Topological transitions of the generalized Pancharatnam-Berry phase.

Distinct from the dynamical phase, in a cyclic evolution, a system's state may acquire an additional component, a.k.a. geometric phase. Recently, it has been demonstrated that geometric phases can be induced by a sequence of generalized measurements implemented on a single qubit. Furthermore, it has been predicted that these geometric phases may exhibit a topological transition as a function of the measurement strength. We demonstrate and study this transition experimentally by using an optical platform where the qubit is represented by the polarization of light and the weak measurement is performed by means of coupling with the spatial degree of freedom. Our protocol can be interpreted in terms of environment-induced geometric phases, whose values are topologically determined by the environment-system coupling strength. Our results show that the two limits of geometric phase induced by sequences of either weak or projective measurements are topologically distinct.

Detection of Quantum Interference without an Interference Pattern.

Quantum interference is typically detected through the dependence of the interference signal on certain parameters (path length, Aharonov-Bohm flux, etc.), which can be varied in a controlled manner. The destruction of interference by a which-path measurement is a paradigmatic manifestation of quantum effects. Here we report on a novel measurement protocol that realizes two objectives: (i) certifying that a measured signal is the result of interference avoiding the need to vary parameters of the underlying interferometer, and (ii) certifying that the interference signal at hand is of quantum nature. In particular, it yields a null outcome in the case of classical interference. Our protocol comprises measurements of cross-correlations between the readings of which-path weakly coupled detectors positioned at the respective interferometer's arms and the current in one of the interferometer's drains. We discuss its implementation with an experimentally available platform: an electronic Mach-Zehnder interferometer (MZI) coupled electrostatically to "detectors" (quantum point contacts).

Topological transition in measurement-induced geometric phases.

The state of a quantum system, adiabatically driven in a cycle, may acquire a measurable phase depending only on the closed trajectory in parameter space. Such geometric phases are ubiquitous and also underline the physics of robust topological phenomena such as the quantum Hall effect. Equivalently, a geometric phase may be induced through a cyclic sequence of quantum measurements. We show that the application of a sequence of weak measurements renders the closed trajectories, hence the geometric phase, stochastic. We study the concomitant probability distribution and show that, when varying the measurement strength, the mapping between the measurement sequence and the geometric phase undergoes a topological transition. Our finding may impact measurement-induced control and manipulation of quantum states-a promising approach to quantum information processing. It also has repercussions on understanding the foundations of quantum measurement.

Efficiency of a cyclic quantum heat engine with finite-size baths.

In this paper we investigate the relationship between the efficiency of a cyclic quantum heat engine with the Hilbert space dimension of the thermal baths. By means of a general inequality, we show that the Carnot efficiency can be obtained only when both the hot and cold baths are infinitely large. By further introducing a specific model where the baths are constituted of ensembles of finite-dimensional particles, we further demonstrate the relationship between the engine's power and efficiency, with the dimension of the working substance and the bath particles.

Ubiquitous Nonlocal Entanglement with Majorana Zero Modes.

Entanglement in quantum mechanics contradicts local realism and is a manifestation of quantum nonlocality. Its presence can be detected through the violation of Bell, or Clauser-Horne-Shimony-Holt (CHSH) inequalities. Paradigmatic quantum systems provide examples of both, nonentangled and entangled states. Here, we consider a minimal complexity setup consisting of six Majorana zero modes. We find that any allowed state in the degenerate Majorana space is nonlocally entangled. We show how to measure (with available techniques) the CHSH-violating correlations using either intermediate strength or weak measurement protocols.

Thermodynamics of Weakly Measured Quantum Systems.

We consider continuously monitored quantum systems and introduce definitions of work and heat along individual quantum trajectories that are valid for coherent superposition of energy eigenstates. We use these quantities to extend the first and second laws of stochastic thermodynamics to the quantum domain. We illustrate our results with the case of a weakly measured driven two-level system and show how to distinguish between quantum work and heat contributions. We finally employ quantum feedback control to suppress detector backaction and determine the work statistics.

