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Quantum computers promise significant speedups in solving problems intractable for conventional computers but, despite recent progress, remain limited in scaling and availability. Therefore, quantum software and hardware development heavily…
Weak measurement is a new technique which allows one to describe the evolution of postselected quantum systems. It appears to be useful for resolving a variety of thorny quantum paradoxes, particularly when used to study properties of pairs…
IIt is shown that a weak measurement of a quantum system produces a new state of the quantum system which depends on the prior state, as well as the (uncontrollable) measured position of the pointer variable of the weak measurement…
Relaxation dynamics of complex quantum systems with strong interactions towards the steady state is a fundamental problem in statistical mechanics. The steady state of subsystems weakly interacting with their environment is described by the…
The aim of this paper is to analyze the reconstructability of quantum mechanics from classical conditional probabilities representing measurement outcomes conditioned on measurement choices. We will investigate how the quantum mechanical…
The generation of arbitrary single-mode quantum states from the vacuum by alternate coherent displacement and photon adding as well as the measurement of the overlap of a signal with an arbitrarily chosen quantum state are studied. With…
Quantum state discrimination for two coherent states with opposite phases as measured relative to a reference pulse is analyzed as functions of the intensities of both the signal states and of the reference pulse. This problem is relevant…
We explore further the suggestion to describe a pre- and post-selected system by a two-state, which is determined by two conditions. Starting with a formal definition of a two-state Hilbert space and basic operations, we systematically…
The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical statistics range from the philosophical…
We derive and experimentally investigate a strong uncertainty relation valid for any $n$ unitary operators, which implies the standard uncertainty relation as a special case, and which can be written in terms of geometric phases. It is…
Quantum simulations of Bell inequality violations are numerically obtained using probabilistic phase space methods, namely the positive P-representation. In this approach the moments of quantum observables are evaluated as moments of…
We demonstrate a fast, robust and non-destructive protocol for quantum state estimation based on continuous weak measurement in the presence of a controlled dynamical evolution. Our experiment uses optically probed atomic spins as a…
Quantum backaction refers to the disturbance of a quantum system caused by measuring it. In sequential measurements, this effect can accumulate and become significant, leading to nontrivial modifications of the system state and the…
"Weak measurements" -- involving a weak unitary interaction between a quantum system and a meter followed by a projective measurement -- are investigated when the system has a non-Hermitian Hamiltonian. We show in particular how the…
For a real or complex one-dimensional map satisfying a weak hyperbolicity assumption, we study the existence and statistical properties of physical measures, with respect to geometric reference measures. We also study geometric properties…
With the recent surge of interest in quantum computation, it has become very important to develop clear experimental tests for ``quantum behavior'' in a system. This issue has been addressed in the past in the form of the inequalities due…
We investigate the sequential composition of weak values in the framework of time-symmetric quantum mechanics. Specifically, we consider a forward'' weak measurement from a preselected state $\ket{\psi}$ to a post-selected state…
Quantum theory provides an extensive framework for the description of the equilibrium properties of quantum matter. Yet experiments in quantum simulators have now opened up a route towards generating quantum states beyond this equilibrium…
Probabilities of the outcomes of consecutive quantum measurements can be obtained by construction probability amplitudes, thus implying unitary evolution of the measured system, broken each time a measurement is made. In practice, the…
We explore the possibility of using "weak measurements" without "weak value" for quantum state estimation. Since for weak measurements the disturbance caused during each measurement is small, we can rescue the state, unlike for the case of…