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We revisit the "counterfactual quantum communication" of Salih et al. [1], who claim that an observer "Bob" can send one bit of information to a second observer "Alice" without any physical particle traveling between them. We show that a locally conserved, massless current - specifically, a current of modular angular momentum, $L_z$ mod 2$\hbar$ - carries the one bit of information. We integrate the flux of $L_z$ mod 2$\hbar$ from Bob to Alice and show that it equals one of the two eigenvalues of $L_z$ mod 2$\hbar$, either 0 or $\hbar$, thus precisely accounting for the one bit of information he sends her. We previously [2] obtained this result using weak values of $L_z$ mod 2$\hbar$; here we do not use weak values., Comment: Physical Review Letters, in press

When incorporated in quantum sensing protocols, quantum error correction can be used to correct for high frequency noise, as the correction procedure does not depend on the actual shape of the noise spectrum. As such, it provides a powerful way to complement usual refocusing techniques. Relaxation imposes a fundamental limit on the sensitivity of state of the art quantum sensors which cannot be overcome by dynamical decoupling. The only way to overcome this is to utilize quantum error correcting codes. We present a superconducting magnetometry design that incorporates approximate quantum error correction, in which the signal is generated by a two qubit Hamiltonian term. This two-qubit term is provided by the dynamics of a tunable coupler between two transmon qubits. For fast enough correction, it is possible to lengthen the coherence time of the device beyond the relaxation limit.

In certain topological effects the accumulation of a quantum phase shift is accompanied by a local observable effect. We show that such effects manifest a complementarity between nonlocal and local attributes of the topology, which is reminiscent but different from the usual wave-particle complementarity. This complementarity is not a consequence of noncommutativity, rather it is due to the noncanonical nature of the observables. We suggest that a local/nonlocal complementarity is a general feature of topological effects that are "dual" to the Aharonov-Bohm effect.

In several situations, most notably when describing metastable states, a system can evolve according to an effective non hermitian Hamiltonian. To each eigenvalue of a non hermitian Hamiltonian is associated an eigenstate $\vert\phi\rangle$ which evolves forward in time and an eigenstate $\langle{\psi}\vert$ which evolves backward in time. Quantum measurements on such systems are analyzed in detail with particular emphasis on adiabatic measurements in which the measuring device is coupled weakly to the system. It is shown that in this case the outcome of the measurement of an observable $A$ is the weak value $\langle{\psi}\vert A\vert\phi\rangle / \langle{\psi}\vert{\phi}\rangle $ associated to the two-state vector $\langle{\psi}\vert$ $\vert\phi\rangle$ corresponding to one of the eigenvalues of the non hermitian Hamiltonian. The possibility of performing such measurements in a laboratory is discussed., Comment: RevTeX, 4 pages

We investigate the phase accumulated by a charged particle in an extended quantum state as it encircles one or more magnetic fluxons, each carrying half a flux unit. A simple, essentially topological analysis reveals an interplay between the Aharonov-Bohm phase and Berry's phase.

For an arbitrary quantum evolution, it is shown that the integral of the uncertainty of energy with respect to time is independent of the particular Hamiltonian used to transport the quantum system along a given curve in the projective Hilbert space. It is the distance along this curve measured by the Fubini-Study metric. This gives a new time-energy uncertainty principle. New geometric meanings to time as measured by a clock and the transition probability during a quantum measurement are also obtained.

A method to obtain a superposition of time evolutions of a quantum system which correspond to different Hamiltonians as well as to different periods of time is derived. Its application to amplification of an effect due to the action of weak forces is considered. A quantum time-translation machine based on the same principle, utilizing the gravitational field, is also considered.

The nonloclal exchange of the conserved, gauge invariant quantity $e^{\frac{i}{\hbar} (p_{k}-\frac{e}{c}A_{k})L^{k}}, L^{k}=const., k=1,2$ between the charged particle and the magnetic flux line (in the $k=3$ direction), is responsible for the Aharonov-Bohm effect. This exchange occurs at a definite time, before the wavepackets are brought together to interfere, and can be verified experimentally., LaTeX, 13 pages with 3 figures

Degenerate perturbation theory, without geometrical tools, directly yields vector potentials in the Born-Oppenheimer approximation. The derivation uses only the algebra of the dynamical operators, and the slow variables need not commute

Constants defining a quantum state can serve as macroscopic parameters specifying the spontaneous breaking of a symmetry. An example is given in which a laser possesses a SU(3) symmetry which is spontaneously broken above threshold. The parameters can be readily observed experimentally.

The neutrino events from the supernova SN1987A observed by the Kamiokande II and Irvine-Michigan-Brookhaven detectors are used to suggest constraints on neutrino physics. In particular, bounds on the value of the electron neutrino magnetic moment ${\mathrm{\ensuremath{\mu}}}_{\mathit{v}\mathit{e}}$\ensuremath{\lesssim}(${10}^{\mathrm{\ensuremath{-}}12}$-${10}^{\mathrm{\ensuremath{-}}13}$)${\mathrm{\ensuremath{\mu}}}_{\mathrm{B}}$ are suggested.

We derive the effective Lagrangian which describes the interaction between a charged particle and a magnetic moment in the nonrelativistic limit. It is shown that neutral particles with a magnetic moment will exhibit the Aharonov-Bohm effect in certain circumstances. We suggest several types of experiments.

A procedure is described whereby the result of the measurement of any of the three Cartesian components of the spin of a single spin-(1/2) particle at a single time can be inferred with certainty from the result of two other measurements, one of which is carried out before, and the other after, the time in question.

Whether quantum mechanical systems, within the interval between two measurements, can be assigned definite, simultaneous values of noncommuting observables has been the subject of a very old dispute. A certain widely held assumption about such systems has been crucial to that dispute. That assumption turns out to be wrong: A previously unknown prediction of quantum mechanics, which fails to satisfy that assumption, is described here, and the consequences of that failure are considered.

A new geometric phase factor is defined for any cyclic evolution of a quantum system. This is independent of the phase factor relating the initial and final state vectors and the Hamiltonian, for a given projection of the evolution on the projective space of rays of the Hilbert space. Some applications, including the Aharonov-Bohm effect, are considered. For the special case of adiabatic evolution, this phase factor is a gauge-invariant generalization of the one found by Berry.

We have found that the usual measuring procedure for preselected and postselected ensembles of quantum systems gives unusual results. Under some natural conditions of weakness of the measurement, its result consistently defines a new kind of value for a quantum variable, which we call the weak value. A description of the measurement of the weak value of a component of a spin for an ensemble of preselected and postselected spin-(1/2 particles is presented.