Quantum Measurement Outcomes Research Articles

Does Quantum Mechanics Require "Conspiracy"?

Quantum states containing records of incompatible outcomes of quantum measurements are valid states in the tensor-product Hilbert space. Since they contain false records, they conflict with the Born rule and with our observations. I show that excluding them requires a fine-tuning to an extremely restricted subspace of the Hilbert space that seems "conspiratorial", in the sense that (1) it seems to depend on future events that involve records (including measurement settings) and on the dynamical law (normally thought to be independent of the initial conditions), and (2) it violates Statistical Independence, even when it is valid in the context of Bell's theorem. To solve the puzzle, I build a model in which, by changing the dynamical law, the same initial conditions can lead to different histories in which the validity of records is relative to the new dynamical law. This relative validity of the records may restore causality, but the initial conditions still must depend, at least partially, on the dynamical law. While violations of Statistical Independence are often seen as non-scientific, they turn out to be needed to ensure the validity of records and our own memories and, by this, of science itself. A Past Hypothesis is needed to ensure the existence of records and turns out to require violations of Statistical Independence. It is not excluded that its explanation, still unknown, ensures such violations in the way needed by local interpretations of quantum mechanics. I suggest that an as-yet unknown law or superselection rule may restrict the full tensor-product Hilbert space to the very special subspace required by the validity of records and the Past Hypothesis.

Nashian game theory is incompatible with quantum physics

We suggest to look at quantum measurement outcomes not through the lens of probability theory, but instead through decision theory. We introduce an original game-theoretical framework, model and algorithmic procedure where measurement scenarios are multiplayer games with a structure all observers agree on. Measurement axes and, newly, measurement outcomes are modeled as decisions with nature being an action-minimizing economic agent. We translate physical notions of causality, correlation, counterfactuals, and contextuality to particular aspects of game theory. We investigate the causal consistency of dynamic games with imperfect information from the quantum perspective and conclude that counterfactual dependencies should be distinguished from causation and correlation as a separate phenomenon of its own. Most significantly, we observe that game theory based on Nash equilibria stands in contradiction with a violation of Bell inequalities. Hence, we propose that quantum physics should be analyzed with non-Nashian game theory, the inner workings of which we demonstrate using our proposed model.

Single-shot quantum measurements sketch quantum many-body states

Quantum measurements allow us to observe quantum many-body systems consisting of a multitude of microscopic degrees of freedom. However, the quantum uncertainty and the exponentially large Hilbert space pose natural barriers to simple interpretations of the quantum measurement outcomes. We propose a nonlinear ``measurement energy'' based upon the measurement outcomes and a general approach akin to quantum machine learning to extract the most probable states (maximum likelihood estimates), naturally reconciling noncommuting observables and getting more out of the quantum measurements. Compatible with established quantum many-body ansatzes and efficient optimization, our strategy offers state-of-art capacity with control and full information. We showcase the versatility and accuracy of our strategy on random long-range fermion and Kitaev quantum spin-liquid models, where smoking-gun signatures were lacking.

Kochen-Specker contextuality

A central result in the foundations of quantum mechanics is the Kochen-Specker theorem. In short, it states that quantum mechanics is in conflict with classical models in which the result of a measurement does not depend on which other compatible measurements are jointly performed. Here compatible measurements are those that can be implemented simultaneously or, more generally, those that are jointly measurable. This conflict is generically called quantum contextuality. In this review, an introduction to this subject and its current status is presented. Several proofs of the Kochen-Specker theorem and different notions of contextuality are reviewed. How to experimentally test some of these notions is explained and connections between contextuality and nonlocality or graph theory are discussed. Finally, some applications of contextuality in quantum information processing are reviewed.

Experimental Shot-by-Shot Estimation of Quantum Measurement Confidence.

We demonstrate the single-shot confidence estimation for individual quantum measurement outcomes using the continuous measurement theory of the quantum counting process applied to the quantum state identification problem. We experimentally obtain single-shot and average confidences for quantum measurements and show that they favorably compare to that of the idealized classical measurement. Finally, we demonstrate that single-shot confidence estimations correctly represent observed experimental outcomes for a large ensemble of measurements.

