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We discuss how, in appropriately designed configurations, solenoids carrying a semifluxon can be used as topological energy barriers for charged quantum systems. We interpret this phenomenon as a consequence of the fact that such solenoids induce nodal lines in the wave function describing the charge, which on itself is a consequence of the Aharonov-Bohm effect. Moreover, we present a thought experiment with a cavity where two solenoids are sufficient to create bound states., Close to published version

Possibility to communicate between spatially separated regions, without even a single photon passing between the two parties, is an amazing quantum phenomenon. The possibility of transmitting one value of a bit in such a way, the interaction-free measurement, was known for quarter of a century. The protocols of full communication, including transmitting unknown quantum states were proposed only few years ago, but it was shown that in all these protocols the particle was leaving a weak trace in the transmission channel, the trace larger than the trace left by a single particle passing through the channel. This made the claim of counterfactuality of these protocols at best controversial. However, a simple modification of these recent protocols eliminates the trace in the transmission channel making all these protocols counterfactual., To be published as Rapid Communication in Physical Review A

Weak quantum measurement (WM) is unique in measuring noncommuting operators and other peculiar, otherwise-undetectable phenomena predicted by the two-state-vector-formalism (TSVF). The aim of this article is threefold: (i) introducing the foundations of WM and TSVF, (ii) studying temporal peculiarities predicted by TSVF and manifested by WM, and (iii) presenting applications of WM to single particles.

A "strongly" interacting, and entangling, heavy, non recoiling, external particle effects a significant change of the environment. Described locally, the corresponding entanglement event is a generalized electric Aharonov Bohm effect, that differs from the original one in a crucial way. We propose a gedanken interference experiment. The predicted shift of the interference pattern is due to a self induced or "private" potential difference experienced while the particle is in vacuum. We show that all non trivial Born Oppenheimer potentials are "private" potentials. We apply the Born Oppenheimer approximation to interference states. Using our approach we calculate the relative phase of the external heavy particle as well as its uncertainty throughout an interference experiment /entanglement event. We thus complement the Born Oppenheimer approximation for interference states., Comment: Accepted for publication in The Physical Review A

We introduce the concept of quantum random walk, and show that due to quantum interference effects the average path length can be much larger than the maximum allowed path in the corresponding classical random walk. A quantum-optics application is described.

So far, the wave function has been interpreted as a probability amplitude, which is given physical meaning by ensemble averages of a large number of identical systems at a given time. We give an alternative interpretation of the wave function for a single system by means of a measurement which lasts a long time. This is a measurement on a single quantum system which determines the expectation values of (not necessarily commuting) observables while the wave function is protected from collapsing because it undergoes another suitably chosen interaction. This type of measurement enables the distinction between states which are not orthogonal, but are protected by a suitable interaction with the states of their environment, even for a single system. It therefore gives a different ontological meaning to the wave function. Several experiments in which such a measurement is realized, which can in principle be performed using electrons, neutrons, or atoms, are studied.

The best qubit one-way quantum key distribution (QKD) protocol can tolerate up to 14.1% in the error rate. It has been shown how this rate can be increased by using larger quantum systems. The polarization state of a biphoton can encode a three level quantum system - a qutrit. The realization of a QKD system with biphotons encounters several problems in generating, manipulating and detecting such photon states. We define those limitations and find within them a few protocols that perform almost as well as the ideal qutrit protocol. One advantage is that these protocols can be implemented with minor modifications into existing single photon systems. The security of one protocol is proved for the most general coherent attacks and the largest acceptable error rate for this protocol is found to be around 17.7%. This is the first time, to the best of our knowledge, that the security of qutrit QKD protocols is rigorously analyzed against general attacks., Comment: 4 pages, 4 figures, calculation error corrected, new Fig. 4, 2 new Refs. and 2 omitted

A description of quantum systems at the time interval between two successive measurements is presented. Two wave functions, the first preselected by the initial measurement and the second postselected by the final measurement, describe quantum systems at a single time. It is shown how this approach leads to a new concept: a weak value of an observable. Weak values represent novel characteristics of quantum systems between two measurements. They are outcomes of a standard measurement procedure that fulfills certain requirements of ``weakness.'' We call it weak measurement. Physical meaning, underlying mathematical structure, and prospects of practical usage of weak measurements are explored.

