The quantum eraser variant of the double-slit experiment, and its 'delayed choice' sub-variant, are considered from the perspective of weak value and weak measurement theory (which is briefly reintroduced here). The interference fringes that appear when measuring certain spin states, which can then be 'erased' when measuring other spin states, are shown to be anomalous weak values that depend on particular post-selection choices. By framing the choice of spin measurement as a weak value of a certain weak measurement, it is then made clear what physical claims can and cannot be made about what occurs in the quantum eraser experiment. Specifically, claims about the choice of spin-state `retrocausally' influencing the choice of slit(s) for the particles to travel through are discredited, and a simple framework is presented for understanding how the fringes arise and why they can be 'erased'.
Wave-particle duality is a bizarre feature at the heart of quantum mechanics which refers to the mutually exclusive dual attributes of quantum objects as the wave and the particle. Quantum eraser presents a counterintuitive aspect of the wave-particle duality. In this work, we show that quantum eraser can be quantitatively understood in terms of the recently developed duality--entanglement relation. In other words, we show that wave-particle-entanglement triality captures all the physics of the quantum erasure. We find that a controllable partial erasure of the which-path information is attain…
We investigate the mechanism of weak measurement by using an interferometric framework. In order to appropriately elucidate the interference effect that occurs in weak measurement, we introduce an interferometer for particles with internal degrees of freedom. It serves as a framework common to quantum eraser and weak measurement. We demonstrate that the geometric phase, particularly the Pancharatnam phase, results from the post-selection of the internal state, and thereby the interference pattern is changed. It is revealed that the extraordinary displacement of the probe wavepackets in weak me…
In this letter, we present a new procedure to determine completely the complex modular values of arbitrary observables of pre- and post-selected ensembles, which works experimentally for all measurement strengths and all post-selected states. This procedure allows us to discuss the physics of modular and weak values in interferometric experiments involving a qubit meter. We determine both the modulus and the argument of the modular value for any measurement strength in a single step, by controlling simultaneously the visibility and the phase in a quantum eraser interference experiment. Modular…
Recently we proposed the linguistic interpretation of quantum mechanics (called quantum and classical measurement theory), which was characterized as a kind of metaphysical and linguistic turn of the Copenhagen interpretation. This turn from physics to language does not only extend quantum theory to classical systems but also yield the quantum mechanical world view (i.e., quantum philosophy or quantum language). The purpose of this paper is to formulate the double-slit experiment, the quantum eraser experiment, Wheeler's delayed choice experiment, Hardy's paradox and the three boxes paradox (t…
We propose an experiment which demonstrates the undoing of a weak continuous measurement of a solid-state qubit, so that any unknown initial state is fully restored. The undoing procedure has only a finite probability of success because of the non-unitary nature of quantum measurement, though it is accompanied by a clear experimental indication of whether or not the undoing has been successful. The probability of success decreases with increasing strength of the measurement, reaching zero for a traditional projective measurement. Measurement undoing (``quantum un-demolition'') may be interpret…
In quantum mechanics, continuously measuring an observable steers the system into one eigenstate of that observable. This property has interesting and useful consequences when the observable is a joint property of two remotely separated qubits. In particular, if the measurement of the two-qubit joint observable is performed in a way that is blind to single-qubit information, quantum back-action generates correlation of the discord type even if the measurement is weak and inefficient. We demonstrate the ability to generate these quantum correlations in a circuit-QED setup by performing a weak j…
It is known that weak measurement can significantly amplify the mean of measurement results, sometimes out of the range limited in usual quantum measurement. This fact, as actively demonstrated recently in both theory and experiment, implies the possibility to estimate a very small parameter using the weak measurement technique. But does the weak measurement really bring about the increase of "information" for parameter estimation? This paper clarifies that, in a general situation, the answer is NO; more precisely, the weak measurement cannot further decrease the lower bound of the estimation …
We quantify the disturbance of a quantum state undergoing a sequence of observations, and particularly focus on a weak measurement followed by post-selection and compare these results to the projective counterpart. Taking into account the distinguishability of both, the system and the device, we obtain the exact trade-off between the system state disturbance and the change of the device pointer state. We show that for particular post-selection procedures the coupling strength between the system and the device can be significantly reduced without loosing measurement sensitivity, which is direct…