Observer Dependent Biases of Quantum Randomness

Quantum mechanics (QM) proposes that a quantum system measurement does not register a pre-existing reality but rather establishes reality from the superposition of potential states. Measurement reduces the quantum state according to a probability function, the Born rule, realizing one of the potential states. Consequently, a classical reality is observed. The strict randomness of the measurement outcome is well-documented (and theoretically predicted) and implies a strict indeterminacy in the physical world’s fundamental constituents. Wolfgang Pauli, with Carl Gustav Jung, extended the QM framework to measurement outcomes that are meaningfully related to human observers, providing a psychophysical theory of quantum state reductions. The Pauli-Jung model (PJM) proposes the existence of observer influences on quantum measurement outcomes rooted in the observer’s unconscious mind. The correlations between quantum state reductions and (un)conscious states of observers derived from the PJM and its mathematical reformulation within the model of pragmatic information (MPI) were empirically tested. In all studies, a subliminal priming paradigm was used to induce a biased likelihood for specific quantum measurement outcomes (i.e., a higher probability of positive picture presentations; Studies 1 and 2) or more pronounced oscillations of the evidence than expected by chance for such an effect (Studies 3 and 4). The replicability of these effects was also tested. Although Study 1 found strong initial evidence for such effects, later replications (Studies 2 to 4) showed no deviations from the Born rule. The results thus align with standard QM, arguing against the incompleteness of standard QM in psychophysical settings like those established in the studies. However, although no positive evidence exists for the PJM and the MPI, the data do not entirely falsify the model’s validity.

Can a hidden-variable-based system violate Bell’s inequality?

Quantum mechanics predicts faster-than-light information transportation in order to satisfy quantum entanglement experimental results. Such a prediction violates the locality principle and Bell’s inequality. Quantum mechanisms also state that the world is intrinsically probabilistic. Such an idea was not welcome by many scientists including Einstein, Podolsky and Rosen. To resolve such a dilemma, the ”Many-world” theory was presented by Hugh Everett in 1975. Such a theory asserts that the universal wave function is real and that there is no wave function collapse. Also, it states that all possible outcomes of quantum measurements are physically realized in other parallel universes. Besides, in quantum mechanics, the observer effect defines a state transition of quantum objects. Such a phenomenon affirms that quantum objects behave differently depending on being observed or not.In this paper, we present few assumptions based on which we build a classical hidden-variable-based system that can violate Bell’s inequality. Therefore, adopting similar assumptions in explaining quantum entanglement could lead to a better explanation of quantum mechanics without violating the locality principle or adopting such weird assumptions. Hence, one can conclude that extending Quantum Mechanism by a set of similar hidden variables can resolve such a paradox and predict the quantum entanglement experimental results without violating the locality principle.

Symmetries of quantum evolutions

A cornerstone of quantum mechanics is the characterization of symmetries provided by Wigner's theorem. Wigner's theorem establishes that every symmetry of the quantum state space must be either a unitary transformation or an antiunitary transformation. Here we extend Wigner's theorem from quantum states to quantum evolutions, including both the deterministic evolution associated with the dynamics of closed systems and the stochastic evolutions associated with the outcomes of quantum measurements. We prove that every symmetry of the space of quantum evolutions can be decomposed into two state space symmetries that are either both unitary or both antiunitary. Building on this result, we show that it is impossible to extend the time-reversal symmetry of unitary quantum dynamics to a symmetry of the full set of quantum evolutions. Our no-go theorem implies that any time-symmetric formulation of quantum theory must either restrict the set of the allowed evolutions or modify the operational interpretation of quantum states and processes. Here we propose a time-symmetric formulation of quantum theory where the allowed quantum evolutions are restricted to a suitable set, which includes both unitary evolution and projective measurements but excludes the deterministic preparation of pure states. The standard operational formulation of quantum theory can be retrieved from this time-symmetric version by introducing an operation of conditioning on the outcomes of past experiments.

Noise-resilient variational hybrid quantum-classical optimization

Variational hybrid quantum-classical optimization represents one of the most promising avenue to show the advantage of nowadays noisy intermediate-scale quantum computers in solving hard problems, such as finding the minimum-energy state of a Hamiltonian or solving some machine-learning tasks. In these devices noise is unavoidable and impossible to error-correct, yet its role in the optimization process is not well understood, especially from the theoretical viewpoint. Here we consider a minimization problem with respect to a variational state, iteratively obtained via a parametric quantum circuit, taking into account both the role of noise and the stochastic nature of quantum measurement outcomes. We show that the accuracy of the result obtained for a fixed number of iterations is bounded by a quantity related to the Quantum Fisher Information of the variational state. Using this bound, we study the convergence property of the quantum approximate optimization algorithm under realistic noise models, showing the robustness of the algorithm against different noise strengths.

Number of quantum measurement outcomes as a resource

The number of outcomes is an intrinsic property of a quantum measurement, which has the potential to improve the performance of quantum information processing. Recently, there have been fruitful results on resource theories of quantum measurements. In this paper, we investigate the number of measurement outcomes as a kind of resource. We cast the robustness of this resource as a semi-definite positive program. Its dual problem confirms that if a measurement cannot be simulated by the measurements with a smaller number of outcomes, there exists a state discrimination task where it outperforms the latter. An upper bound of this advantage is derived, which can be saturated if the number of outcomes is smaller than the dimension of the Hilbert space. We also show that the possible tasks to reveal the advantage can be more general and not restricted to state discrimination.