We discuss the consequences of the Aharonov-Bohm (AB) effect in setups involving several charged particles, wherein none of the charged particles encloses a closed loop around the magnetic flux. We show that in such setups, the AB phase is encoded either in the relative phase of a bipartite or multipartite entangled photons states, or alternatively, gives rise to an overall AB phase that can be measured relative to another reference system. These setups involve processes of annihilation or creation of electron-hole pairs. We discuss the relevance of such effects in ``vacuum birefringence" in QED, and comment on their connection to other known effects.

A system consisting of two neutral spin-1/2 particles is analyzed for two magnetic field perturbations: (1) an inhomogeneous magnetic field over all space, and (2) external fields over a half space containing only one of the particles. The field is chosen to point from one particle to the other, which results in essentially a one-dimensional problem. A number of interesting features are revealed for the first case: the singlet, which has zero potential energy in the unperturbed case, remains unstable in the perturbing field. The spin-zero component of the triplet evolves into a bound state with a double well potential, with the possibility of tunneling. Superposition states can be constructed which oscillate between entangled and unentangled states. For the second case, we show that changes in the magnetic field around one particle affect measurements of the spin of the entangled particle not in the magnetic field nonlocally. By using protective measurements, we show it is possible in principle to establish a nonlocal interaction using the two particles, provided the dipole-dipole potential energy does not vanish and is comparable to the potential energy of the particle in the external field.

In order to reduce errors, error correction codes need to be implemented fast. They can correct the errors corresponding to the first few orders in the Taylor expansion of the time evolution operator corresponding to the Hamiltonian of the interaction with the environment. If implemented fast enough, the zeroth order error predominates and the dominant effect is of error prevention by measurement (Zeno effect) rather than correction. In this ``Zeno regime,'' codes with less redundancy are sufficient for protection. We describe such a simple scheme, which uses two ``noiseless'' qubits to protect a large number, $n$, of information qubits from noise from the environment. The ``noisless qubits'' can be realized by treating them as logical qubits to be encoded by one of the previously introduced encoding schemes.

Any charged particle moving faster than light through a medium emits Cherenkov radiation. We show that charged particles moving faster than light through the v a c u u m emit Cherenkov radiation. How can a particle move faster than light? The w e a k speed of a charged particle can exceed the speed of light. By definition, the weak velocity is / where v is the velocity operator and |a> and |b> are, respectively, the states of a particle before and after a velocity measurement. We discuss the consistency of weak values and show that superluminal weak speed is consistent with relativistic causality., RevTeX, 18 pages, no figures. Revised and expanded for clarity; to appear in Physical Review A

We argue that the quantum probability law follows, in the large N limit, from the compatibility of quantum mechanics with classical-like properties of macroscopic objects. For a finite sample, we find that likely and unlikely measurement outcomes are associated with distinct interference effects in a sample weakly coupled to an environment., Comment: 4 pages. Revised and expanded version. A microscopic distinction between rare and expected sequences is discussed

Comment on [R.L. Ingraham, Phys. Rev. A 50, 4502 (1994)]. Ingraham suggested ``a delayed-choice experiment with partial, controllable memory erasing''. It is shown that he cannot be right since his predictions contradict relativistic causality. A subtle quantum effect which was overlooked by Ingraham is explained., Comment: 4 pages, LaTeX

It is shown that the method of logarithmic perturbation expansion can be used to obtain the corrections to the energy and the logarithm of the wave function of the ground state of a hydrogen atom in a static multipole field, or a linear combination of static multipole fields to any order in perturbation theory.

A method previously developed for one-dimensional nonrelativistic perturbation theory is extended to three-dimensional problems. This method essentially consists of performing the perturbation expansion on the logarithm of the wave function instead of on the wave function itself. It is shown that, for the first-order corrections in problems that are not reducible to one dimension, this method is equivalent to that of Sternheimer and to that of Dalgarno and Lewis. In the present approach, the higher-order corrections can be obtained in a hierarchical scheme and there exists an isomorphisim between the equation for the first-order correction and the equation for the $i\mathrm{th}$-order correction. As an illustration of the technique developed, the authors consider the hydrogen atom in an external multipole field and in two different spherically symmetric perturbation potentials, $\ensuremath{\delta}(r\ensuremath{-}a)$ and ${e}^{\ensuremath{-}\ensuremath{\alpha}r}$. The last potential is related to the problem of the screened Coulomb potential. By considering the $\ensuremath{\delta}(r\ensuremath{-}a)$-type potential, two interesting sum rules are obtained.