitrary multi-qudit case. In our schemes, various partially entangled GHZ-like states with arbitrary complex parameters are used as the quantum channels. It overcomes state preparation failure leading to the loss of valuable quantum channel resource and ensures the prepared data available for the remote terminals under extreme conditions such as limited number of quantum channels and limited quantum information processing technologies.     

Generation of arbitrary frequency-entangled states of two-photon light

We consider a new method for the generation of polarization-frequency entangled states of photon pairs. We use a frequency-nondegenerate regime of spontaneous parametric down conversion where the photon pairs (biphotons) are produced with identical polarizations, propagate mostly in the same direction, but differ in frequency. Entanglement is achieved by a coherent superposition of pairs emitted from two nonlinear crystals, with the polarization of the biphotons from the first crystal being changed by a transformer placed between the two crystals. We show that this scheme allows the degree of entanglement to be controlled by the choice of biphoton frequencies.     

Density of states in SF bilayers with arbitrary strength of magnetic scattering

We developed a self-consistent method for the calculation of the density of states N(ε) in SF bilayers. It is based on the quasi-classical Usadel equations and takes into account the suppression of superconductivity in the S layer due to the proximity effect of the F metal, as well as existing mechanisms of the spin dependent electron scattering. We demonstrate that the increase of the spin orbit or spin flip electron scattering rates results in completely different transformations of N(ε) at the free F layer interface. The developed formalism has been applied for the interpretation of the available experimental data. The text was submitted by the authors in English.     

Dose rate measurements with a ruby-based fiber optic radioluminescent probe

Fiber optic radioluminescence dosimetry allows real-time dose rate measurements in complex, narrow geometries and at places of high dose rates, without exposing the operator or the susceptible electronics. The keys are the spatial separation of radiation sensitive probe and electronic processing system and their optical connection by a flexible light guide. The small probes are capable of measuring fields of high dose rate gradients and the sealed probe-tip qualifies for applications in the fluid milieu and even for in-vivo-dosimetry. One problem of fiber optic dosimetry is the generation of Cherenkov radiation and fiber luminescence in the irradiated light guide, the so called stem effect. Ruby (Al₂O₃:Cr) has a narrow radioluminescent emission at 694 nm and is a potential luminophor for fiber optic radioluminescence dosimetry. In this work the influence of the stem effect on our ruby-based fiber optic dosimetry system is examined. The behavior of ruby probes under irradiation up to 0.5 kGy, as well as their luminescence decay characteristics and the applicability for measurements in radiotherapeutic fields are investigated.     

Entanglement detection in the vicinity of arbitrary Dicke states

Dicke states represent a class of multipartite entangled states that can be generated experimentally with many applications in quantum information. We propose a method to experimentally detect genuine multipartite entanglement in the vicinity of arbitrary Dicke states. The detection scheme can be used to experimentally quantify the entanglement depth of many-body systems and is easy to implement as it requires measurement of only three collective spin operators. The detection criterion is strong as it heralds multipartite entanglement even in cases where the state fidelity goes down exponentially with the number of qubits.