Weak valued statistics as fundamental explanation of quantum physics

Recently, weak measurements have attracted a lot of interest as an experimental method for the investigation of non-classical correlations between observables that cannot be measured jointly. Here, I explain how the complex valued statistics observed in weak measurements relate to the operator algebra of the conventional Hilbert space formalism and show that the algebra of operators originates from more fundamental relations between the physical properties of a quantum system that can be expressed in terms of complex conditional probabilities. In particular, commutation relations can be identified with fundamental imaginary correlations that characterize the relations between physical properties in terms of their transformation dynamics. Non-commutativity thus originates from a definition of relations between physical properties that replaces the assumption of joint reality with a complex-valued probability reflecting the dynamical response of the system to external forces, e.g. in measurement interactions.Comment: 5 pages, contribution to the proceedings of QIT28 held May 27th to 28th in Sappor

All path-symmetric pure states achieve their maximal phase sensitivity in conventional two-path interferometry

It is shown that the condition for achieving the quantum Cramer-Rao bound of phase estimation in conventional two-path interferometers is that the state is symmetric with regard to an (unphysical) exchange of the two paths. Since path symmetry is conserved under phase shifts, the maximal phase sensitivity can be achieved at arbitrary bias phases, indicating that path symmetric states can achieve their quantum Cramer-Rao bound in Bayesian estimates of a completely unknown phase.Comment: 4 pages, no figure

Efficient tests for experimental quantum gates

Realistic quantum gates operate at non-vanishing noise levels. Therefore, it is necessary to evaluate the performance of each device according to some experimentally observable criteria of device performance. In this presentation, the characteristic properties of quantum operations are discussed and efficient measurement strategies are proposed.Comment: 5 pages, including one table, contribution to the proceedings of QIT11, held December 6th to 7th 2004 in Kyot

On the resolution of quantum paradoxes by weak measurements

In this presentation, I argue that weak measurements empirically support the notion of quantum superpositions as statistical alternatives. In short, weak measurements show that Schroedinger's cat is already dead or alive before the measurement. The collapse of the wavefunction in a strong measurement should therefore be separated into the statistical selection of one of the available alternatives and a physical interaction that causes decoherence. The application to entanglement reveals that measurements in A have no physical effect in B, resolving the paradox of Bell`s inequality violation in favor of locality and against (non-empirical) realism.Comment: 5 pages, contribution to the proceedings of QIT21, held Nov. 4-5 2009 in Toky

Information and noise in photon entanglement

By using finite resolution measurements it is possible to simultaneously obtain noisy information on two non-commuting polarization components of a single photon. This method can be applied to a pair of entangled photons with polarization statistics that violate Bell's inequalities. The theoretically predicted results show that the non-classical nature of entanglement arises from negative joint probabilities for the non-commuting polarization components. These negative probabilities allow a "disentanglement" of the statistics, providing new insights into the non-classical properties of quantum information.Comment: 6 pages, contribution to the proceedings of the Quantum Information Technology conference QIT4 held November 29th to 30th 2000 near Toky

Quantum interference of position and momentum: a particle propagation paradox

Optimal simultaneous control of position and momentum can be achieved by maximizing the probabilities of finding their experimentally observed values within two well-defined intervals. The assumption that particles move along straight lines in free space can then be tested by deriving a lower limit for the probability of finding the particle in a corresponding spatial interval at any intermediate time t. Here, it is shown that this lower limit can be violated by quantum superpositions of states confined within the respective position and momentum intervals. These violations of the particle propagation inequality show that quantum mechanics changes the laws of motion at a fundamental level, providing a new perspective on causality relations and time evolution in quantum mechanics.Comment: 6 pages, including one figure, added discussions of experimental possibilities and the selection of localized state

Local measurement uncertainties impose a limit on non-local quantum correlations

In quantum mechanics, joint measurements of non-commuting observables are only possible if a minimal unavoidable measurement uncertainty is accepted. On the other hand, correlations between non-commuting observables can exceed classical limits, as demonstrated by the violation of Bell's inequalities. Here, the relation between the uncertainty limited statistics of joint measurements and the limits on expectation values of possible input states is analyzed. It is shown that the experimentally observable statistics of joint measurements explain the uncertainty limits of local states, but result in less restrictive bounds when applied to identify the limits of non-local correlations between two separate quantum systems. A tight upper bound is obtained for the four correlations that appear in the violation of Bell's inequalities and the statistics of pure states saturating the bound is characterized. The results indicate that the limitations of quantum non-locality are a necessary consequence of the local features of joint measurements, suggesting the possibility that quantum non-locality could be explained in terms of the local characteristics of quantum statistics.Comment: 10 pages, no figures, added explanation of joint and sequential measurements and corrections in the reference

On the relation between transformation dynamics and quantum statistics in weak measurements

Experimentally, the imaginary parts of complex weak values are obtained from the response of the system to small unitary phase shifts generated by the target observable. The complex conditional probabilities obtained from weak measurements can therefore be explained in terms of transformation dynamics. Specifically, the complex phase of weak conditional probabilities provides a complete description of the transformation dynamics between the initial and the final state generated by the intermediate states. The result is a measure of quantum state overlap that relates quantum statistical properties directly to the dynamical action of unitary transformations.Comment: 4 pages including 1 figure, contribution to the proceedings of QIT24 held May 12-13 2011 in Toky

Quantum states as complex probabilities: The physics behind direct observations of photon wavefunctions in weak measurements

Weak measurements of photon position can be used to obtain direct experimental evidence of the wavefunction of a photon between generation and ultimate detection. Significantly, these measurement results can also be understood as complex valued conditional probabilities of intermediate photon positions. It is therefore possible to interpret the quantum state as a complex valued probability distribution from which measurement probabilities can be derived according to Bayesian rules. The conventional measurement probabilities derived from squares of the wavefunction then describes the effects of measurement back-action, which originate from a non-classical relation between dynamics and statistics that is characteristic of quantum mechanics. It is pointed out that this relation can be used to derive the complete Hilbert space formalism directly from complex probabilities, without the axiomatic introduction of quantum states or operators.Comment: 5 pages, contribution to the proceedings of the 10th Rochester Conference on Coherence and Quantum Optics, CQO-X, held June 17-20 2013 at Rochester, NY, US

Measurement uncertainties in the quantum formalism: quasi-realities of individual systems

The evaluation of uncertainties in quantum measurements is problematic since the correct value of an observable between state preparation and measurement is experimentally inaccessible. In Ozawa's formulation of uncertainty relations for quantum measurements, the correct value of an observable is represented by the operator of that observable. Here, I consider the implications of this operator-based assignment of values to individual systems and discuss the relation with weak values and weak measurement statistics.Comment: 5 pages, contribution to the proceedings of QIT26, held May 21st to 22nd 2012 in Fukui, Japa