We address two major conceptual developments introduced by Aharonov and collaborators through a \textit{quantum phase space} approach: the concept of \textit{modular variables} devised to explain the phenomena of quantum dynamical non-locality and the \textit{two-state formalism} for Quantum Mechanics which is a retrocausal time-symmetric interpretation of quantum physics which led to the discovery of \textit{weak values.} We propose that a quantum phase space structure underlies these profound physical insights in a unifying manner. For this, we briefly review the Weyl-Wigner and the coherent…
In this article we present an experimental proposal for the estimation of an optomechanical parameter in the presence of noise. The estimation is based on the technique of weak value amplification which can enlarge the radiation pressure effect of a single photon on a mechanical oscillator. In our setup we show that the weak value amplification technique is preferable for the estimation over a method that relies on a strong measurement with postselection, because the first method does not require a good prior knowledge of the parameter we wish to estimate, while both strategies reach the same …
We derive a tight bound between the quality of estimating a quantum state by measurement and the success probability of undoing the measurement in arbitrary dimensional systems, which completely describes the tradeoff relation between the information gain and reversibility. In this formulation, it is clearly shown that the information extracted from a weak measurement is erased through the reversing process. Our result broadens the information-theoretic perspective on quantum measurement as well as provides a standard tool to characterize weak measurements and reversals.
We point out a contrasting role the entanglement plays in communication and estimation scenarios. In the first case it brings noticeable benefits at the measurement stage (output super-additivity), whereas in the latter it is the entanglement of the input probes that enables significant performance enhancement (input super-additivity). We identify a weak estimation regime where a strong connection between concepts crucial to the two fields is demonstrated; the accessible information and the Holevo quantity on one side and the quantum Fisher information related quantities on the other. This all…
Quantum-limited microwave parametric amplifiers are genuine key pillars for rising quantum technologies and in general for applications that rely on the successful readout of weak microwave signals by adding only the minimum amount of noise allowed by quantum mechanics. In this perspective, after providing a brief overview on the different families of parametric microwave amplifiers, we focus on traveling wave parametric amplifiers (TWPAs), underlining the key achievements of the last years and the present open challenges. We discuss also possible new research directions beyond amplification s…
We study the effect of large acceleration of an uniformly accelerated frame on the validity of weak equivalence principle. Specifically we demonstrate how the behaviour of free quantum particle, as observed by an observer with large uniform acceleration, completely changes from that of a quantum particle emmarsed in a uniform gravitational field. We also extend our analysis to the simplest noncommutative space scenario to show that while spatial noncommutativity does not affect the quantum particle in a gravitational field, it does alter the energy eigenvalues of a quantum particle as seen fro…
We study the classical optics effects known as Goos-Hänchen (GH) and Imbert-Fedorov (IF) shifts, occurring when reflecting a bounded light beam from a planar surface, by using a quantum-mechanical formalism. This new approach allows us to naturally separate the spatial shift into two parts, one independent on orbital angular momentum (OAM) and the other one showing OAM-induced spatial-vs-angular shift mixing. In addition, within this quantum-mechanical-like formalism, it becomes apparent that the angular shift is proportional to the beams angular spread, namely to the variance of the transvers…
The quantification of simultaneously present weak polarization anisotropy effects are of practical interest from polarimetric and metrological perspective. Recently, in Phys. Rev. A 103, 053518, we experimentally demonstrated a classical analog of post-selected quantum weak measurement through optical interferometry to amplify all possible weak polarization anisotropy effects individually. Here, we propose an extension of this interferometric framework to quantify simultaneously present polarization anisotropy effects. Moreover, a clear correspondence of differential Jones matrix approach with…
A fundamentally different approach to path integral quantum mechanics in curved space-time is presented, as compared to the standard approaches currently available in the literature. Within the context of scalar particle propagation in a locally curved background, such as described by Fermi or Riemann normal co-ordinates, this approach requires use of a constructed operator to rotate the initial, intermediate, and final position ket vectors onto their respective local tangent spaces, defined at each local time step along some arbitrary classical reference worldline. Local time translation is d…
