Malley discussed {[Phys. Rev. A {\bf 69}, 022118 (2004)]} that all quantum observables in a hidden-variable model for quantum events must commute simultaneously. In this comment, we discuss that Malley's theorem is indeed valid for the hidden-variable theoretical assumptions, which were introduced by Kochen and Specker. However, we give an example that the local hidden-variable (LHV) model for quantum events preserves noncommutativity of quantum observables. It turns out that Malley's theorem is not related with the LHV model for quantum events, in general.
Under a standard set of assumptions for a hidden-variables model for quantum events, we show that all observables must commute simultaneously. And, despite Bell's complaint that a key condition of von Neumann's was quite unrealistic, we show these these conditions are entirely equivalent to those later introduced by Bell, Kochen and Specker. As is it known that these conditions are also equivalent to those under which the Bell-Clauser-Horne inequalities are derived, we see that any experimental violations of the inequalities demonstrate only that quantum observables do not commute.The same con…
It is shown that the conclusion of the paper "Hidden assumptions in decoherence theory" (quant-ph/0001021) is the result of a misunderstanding of the concept of pointer states. It is argued that pointer states are selected by the interaction of quantum systems with the environment, and are not based on any measurement by a conscious observer.
In his recent paper [arXiv:1104.1938], Bedingham discussed a hybrid between a theory of spontaneous wave function collapse and Bohmian mechanics. I offer a simpler way of conveying the substance of Bedingham's paper.
Kent's conclusion that ``non-contextual hidden variable theories cannot be excluded by theoretical arguments of the Kochen-Specker type once the imprecision in real world experiments is taken into account'' [Phys. Rev. Lett. 83, 3755 (1999)], is criticized. The Kochen-Specker theorem just points out that it is impossible even conceive a hidden variable model in which the outcomes of all measurements are pre-determined; it does not matter if these measurements are performed or not, or even if these measurements can be achieved only with finite precision.
In [Physical Review Letters 101, 050403 (2008)], we showed that quantum theory cannot be explained by a hidden variable model with a non-trivial local part. The purpose of this comment is to clarify our notion of local part, which seems to have caused some confusion in the recent literature. This notion is based on Bell's and demands that local hidden variables are physical, the idea being that, if discovered, they would not contradict basic physical principles. We explain why the recent supposed "counterexamples" that have appeared are not counterexamples to our theorem--in fact they are base…
In Section 3 of his paper (N. Gisin, Phys. Lett. A 210 (1996) 151), Gisin argues that a ``careless application of generalized quantum measurements can violate Bell's inequality even for mixtures of product states.'' However, the observed violation of the CHSH inequality is not in fact due to the application of generalized quantum measurements, but rather to a misapplication of the inequality itself -- to conditional expectations in which the conditioning depends upon the measurements under consideration.
In a recent article Giustina et al. [Phys. Rev. Lett. 115, 250401 (2015)] report on an advanced Bell experiment, simultaneously closing loopholes for local hidden-variable theories. The authors claim that 'local realism' has been refuted, unless 'truly exotic hypotheses' are made. Here I argue that a particularly wide and natural class of local hidden-variable theories survives, for instance when the hidden variables describe a background field. Such background-based theories exploit the freedom-of-choice loophole, which cannot be closed for this type of hidden variables. The dynamics of such …
In the above paper, it is claimed that with a particular use of the Bell inequality a simple single photon experiment could be performed to show the impossibility of any deterministic hidden variable theory in quantum optics. A careful analysis of the concept of probability for hidden variables and a detailed discussion of the hidden variable model of de Broglie-Bohm show that the reasoning and main conclusion of this paper are not correct.
In a recent article Hensen et al. [Nature 526, 682 (2015)] report on a sophisticated Bell experiment, simultaneously closing, for the first time, loopholes for local hidden-variable theories (HVTs). The authors claim that 'local realism' has been refuted, under certain natural assumptions. The aim of the present Comment is twofold. First, it is urged that the class of local HVTs that is eliminated by the reported experiment should be specified in greater detail than is done by the authors. Second, it is argued that the class of local HVTs that still survives is wide and natural. For instance, …
Contrary to what Lambare [arXiv:2008.00369] assumes, in non-Newtonian calculus (a calculus based on non-Diophantine arithmetic) an integral is typically given by a nonlinear map. This is the technical reason why all the standard proofs of Bell-type inequalities fail if non-Newtonian hidden variables are taken into account. From the non-Newtonian perspective, Bell's inequality is a property of a limited and unphysical class of hidden-variable models. An explicit counterexample to Bell's theorem can be easily constructed.
