Simulating Quantum Mechanics by Non-Contextual Hidden Variables

No physical measurement can be performed with infinite precision. This leaves a loophole in the standard no-go arguments against non-contextual hidden variables. All such arguments rely on choosing special sets of quantum-mechanical observables with measurement outcomes that cannot be simulated non-contextually. As a consequence, these arguments do not exclude the hypothesis that the class of physical measurements in fact corresponds to a dense subset of all theoretically possible measurements with outcomes and quantum probabilities that \emph{can} be recovered from a non-contextual hidden variable model. We show here by explicit construction that there are indeed such non-contextual hidden variable models, both for projection valued and positive operator valued measurements.Comment: 15 pages. Journal version. Only minor typo corrections from last versio

Negativity and contextuality are equivalent notions of nonclassicality

Two notions of nonclassicality that have been investigated intensively are: (i) negativity, that is, the need to posit negative values when representing quantum states by quasiprobability distributions such as the Wigner representation, and (ii) contextuality, that is, the impossibility of a noncontextual hidden variable model of quantum theory (also known as the Bell-Kochen-Specker theorem). Although both of these notions were meant to characterize the conditions under which a classical explanation cannot be provided, we demonstrate that they prove inadequate to the task and we argue for a particular way of generalizing and revising them. With the refined version of each in hand, it becomes apparent that they are in fact one and the same. We also demonstrate the impossibility of noncontextuality or nonnegativity in quantum theory with a novel proof that is symmetric in its treatment of measurements and preparations.Comment: 5 pages, published version (modulo some supplementary material

Covariant quantum measurements may not be optimal

Quantum particles, such as spins, can be used for communicating spatial directions to observers who share no common coordinate frame. We show that if the emitter's signals are the orbit of a group, then the optimal detection method may not be a covariant measurement (contrary to widespread belief). It may be advantageous for the receiver to use a different group and an indirect estimation method: first, an ordinary measurement supplies redundant numerical parameters; the latter are then used for a nonlinear optimal identification of the signal.Comment: minor corrections, to appear in J. Mod. Opt. (proc. of Gdansk conf.

Is there contextuality for a single qubit?

It was presented by Cabello and Nakamura [A. Cabello, Phys. Rev. Lett. 90, 190401 (2003)], that the Kochen-Specker theorem applies to two dimensions if one uses Positive Operator-Valued Measures. We show that contextuality in their models is not of the Kochen-Specker type. It is rather the result of not keeping track of the whole system on which the measurement is performed. This is connected to the fact that there is no one-to-one correspondence between POVM elements and projectors on the extended Hilbert space and the same POVM element has to originate from two different projectors when used in Cabello's and Nakamura's models. Moreover, we propose a hidden-variable formulation of the above models.Comment: 4 pages, 1 figure, comments welcom

A Bayesian Analogue of Gleason's Theorem

We introduce a novel notion of probability within quantum history theories and give a Gleasonesque proof for these assignments. This involves introducing a tentative novel axiom of probability. We also discuss how we are to interpret these generalised probabilities as partially ordered notions of preference and we introduce a tentative generalised notion of Shannon entropy. A Bayesian approach to probability theory is adopted throughout, thus the axioms we use will be minimal criteria of rationality rather than ad hoc mathematical axioms.Comment: 14 pages, v2: minor stylistic changes, v3: changes made in-line with to-be-published versio

Synaptic transmission between pairs of retinal amacrine cells in culture

We have examined synaptic transmission between isolated pairs of chick GABAergic amacrine cells, maintained in sparse culture and identified by their binding of an amacrine cell-selective antibody. Using the perforated- patch method to whole-cell clamp both cells of a pair, postsynaptic currents were examined for step depolarizations of the \u27presynaptic\u27 cell. Synaptic transmission, frequently reciprocal, was calcium dependent and reversibly blocked by bicuculline. Postsynaptic currents, excluding those due to ohmic electrical coupling, were elicited only for presynaptic voltage steps positive to about -40 mV and were always very noisy, suggesting that they were summed from relatively small numbers of quanta. Postsynaptic currents continued well after the termination of the 100 msec presynaptic voltage step when the step was to -10 mV, or positive to this value. This result is interpreted to imply that presynaptic calcium concentration remains elevated after the membrane is returned to its holding potential. When presynaptic voltages were kept low or else presynaptic voltage was uncontrolled, spontaneous quantal events mediated by GABA(A) receptors could often be seen. Quanta rose quickly (less than 4 msec) and decayed with a mean time constant of 19.3 msec. The amplitude distributions of quantal currents were positively skewed, sometimes showing rare quanta of exceptionally large amplitude. Peak conductance per quantum was about 300 pS, corresponding to the simultaneous opening of only 17 GABA(A) channels and corresponding to a net flux of only 32 x 103 Cl- ions per millivolt of driving force. Estimates of the maximum sustained release rate at individual release sites suggest an upper bound of between 19 and 42 quanta per second

Electrogenic Na-Ca exchange clears Ca\u3csup\u3e2+\u3c/sup\u3e loads from retinal amacrine cells in culture

Calcium influx into cultured retinal amacrine cells is followed by a small, slow, inward current that we show here results from the operation of electrogenic Na-Ca exchange. The activity of the exchanger is shown to correlate with the magnitude of the Ca2+ load and to depend on both the Ca2+ and Na+ gradients. Li+ is unable to substitute for Na+ and in the absence of Na+, slow tail currents are almost entirely suppressed. A rapid change in [K+](o) does not affect the activity of the exchanger, suggesting that only Na+ and Ca2+ are transported. The ratio of charge entering as Ca2+ current to the charge entering as exchange current is highly variable between cells. We suggest that variability results from a variable fraction of Ca2+ load, we estimate typically 40%, being removed by a process other than Na-Ca exchange. This process is likely to involve internal buffering or sequestration since inhibition of the plasmalemmal Ca2+ATPase does not increase the fraction of Ca2+ expelled by the exchanger. Ca2+ loading performed in the absence of Na+(o) generates smaller exchange charge the longer the delay in returning Na+(o) to the neuron. About 30% of exchange charge is lost for a delay of 1 sec

The extension problem for partial Boolean structures in Quantum Mechanics

Alternative partial Boolean structures, implicit in the discussion of classical representability of sets of quantum mechanical predictions, are characterized, with definite general conclusions on the equivalence of the approaches going back to Bell and Kochen-Specker. An algebraic approach is presented, allowing for a discussion of partial classical extension, amounting to reduction of the number of contexts, classical representability arising as a special case. As a result, known techniques are generalized and some of the associated computational difficulties overcome. The implications on the discussion of Boole-Bell inequalities are indicated.Comment: A number of misprints have been corrected and some terminology changed in order to avoid possible ambiguitie

Local Quantum Measurement and No-Signaling Imply Quantum Correlations

We show that, assuming that quantum mechanics holds locally, the finite speed of information is the principle that limits all possible correlations between distant parties to be quantum mechanical as well. Local quantum mechanics means that a Hilbert space is assigned to each party, and then all local positive-operator-valued measurements are (in principle) available; however, the joint system is not necessarily described by a Hilbert space. In particular, we do not assume the tensor product formalism between the joint systems. Our result shows that if any experiment would give nonlocal correlations beyond quantum mechanics, quantum theory would be invalidated even locally.Comment: Published version. 5 pages, 1 figure