Measurement of a spin-1 system

We derive exact formulas describing an indirect von Neumann measurement of a spin-1 system. The results hold for any interaction strength and for an arbitrary output variable \Hat{O}.Comment: 13 pages; comments welcome. V2 25 pages, close to published version, added two appendices reformulating a result from Dressel and Jordan in terms of the quantum characteristic functio

Post-selection induced deterministic and probabilistic entanglement with strong and weak interactions

A scheme is proposed to entangle two systems that have not interacted by using an ancillary particle in a Mach-Zehnder interferometer, by making a suitable post--selection of the particle followed by a conditional feedback on one of the subsystems to be entangled. For a strong interaction, the process works deterministically. For a weaker interaction only the probability of success is reduced, but the output continues to be a maximally entangled state

Hidden-variable models for the spin singlet. II. Local theories violating Bell and Leggett inequalities

Three classes of local hidden-variable models that violate both Bell and Leggett inequalities are presented. The models, however, do not reproduce the quantum mechanical predictions, hence they are experimentally testable. It is concluded that on one hand neither Bell or Leggett inequality fully captures the essential counterintuitiveness of quantum mechanics, while on the other hand the hypothesis of outcome independence and that of locality are uncorrelated.Comment: 10 pages, no figures, comments welcom

Postselection induced entanglement swapping from a vacuum--excitation entangled state to separate quantum systems

We show that a single particle in a superposition of different paths can entangle two objects located on each path. The entanglement has its maximum visibility for intermediate coupling strengths. In particular, when the two quantum systems with which the particle interacts are detectors that measure its presence and its polarization, the so-called quantum Cheshire cat is realized

Beyond Bell's theorem: Admissible hidden-variable models for the spin-singlet

Assuming that quantum mechanics is obeyed exactly after averaging over hidden variables, and considering models that obey both the hypotheses of free will and locality, we establish the form of all possible hidden-variable models that reproduce the spin-singlet.Comment: Based on the oral presentation given at DICE 2012, submitted to J. Phys. Conf. Ser. No new results compared to arXiv:1105.1286 [quant-ph], just a different exposition. Reused an appendix reviewing some HV models that was excised in the final version of 1105.128

Correlations between detectors allow violation of the Heisenberg noise-disturbance principle for position and momentum measurements

Heisenberg formulated a noise-disturbance principle stating that there is a tradeoff between noise and disturbance when a measurement of position and a measurement of momentum are performed sequentially, and another principle imposing a limitation on the product of the uncertainties in a joint measurement of position and momentum. We prove that the former, the Heisenberg sequential noise-disturbance principle, holds when the detectors are assumed to be initially uncorrelated from each other, but that it can be violated for some properly correlated initial preparations of the detectors.Comment: v2, minor changes. "Resolution" substitutes "sensitivity," according to current usage; v3, changed title and abstract, simplified derivation, corrected an error about the joint measurement, extra appendix to appear as part of a longer version of the pape

Weak values and weak coupling maximizing the output of weak measurements

In a weak measurement, the average output $\langle o\rangle$ of a probe that measures an observable $\hat{A}$ of a quantum system undergoing both a preparation in a state $\rho_i$ and a postselection in a state $E_\mathrm{f}$ is, to a good approximation, a function of the weak value $A_w=\mathrm{Tr} [E_f \hat{A} \rho_i]/\mathrm{Tr}[E_f\rho_i]$, a complex number. For a fixed coupling $\lambda$, when the overlap $\mathrm{Tr}[E_f\rho_i]$ is very small, $A_w$ diverges, but $\langle o\rangle$ stays finite, often tending to zero for symmetry reasons. This paper answers the questions: what is the weak value that maximizes the output for a fixed coupling? what is the coupling that maximizes the output for a fixed weak value? We derive equations for the optimal values of $A_w$ and $\lambda$, and provide the solutions. The results are independent of the dimensionality of the system, and they apply to a probe having a Hilbert space of arbitrary dimension. Using the Schr\"{o}dinger-Robertson uncertainty relation, we demonstrate that, in an important case, the amplification $\langle o\rangle$ cannot exceed the initial uncertainty $\sigma_o$ in the observable $\hat{o}$, we provide an upper limit for the more general case, and a strategy to obtain $\langle o\rangle\gg \sigma_o$.Comment: v4 close to published version; v3 provides a simpler, more elegant solution based on geometrical considerations; v2 extends the results for an arbitrary observable of the probe, which can be even a finite-dimensional system, and provides an upper bound to the output by exploiting the Schroedinger-Robertson uncertainty relatio

Comment on `Observation of a quantum Cheshire Cat in a matter-wave interferometer experiment', Nature Comm. 5, 4492

It is shown that a classical experiment using an ordinary cat can reproduce the same results and it is argued that the quantum nature of the phenomenon could be revealed instead by making an experiment that detects cross-moments

Does the wavefunction describe individual systems?

We analyze the issue of the interpretation of the wavefunction, namely whether it should be interpreted as describing individual systems or ensembles of identically prepared systems. We propose an experiment which can decide the issue, based on the simultaneous measurement of the same observable with different detectors, and we discuss the theoretical implications of the possible experimental outcomes

Measurement of a qubit and measurement with a qubit

Generally, the measurement process consists in coupling a system to a detector that can give a continuous output. However, it may be interesting to use as a detector a system with a discrete spectrum, especially in view of applications to quantum information. Here, we study 1) a two-level system measuring another two-level system (qubit); 2) a generic system measuring a qubit; 3) a qubit measuring a generic system. The results include the case when a postselection on the measured system is made. We provide the exact solution, and also a controlled expansion in the coupling parameter, giving formulas valid in the weak measurement regime for arbitrary preparation and postselection. The concept of generalized Wigner functions is introduced.Comment: 18 pages, 1 figure, 1 table. Comments welcom