In a recent paper it was shown that if a Hamiltonian H has an unbroken PT symmetry, then it also possesses a hidden symmetry represented by the linear operator C. The operator C commutes with both H and PT. The inner product with respect to CPT is associated with a positive norm and the quantum theory built on the associated Hilbert space is unitary. In this paper it is shown how to construct the operator C for the non-Hermitian PT-symmetric Hamiltonian $H={1\over2}p^2+{1\over2}x^2 +iεx^3$ using perturbative techniques. It is also shown how to construct the operator C for $H={1\over2}p^2+{1\ov…
Bosonic bunching occurs within quantum physics and can be mimicked classically by noncontextual hidden-variable models, which excludes this phenomenon as a means to prove stronger-than-quantum contextuality.
In a recent note, Cavalcanti and Scarani (CS) constructed a counter local-hidden-variable model to explain the violation of our inequalities in Phys. Rev. Lett. 105, 170404 (2010). Here, we briefly discuss some issues in response to the comments raised by CS.
A new supersymmetric approach to the analysis of dynamical symmetries for matrix quantum systems is presented. Contrary to standard one dimensional quantum mechanics where there is no role for an additional symmetry due to nondegeneracy, matrix hamiltonians allow for non-trivial residual symmetries. This approach is based on a generalization of the intertwining relations familiar in SUSY Quantum Mechanics. The corresponding matrix supercharges, of first or of second order in derivatives, lead to an algebra which incorporates an additional block diagonal differential matrix operator (referred t…
We exhibit a local-hidden-variable model in agreement with the results of the two-photon coincidence experiment made by Torgerson et al. [Phys. Lett. A 204 (1995) 323]. The existence of any such model shows that the experiment does not exclude local realism.
In a series of very interesting papers [1-7], Joy Christian constructed a counterexample to Bell's theorem. This counterexample does not have the same assumptions as the original Bell's theorem, and therefore it does not represent a genuine disproof in a strict mathematical sense. However, assuming the physical relevance of the new assumptions, the counterexample is shown to be a contextual hidden variable theory. If Bell's theorem's importance is to rule out contextual hidden variable theories obeying relativistic locality, then Joy Christian's counterexample achieves its aim. If however cont…
It is argued that both the "Free Will Theorem" (FWT) and the "relativistic GRW model with Flash Ontology" (rGRWf) hiddenly assume the result of the before-before experiment, and for this reason both FWT and rGRWf imply free will in the world outside free experimenters.
Unruh has commented upon my recent proof that certain predictions of quantum theory are incompatible with the assertion that no influence of any kind acts backward in time in any Lorentz frame. Unruh fails to make a necessary distinction between statements that assert the existence of values, and statements that assert the existence merely of correlations between possible values. Consequently his argument fails to show that my proof involves a tacit or hidden reality assumption that is alien to quantum theory.
A suggestion for an observational test of the difference between quantum mechanics and noncontextual hidden variables theories requires the measurement of a product of two commuting observables without measuring either observable separately. A proposal has been made for doing this, but it is shown to be problematic.
It is shown that theoretically viable noncontextual hidden variables models in $d=2$ lead to conflicting dispersion free expressions in the analysis of the conditional measurement of two non-orthogonal projectors. No satisfactory criterion of the quantum discord, which relies on the analysis of conditional measurement, is formulated in the $d=2$ hidden variables space due to a lack of uniqueness of the dispersion free representation. We also make a speculative comment on a "many-worlds interpretation" of hidden variables models to account for the conditional measurement.
In a recent paper [T. C. Ralph, W. J. Munro, R. E. S. Polkinghorne, Phys. Rev. Lett. 85, 2035 (2000)], the authors propose a test for Bell's inequalities based on quadrature measurements for a correlated parametric source. We present here a local hidden variable model which reproduces all the expectation values predicted in the described experimental scheme, and point out that the proposal is based on an inconsistent use of Bell's inequalities.
It is stated by C. Simon, quant-ph/0410032, that the definition of "classicality" used in quant-ph/0310116 is "much narrower than Bell's concept of local hidden variables" and that, in the separable quantum case, the validity of the perfect correlation form of the original Bell inequality is necessarily linked with "the assumption of perfect correlations if the same (quantum) observable is measured on both sides". Here, I prove that these and other statements in quant-ph/0410032 are misleading.
A recent experiment yielding results in agreement with quantum theory and violating Bell inequalities was interpreted [Nature 526 (29 Octobert 2015) p. 682 and p. 649] as ruling out any local realistic theory of nature. But quantum theory itself is both local and realistic when properly interpreted using a quantum Hilbert space rather than the classical hidden variables used to derive Bell inequalities. There is no spooky action at a distance in the real world we live in if it is governed by the laws of quantum mechanics.
