Adam Bednorz

Quasiprobabilistic Interpretation of Weak Measurements in Mesoscopic Junctions

The impossibility of measuring noncommuting quantum mechanical observables is one of the most fascinating consequences of the quantum mechanical postulates. Hence, to date the investigation of quantum measurement and projection is a fundamentally interesting topic. We propose to test the concept of weak measurement of noncommuting observables in mesoscopic transport experiments, using a quasiprobabilistic description. We derive an inequality for current correlators, which is satisfied by every classical probability but violated by high-frequency fourth-order cumulants in the quantum regime for experimentally feasible parameters.

Formulation of Time‐Resolved Counting Statistics Based on a Positive‐Operator‐Valued Measure

We propose a derivation of the full counting statistics of electronic current based on a positive-operator-valued measure. Our approach justifies the Levitov-Lesovik formula in the long-time limit, but can be generalized to the detection of finite-frequency noise correlations. The combined action of the projection postulate and the quantum formula for current noise at high frequencies imply an additional white noise. Estimates for this additional noise are in accordance with known experiments. We propose an experimental test of our conjecture by a simultaneous measurement of high- and low-frequency noise.

Models of mesoscopic time-resolved current detection

Quantum transport in mesoscopic conductors is essentially governed by the laws of quantum mechanics. One of the major open questions of quantum mechanics is what happens if non-commuting observables are measured simultaneously. Since current operators at different times do not commute, the high-frequency correlation functions of the current are realization of this fundamental quantum question. We formulate this problem in the context of measurements of finite-frequency current cumulants in a general quantum point contact, which are the subject to ongoing experimental effort. To this end, we present two models of detectors that correspond to a weak time-resolved measurement of the electronic current in a mesoscopic junction. In both cases, the backaction of the detector leads to observable corrections to the current correlations functions involving the so-called noise susceptibilities. As a result, we propose a reinterpretation of environmental corrections to the finite-frequency cumulants as inevitable effect resulting from basic quantum mechanical principles. Finally we make concrete predictions for the temperature-, voltage-, and frequency-dependence of the third cumulant, which could be verified directly using current experimental techniques.

Nonsymmetrized Correlations in Quantum Noninvasive Measurements

A long-standing problem in quantum mesoscopic physics is which operator order corresponds to noise expressions like , where I(ω) is the measured current at frequency ω. Symmetrized order describes a classical measurement while nonsymmetrized order corresponds to a quantum detector, e.g., one sensitive to either emission or absorption of photons. We show that both order schemes can be embedded in quantum weak-measurement theory taking into account measurements with memory, characterized by a memory function which is independent of a particular experimental detection scheme. We discuss the resulting quasiprobabilities for different detector temperatures and how their negativity can be tested on the level of second-order correlation functions already. Experimentally, this negativity can be related to the squeezing of the many-body state of the transported electrons in an ac-driven tunnel junction.

Noninvasiveness and time symmetry of weak measurements

Measurements in classical and quantum physics are described in fundamentally different ways. Nevertheless, one can formally define similar measurement procedures with respect to the disturbance they cause. Obviously, strong measurements, both classical and quantum, are invasive—they disturb the measured system. We show that it is possible to define general weak measurements, which are noninvasive: the disturbance becomes negligible as the measurement strength goes to zero. Classical intuition suggests that noninvasive measurements should be time symmetric (if the system dynamics is reversible) and we confirm that correlations are time-reversal symmetric in the classical case. However, quantum weak measurements—defined analogously to their classical counterparts—can be noninvasive but not time symmetric. We present a simple example of measurements on a two-level system which violates time symmetry and propose an experiment with quantum dots to measure the time- symmetry violation in a third-order current correlation function.

Analysis of assumptions of recent tests of local realism

Local realism in recent experiments is excluded on condition of freedom or randomness of choice combined with no signaling between observers by implementations of simple quantum models. Both no-signaling and the underlying quantum model can be directly checked by analysis of experimental data. For particular tests performed on the data, it is shown that two of these experiments give the probability of the data under no-signaling (or choice independence in one of them) hypothesis at the level of 5%, accounting for the look-elsewhere-effect, moderately suggesting that no-signaling is violated with 95% confidence. On the other hand the data from the two other experiments violate the assumption of the simple quantum model. Further experiments are necessary to clarify these issues and freedom and randomness of choice.

Proposal for a cumulant-based Bell test for mesoscopic junctions

The creation and detection of entanglement in solid state electronics is of fundamental importance for quantum information processing. We prove that second-order quantum correlations can be always interpreted classically andproposeageneraltestofentanglementbasedontheviolationofaclassicallyderivedinequalityforcontinuous variables by fourth-order quantum correlation functions. Our scheme provides a way to prove the existence of entanglement in a mesoscopic transport setup by measuring higher order cumulants without requiring the additional assumption of a single-charge detection.

Interfacial fluctuations near the critical filling transition.

We advance a method to describe the short-distance fluctuations of an interface spanning a wedge-shaped substrate near the critical filling transition. Two different length scales determined by the average distance of the interface from the substrate at the wedge center can be identified. On one length scale, the one-dimensional approximation of A. O. Parry, C. Rascon, and A. J. Wood [Phys. Rev. Lett. 85, 345 (2000)], which allows one to determine the interfacial critical exponents, is extracted from the full description. On the other scale, the short-distance fluctuations are analyzed by mean-field theory.

Massless charges without self-interaction

The solutions of Maxwell equations with electric and magnetic fields existing only in a finite part of space are given, due to massless charges moving with speed of light. Under proper conditions, there is no interaction between charges and the field.

Graphical representation of the excess entropy

The generalized Mayer graphs invented by Nettleton and Green are used to express the probability distribution of statistical systems by reduced distribution functions. The entropy is expressed in terms of graphs and a simple rule of counting them is presented. The hyper-netted chain approximations are discussed.