2022-03-23T11:39:25Z, Bednorz, Adam, Belzig, Wolfgang

Vacuum fluctuations can obscure the detection signal of the measurement of the smallest quantum objects like single particles seemingly implying a fundamental limit to measurement accuracy. However, as we show relativistic invariance implies the disappearance of fluctuations for the space-like %frequency-wavevector spectrum of an observable at zero temperature. This complete absence of noise can be harnessed to perform noiseless measurement of single particles, as we illustrate for electrons or photons. We outline a general scheme to illustrate the noiseless measurement involving the space-like spectrum of observables based on the self-interference of counter-propagating paths of a single particle in a triangular Sagnac interferometer.

2018, Bülte, Johannes, Bednorz, Adam, Bruder, Christoph, Belzig, Wolfgang

The development of solid-state quantum technologies requires the understanding of quantum measurements in interacting, nonisolated quantum systems. In general, a permanent coupling of detectors to a quantum system leads to memory effects that have to be taken into account in interpreting the measurement results. We analyze a generic setup of two detectors coupled to a quantum system and derive a compact formula in the weak-measurement limit that interpolates between an instantaneous (text-book type) and almost continuous—detector dynamics-dependent—measurement. A quantum memory effect that we term “system-mediated detector-detector interaction” is crucial to observe noncommuting observables simultaneously. Finally, we propose a mesoscopic double-dot detector setup in which the memory effect is tunable and that can be used to explore the transition to non-Markovian quantum measurements experimentally.

2015, Bülte, Johannes, Bednorz, Adam, Belzig, Wolfgang

Generalized quantum measurement schemes are described by positive operator-valued measures going beyond the projection postulate, which predicts the instantaneous collapse of the systems wave function. This allows to take the noninvasive limit and investigate the correlations of such weak measurements which facilitate the observation of non-commuting observables within the same system. We propose a scheme in which the detector is coupled to the measured system for a finite time, as it is the case in many real setups. This leads to non-Markovian effects appearing by memory functions which are related to symmetric and antisymmetric correlators of the detector variables. We investigate these functions addressing the role of equilibrium and non-equilibrium detectors and how they differ from and could realize the standard Markovian measurement respectively. The latter scheme leads to the symmetrized operator order (aka Keldysh ordering), which is widely used in quantum measurement discussions. We show that the non-Markovian measurement scheme yields information beyond the standard approach, allowing e.g. for the prove of the non classical nature of a system (quasiprobability statistics) by second-order correlation functions.

2013, Bednorz, Adam, Bednorz, Witold, Belzig, Wolfgang

The quest for fundamental test of quantum mechanics is an ongoing effort. We are addressing the question of what are the lowest possible moments to prove quantum nonlocality and noncontextuality without any further assumption - in particular without the often assumed dichotomy. We first show that second order correlations can always be explained by a classical noncontextual local hidden variable theory. Similar third order correlations cannot violate classical inequalities as well in general, except for a special state-dependent noncontextuality. However, we show that fourth order correlations can violate locality and state-independent noncontextuality. Finally we obtain a fully scalable continuous variable Bell inequality, which might be useful in Bell tests closing all loopholes simultaneously.

2021-06-01, Sołtan, Stanisław, Frączak, Mateusz, Belzig, Wolfgang, Bednorz, Adam

We discuss quantum mechanical detection models in the weak limit in the context of conservation laws of physical quantities. In particular, we analyze what kind of system–detector interaction can preserve the global conservation or the related symmetry, and how the final measurement on the detector affects the measured observable of the systems and its presumed conservation. It turns out that the order of noncommuting measurements results in observable differences on the level of third-order correlations functions.