If YES, then we can look forward to physical realization of superluminal communication, as the original considerations of the ``no-cloning'' theorem were motivated in part as an explanation of why certain schemes for superluminal signaling cannot work. If NO, then it would seem that some aspects of the ``hidden'' variables must be ``intrinsically hidden'', i.e., ``unknowable'', such that ``hidden-variable'' theories belong more to the ``idealist'' than to the ``realist'' school of thought. I pose this question without proposing a definite answer. I am unaware of any commentary on this topic du…
The asymmetric quantum Rabi model (AQRM) exhibits level crossings in the eigenspectrum for the values $ε\in\frac{1}{2}\mathbb{Z}$ of the bias parameter $ε$. Such level crossings are expected to be associated with some hidden symmetry of the model. The origin of this hidden symmetry is established by finding the operators which commute with the AQRM hamiltonian at these special values. The construction is given explicitly for the first several cases and can be applied to other related light-matter interaction models for which similar level crossings have been observed in the presence of a bias …
The statement of E.R. Loubenets, Phys. Rev. A 69, 042102 (2004), that separable states can violate classical probabilistic constraints is based on a misleading definition of classicality, which is much narrower than Bell's concept of local hidden variables. In a Bell type setting the notion of classicality used by Loubenets corresponds to the assumption of perfect correlations if the same observable is measured on both sides. While it is obvious that most separable states do not satisfy this assumption, this does not constitute "non-classical" behaviour in any usual sense of the word.
This is an analysis of the recently published article `Quantum theory cannot consistently describe the use of itself' by D. Frauchiger and R. Renner~\cite{1}. Here I decipher the paradox and analyze it from the point of view of de Broglie-Bohm hidden variable theory (i.e., Bohmian mechanics). I also analyze the problem from the perspective obtained by the Copenhagen interpretation (i.e., the Bohrian interpretation) and show that both views are self consistent and do not lead to any contradiction with a `single-world' description of quantum theory.
In Phys. Rev. A 101, 022117 (2020), it was argued that Bell inequalities are based on classical, not quantum, physics, and hence their violation in experiments provides no support for the claimed existence of peculiar nonlocal and superluminal influences in the real (quantum) world. This Reply to Lambare's Comment, Phys. Rev. A 104, 066201 (2021), on that paper seeks to clarify some issues related to the correct use of Hilbert space quantum mechanics for identifying the microscopic causes of later macroscopic measurement outcomes, a matter not properly addressed by Bell, who used classical hid…
A recent Letter by Hess and Philipp claims that Bell's theorem neglects the possibility of time-like dependence in local hidden variables, hence is not conclusive. Moreover the authors claim that they have constructed, in an earlier paper, a local realistic model of the EPR correlations. However, they themselves have neglected the experimenter's freedom to choose settings, while on the other hand, Bell's theorem can be formulated to cope with time-like dependence. This in itself proves that their toy model cannot satisfy local realism, but we also indicate where their proof of its local realis…
Bell inequalities may only be derived, if hidden variables do not depend on the experimental settings. The stochastic independence of hidden and setting variables is called: freedom of choice, free will, measurement independence or no conspiracy. By imbedding the Bell causal structure in a larger causal network the authors correctly prove, that one can explain and quantify possible violation of measurement independence without evoking the super-determinism. They assume the independence of the variables that causally determine the settings and investigate how they might become correlated with h…
This paper furthers the long historical examination of and debate on the foundations of quantum mechanics (QM) by presenting two local hidden variable (LHV) rules in the context of the EPRB experiment which violate Bell's inequality, but which are nevertheless local and deterministic under reasonable definitions of the terms, and coincide approximately with the conventional QM prediction. The theories are based on the general idea of probabilistic detection of particles depending on an interaction of hidden variables within the measuring device and particle, and relate mathematically to Fourie…
The main assumptions the Copenhagen quantum mechanics has been based on will be summarized and the known (not yet decided) contradiction between Einstein and Bohr will be newly analyzed. The given assumptions have been represented basically by time-dependent Schroedinger equation, to which some further assumptions have been added. Some critical comments have been raised against the given mathematical model structure by Pauli (1933) and by Susskind and Glogover (1964). They may be removed if only the Schroedinger equation is conserved and the additional assumptions are abandoned, as shown recen…
This is a comment on J. A. Barrett's article ``The Preferred-Basis Problem and the Quantum Mechanics of Everything'' in Brit. J. Phil. Sci. 56 (2005), which concerns theories postulating that certain quantum observables have determinate values, corresponding to additional (often called ``hidden'') variables. I point out that it is far from clear, for most observables, what such a postulate is supposed to mean, unless the postulated additional variable is related to a clear ontology in space-time, such as particle world lines, string world sheets, or fields.