Respecting One’s Fellow: QBism’s Analysis of Wigner’s Friend

According to QBism, quantum states, unitary evolutions, and measurement operators are all understood as personal judgments of the agent using the formalism. Meanwhile, quantum measurement outcomes are understood as the personal experiences of the same agent. Wigner's conundrum of the friend, in which two agents ostensibly have different accounts of whether or not there is a measurement outcome, thus poses no paradox for QBism. Indeed the resolution of Wigner's original thought experiment was central to the development of QBist thinking. The focus of this paper concerns two very instructive modifications to Wigner's puzzle: One, a recent no-go theorem by Frauchiger and Renner, and the other a thought experiment by Baumann and Brukner. We show that the paradoxical features emphasized in these works disappear once both friend and Wigner are understood as agents on an equal footing with regard to their individual uses of quantum theory. Wigner's action on his friend then becomes, from the friend's perspective, an action the friend takes on Wigner. Our analysis rests on a kind of quantum Copernican principle: When two agents take actions on each other, each agent has a dual role as a physical system for the other agent. No user of quantum theory is more privileged than any other. In contrast to the sentiment of Wigner's original paper, neither agent should be considered as in "suspended animation." In this light, QBism brings an entirely new perspective to understanding Wigner's friend thought experiments.

Extending qubit coherence by adaptive quantum environment learning

Decoherence, resulting from unwanted interaction between a qubit and its environment, poses a serious challenge towards the development of quantum technologies. Recently, researchers have started analysing how real-time Hamiltonian learning approaches, based on estimating the qubit state faster than the environmental fluctuations, can be used to counteract decoherence. In this work, we investigate how the back-action of the quantum measurements used in the learning process can be harnessed to extend qubit coherence. We propose an adaptive protocol that, by learning the qubit environment, narrows down the distribution of possible environment states. While the outcomes of quantum measurements are random, we show that real-time adaptation of measurement settings (based on previous outcomes) allows a deterministic decrease of the width of the bath distribution, and hence an increase of the qubit coherence. We numerically simulate the performance of the protocol for the electronic spin of a nitrogen-vacancy centre in diamond subject to a dilute bath of 13C nuclear spin, finding a considerable improvement over the performance of non-adaptive strategies.

Analysis of single-particle nonlocality through the prism of weak measurements

Although regarded today as an important resource in quantum information, nonlocality has yielded over the years many conceptual conundrums. Among the latter are nonlocal aspects of single particles which have been of major interest. In this paper, the nonlocality of single quanta is studied in a square nested Mach–Zehnder interferometer with spatially separated detectors using a delayed choice modification of quantum measurement outcomes that depend on the complex-valued weak values. We show that if spacelike separated Bob and Alice are allowed to freely control their quantum devices, the geometry of the setup constrains the local hidden variable models. In particular, hidden signaling and a list of contextual instructions are required to split a quantum state characterized by a positive Wigner function into two quantum states with nonpositive Wigner functions. This implies that local hidden variable models could rely neither on only two hidden variables for position and momentum, nor on simultaneous factorizability of both the hidden probability densities and weights of splitting to reproduce the correct quantum distributions. While our analysis does not fully exclude the existence of nonfactorizable local hidden variable models, it demonstrates that the recently proposed weak values of quantum histories necessitate contextual splitting of prior commitments to measurement outcomes, due to functional dependence on the total Feynman sum that yields the complex-valued quantum probability amplitude for the studied quantum transition. This analysis also highlights the quantum nature of weak measurements.

Agent Inaccessibility as a Fundamental Principle in Quantum Mechanics: Objective Unpredictability and Formal Uncomputability.

The inaccessibility to the experimenter agent of the complete quantum state is well-known. However, decisive answers are still missing for the following question: What underpins and governs the physics of agent inaccessibility? Specifically, how does nature prevent the agent from accessing, predicting, and controlling, individual quantum measurement outcomes? The orthodox interpretation of quantum mechanics employs the metaphysical assumption of indeterminism—‘intrinsic randomness’—as an axiomatic, in-principle limit on agent–quantum access. By contrast, ontological and deterministic interpretations of quantum mechanics typically adopt an operational, in-practice limit on agent access and knowledge—‘effective ignorance’. The present work considers a third option—‘objective ignorance’: an in-principle limit for ontological quantum mechanics based upon self-referential dynamics, including undecidable dynamics and dynamical chaos, employing uncomputability as a formal limit. Given a typical quantum random sequence, no formal proof is available for the truth of quantum indeterminism, whereas a formal proof for the uncomputability of the quantum random sequence—as a fundamental limit on agent access ensuring objective unpredictability—is a plausible option. This forms the basis of the present proposal for an agent-inaccessibility principle in quantum mechanics.