Scattering matrix formulation of the topological index of interacting fermions in one-dimensional superconductors.

We construct a scattering matrix formulation for the topological classification of one-dimensional superconductors with effective time-reversal symmetry in the presence of interactions. For an isolated system, Fidkowski and Kitaev have shown that such systems have a Z_{8} topological classification. We here show that these systems have a unitary scattering matrix at zero temperature when weakly coupled to a normal-metal lead, with a topological index given by the trace of the Andreev-reflection matrix, trr_{he}. With interactions, trr_{he} generically takes on the finite set of values 0, ±1, ±2, ±3, and ±4. We show that the two topologically equivalent phases with trr_{he}=±4 support emergent many-body end states, which we identify to be a topologically protected Kondo-like resonance. The path in phase space that connects these equivalent phases crosses a non-Fermi-liquid fixed point where a multiple-channel Kondo effect develops. Our results connect the topological index to transport properties, thereby highlighting the experimental signatures of interacting topological phases in one dimension.

Null values and quantum state discrìmination.

We present a measurement protocol for discriminating between two different quantum states of a qubit with high fidelity. The protocol, called null value, is comprised of a projective measurement performed on the system with a small probability (also known as partial collapse), followed by a tuned postselection. We report on an optical experimental implementation of the scheme. We show that our protocol leads to an amplified signal-to-noise ratio (as compared with a straightforward strong measurement) when discerning between the two quantum states.

Enhanced zero-bias Majorana peak in the differential tunneling conductance of disordered multisubband quantum-wire/superconductor junctions.

A recent experiment Mourik et al. [Science 336, 1003 (2012)] on InSb quantum wires provides possible evidence for the realization of a topological superconducting phase and the formation of Majorana bound states. Motivated by this experiment, we consider the signature of Majorana bound states in the differential tunneling conductance of multisubband wires. We show that the weight of the Majorana-induced zero-bias peak is strongly enhanced by mixing of subbands, when disorder is added to the end of the quantum wire. We also consider how the topological phase transition is reflected in the gap structure of the current-voltage characteristic.

Probability distribution of Majorana end-state energies in disordered wires.

One-dimensional topological superconductors harbor Majorana bound states at their ends. For superconducting wires of finite length L, these Majorana states combine into fermionic excitations with an energy ε(0) that is exponentially small in L. Weak disorder leaves the energy splitting exponentially small, but affects its typical value and causes large sample-to-sample fluctuations. We show that the probability distribution of ε(0) is log normal in the limit of large L, whereas the distribution of the lowest-lying bulk energy level ε(1) has an algebraic tail at small ε(1). Our findings have implications for the speed at which a topological quantum computer can be operated.

Charge sensing amplification via weak values measurement.

A protocol employing weak values (WVs) to obtain ultrasensitive amplification of weak signals in the context of a solid-state setup is proposed. We consider an Aharonov-Bohm interferometer where both the orbital and the spin degrees of freedom are weakly affected by the presence of an external charge to be detected. The interplay between the spin and the orbital WVs leads to a significant amplification even in the presence of finite temperature, voltage, and external noise.

Tomography of many-body weak values: Mach-Zehnder interferometry.

We propose and study a weak value (WV) protocol in the context of a solid state setup, specifically, an electronic Mach-Zehnder interferometer. This is the first specific proposal to measure both the real and imaginary part (i.e., complete tomography) of a WV. We also analyze the manifestation of many-body physics in the WV to be measured, including finite temperature and shot-noise-like contributions.

Weak values of electron spin in a double quantum dot.

We propose a protocol for a controlled experiment to measure a weak value of the electron's spin in a solid state device. The weak value is obtained by a two step procedure--weak measurement followed by a strong one (postselection), where the outcome of the first measurement is kept provided a second postselected outcome occurs. The setup consists of a double quantum dot and a weakly coupled quantum point contact to be used as a detector. Anomalously large values of the spin of a two electron system are predicted, as well as negative values of the total spin. We also show how to incorporate the adverse effect of decoherence into this procedure.