2017, Belzig, Wolfgang, Bülte, Johannes, Bednorz, Adam, Bruder, Christoph

Generalized quantum measurement schemes are described by positive operator-valued measures going beyond the projection postulate, which predicts the instantaneous collapse of the systems wave function. This allows to take the noninvasive limit and investigate the correlations of such weak measurements which enables the observation of non-commuting observables within the same system. We propose a scheme in which the detector is coupled to the measured system for a finite time, as it is the case in many real setups. This leads to non-Markovian effects appearing by memory functions which are related to symmetric and antisymmetric correlators of the detector variables [12]. We investigate these functions addressing the role of equilibrium and non-equilibrium detectors and how they differ from and could realize the standard Markovian measurement respectively. The latter scheme leads to the symmetrized operator order (aka Keldysh ordering), which is widely used in quantum measurement discussions. We show that the non-Markovian measurement scheme yields information beyond the standard approach, allowing e.g. for the proof of the non classical nature of a system (quasiprobability statistics) by second-order correlation functions [13].We further propose setups in mesoscopic electronic circuits to realise those concepts. One possibility is to use two double quantum dots coupled to a common quantum system. The detectors cross correlations are read out and by tuning the dot parameters, it is possible to explore the non-Markovian nature of the measurement setup.

2014, Belzig, Wolfgang, Bednorz, Adam

Entanglement, viz. the non-separability of quantum states, is a fundamental prediction of quantum mechanics, which is at odds with the classical perception of reality. Furthermore, it constitutes a resource for quantum computation and quantum communication. Electronic degrees of freedom in nanostructures – in particular the spin – constitute promising candidates to implement quantum information architectures in scalable solid state circuits. In this topical review, we will summarize some efforts to create and detect entanglement in such structures.
We concentrate first on entanglement in double quantum dots, since they promise to be viable candidates to produce entanglement by confining electrons to a small interaction region. The quantitative detection of the entanglement through transport measurements can be done via current and noise. Secondly, we concentrate on the creation of spin entanglement at quantum point contacts, which has the advantage that the two electrons are automatically spatially separated. We discuss the possibility of performing a Bell test of non-local correlations. However, as we will point out, a reliable entanglement detection can be performed by current-correlation measurements, although they require some trust in the experimental setup. Finally,we present a hierarchy of mesoscopic Bell tests, which could be useful to evaluate theoretical proposals and experimental setups.

2019-07-15T07:55:44Z, Sołtan, Stanisław, Frączak, Mateusz, Belzig, Wolfgang, Bednorz, Adam

Conservation principles are essential to describe and quantify classical and quantum mechanical processes. Classically, the conservation holds objectively because the description of reality can be considered independent of observation. In quantum mechanics, however, invasive observations change quantities drastically, even if they are expected to be conserved classically. One may hope to overcome this problem by considering weak, non-invasive quantum measurements. Interestingly, we find that the non-conservation is manifest even in weakly measured correlations if some of the observables don't commute with the conserved quantity. Our observation casts some doubt on the fundamental compatibility of conservation laws and quantum objectivity.

2015, Bülte, Johannes, Bednorz, Adam, Belzig, Wolfgang

In many real quantum systems the measurement is much less invasive than described by the projection postulate. For example, it is performed by weakly coupling a detector for a finite time to the system. The finite coupling time might lead to different measurement outcomes depending on the details of the interaction. We first investigate a generalized measurements scheme by means of positive operator-valued measures in the weak coupling limit and discuss the consequences appearing due to the non-Markovian interaction. Second we discuss the resulting quasiprobabilities, which in the case of a Markovian measurement scheme obey the so-called weak positivity, i.e. second-order correlation functions are positive semi-definite. In particular, we show a possible violation of weak positivity by second-order correlation functions for a frequency dependent detector measuring a spin-1/2 system. When both are themselves in an equilibrium state but at different respective temperatures, we find that the detection of the quantum behavior vanishes if the system temperature is larger than that of the detector.

2014, Bednorz, Adam, Bednorz, Witold, Belzig, Wolfgang

The quest for fundamental tests of quantum mechanics is an ongoing effort.We here address the question of what are the lowest possible moments needed to prove quantum nonlocality and noncontextuality without any further assumptions — in particular, without the often assumed dichotomy. We first show that second-order correlations can always be explained by a classical noncontextual local-hidden-variable theory. Similar third-order correlations also cannot violate classical inequalities in general, except for a special state-dependent noncontextuality. However, we show that fourth-order correlations can violate locality and state-independent noncontextuality. Finally we obtain a fourth-order continuous-variable Bell inequality for position and momentum, which can be violated and might be useful in Bell tests, closing all loopholes simultaneously.