Observer Effects on Quantum Randomness: Testing Micro-Psychokinetic Effects of Smokers on Addiction-Related Stimuli

A vivid discussion revolves around the role of the human mind in the quantum measurement process. While some authors argue that conscious observation is a necessary element to achieve the transition from quantum to classical states during measurement (Wigner 1963), some go even further and propose a more active influence of the human mind on the probabilities of quantum measurement outcomes (e.g., Atmanspacher, Romer, & Walach 2002, Penrose & Hameroff 2011). This proposition was tested in micro-psychokinesis (micro-Pk) research in which intentional observer effects on quantum random number generators (RNGs) were investigated. In the studies presented here, we extended this line of research and tested the impact of unconscious goals on micro-Pk. Our focus lies in cigarette addiction as an unconscious drive, and we hypothesized that regular cigarette smokers would influence the outcome of a quantum RNG that determined whether the participant was going to see a smoking-related or a neutral picture. Study 1 revealed strong evidence for micro-Pk (BF10 = 66.06), supporting H1. As expected, no deviation from chance was found with non-smokers. Study 2, a pre-registered highly powered replication attempt, failed to reproduce this result and showed strong evidence for H0 (BF01 = 11.07). When the data from both studies are combined, a remarkable change in effect across time (resembling a combination of appearance followed by decline) can be seen only in the smokers’ subsample. Appearance and decline effects were absent in the non-smokers’ sample and in a simulation. Based on von Lucadou’s Model of Pragmatic Information, we suggest that (micro-)Pk effects follow a systematic pattern comparable to a dampened harmonic oscillation. This concept may shed new light on past and future Pk research.

Principles of a second quantum mechanics constructed bottom-up

Principles of a second quantum mechanics constructed bottom-up

Extracting the physical sector of quantum states

The physical nature of any quantum source guarantees the existence of an effective Hilbert space of finite dimension, the physical sector, in which its state is completely characterized with arbitrarily high accuracy. The extraction of this sector is essential for state tomography. We show that the physical sector of a state, defined in some pre-chosen basis, can be systematically retrieved with a procedure using only data collected from a set of commuting quantum measurement outcomes, with no other assumptions about the source. We demonstrate the versatility and efficiency of the physical-sector extraction by applying it to simulated and experimental data for quantum light sources, as well as quantum systems of finite dimensions.

Reciprocal Ontological Models Show Indeterminism Comparable to Quantum Theory

The question whether indeterminism in quantum measurement outcomes is fundamental or is there a possibility of constructing a finer theory underlying quantum mechanics that allows no such indeterminism, has been debated for a long time. We show that within the class of ontological models due to Harrigan and Spekkens, those satisfying preparation-measurement reciprocity must allow indeterminism of the order of quantum theory. Our result implies that one can design quantum random number generator, for which it is impossible, even in principle, to construct a reciprocal deterministic model.

Quantum randomness and unpredictability

Quantum mechanics is a physical theory supplying probabilities corresponding to expectation values for measurement outcomes. Indeed, its formalism can be constructed with measurement as a fundamental process, as was done by Schwinger, provided that individual measurements outcomes occur in a random way. The randomness appearing in quantum mechanics, as with other forms of randomness, has often been considered equivalent to a form of indeterminism. Here, it is argued that quantum randomness should instead be understood as a form of unpredictability because, amongst other things, indeterminism is not a necessary condition for randomness. For concreteness, an explication of the randomness of quantum mechanics as the unpredictability of quantum measurement outcomes is provided. Finally, it is shown how this view can be combined with the recently introduced view that the very appearance of individual quantum measurement outcomes can be grounded in the Plenitude principle of Leibniz, a principle variants of which have been utilized in physics by Dirac and Gell‐Mann in relation to the fundamental processes. This move provides further support to Schwinger's “symbolic” derivation of quantum mechanics from measurement.

What Does One Measure When One Measures the Arrival Time of a Quantum Particle?

What is the right statistics for the measurements of arrival times of a quantum particle? Although this question is very old, it is still open. The usual experiments are performed in the far-field regime and this question becomes unimportant, as a semiclassical analysis suffices. Nevertheless, the development in the detector technology will soon allow for near-field investigations; thus, a better understanding of arrival time measurements is needed. Since outcomes of quantum measurements are always described by positive-operator-valued measures (POVMs), various arrival time POVMs have been proposed. On the other hand, many physicists would agree that the arrival time statistics is given by the quantum flux. This urges the question whether a POVM exists, which agrees approximately with the quantum flux values on a reasonable set of wave functions. We answer this question negatively for a very natural set of wave functions, but we remark that the answer is very sensitive to the choice of the set and provide evidence for the existence of a POVM that agrees with the quantum flux on a more restrictive set.