scholarly journals Observer Dependent Biases of Quantum Randomness

2021 ◽  
Vol 1 (1-2) ◽  
Author(s):  
Moritz C. Dechamps ◽  
Markus A. Maier ◽  
Markus Pflitsch ◽  
Michael Duggan
Keyword(s):  
Quantum State ◽  
Quantum Measurement ◽  
Probability Function ◽  
Born Rule ◽  
Wolfgang Pauli ◽  
Quantum Randomness ◽  
Pragmatic Information ◽  
Priming Paradigm ◽  
Unconscious Mind ◽  
Specific Quantum

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.

Probability and Explanation

2017 ◽  
Author(s):  
Richard Healey
Keyword(s):  
Quantum Theory ◽  
Quantum State ◽  
Causal Explanation ◽  
Born Rule ◽  
Correct Application

We can use quantum theory to explain an enormous variety of phenomena by showing why they were to be expected and what they depend on. These explanations of probabilistic phenomena involve applications of the Born rule: to accept quantum theory is to let relevant Born probabilities guide one’s credences about presently inaccessible events. We use quantum theory to explain a probabilistic phenomenon by showing how its probabilities follow from a correct application of the Born rule, thereby exhibiting the phenomenon’s dependence on the quantum state to be assigned in circumstances of that type. This is not a causal explanation since a probabilistic phenomenon is not constituted by events that may manifest it: but each of those events does depend causally on events that actually occur in those circumstances. Born probabilities are objective and sui generis, but not all Born probabilities are chances.

Assigning Values and States

2017 ◽  
Author(s):  
Richard Healey
Keyword(s):  
Quantum State ◽  
Density Operator ◽  
Entangled State ◽  
Physical Situation ◽  
Born Rule ◽  
Correct Assignment ◽  
Significant Magnitude ◽  
Good Advice ◽  
Empirical Significance ◽  
Important Idea

If a quantum state is prescriptive then what state should an agent assign, what expectations does this justify, and what are the grounds for those expectations? I address these questions and introduce a third important idea—decoherence. A subsystem of a system assigned an entangled state may be assigned a mixed state represented by a density operator. Quantum state assignment is an objective matter, but the correct assignment must be relativized to the physical situation of an actual or hypothetical agent for whom its prescription offers good advice, since differently situated agents have access to different information. However this situation is described, it is true, empirically significant magnitude claims that make the description correct, while others provide the objective grounds for the agent’s expectations. Quantum models of environmental decoherence certify the empirical significance of these magnitude claims while also licensing application of the Born rule to others without mentioning measurement.

scholarly journals A Unified Scheme of Measurement and Amplification Processes Based on Micro-Macro Duality — Stern-Gerlach Experiment as a Typical Example

2009 ◽  
Vol 16 (01) ◽  
pp. 55-74 ◽  
Author(s):  
Ryo Harada ◽  
Izumi Ojima
Keyword(s):  
Quantum State ◽  
Quantum Measurement ◽  
Radon Transform ◽  
Mathematical Expression ◽  
General Idea ◽  
Classical Correspondence ◽  
Probe System ◽  
State Changes ◽  
Concrete Model

A unified scheme for quantum measurement processes is formulated on the basis of micro-macro duality as a mathematical expression of the general idea of quantum-classical correspondence. In this formulation, we can naturally accommodate the amplification processes necessary for magnifying quantum state changes at the microscopic end of the probe system into the macroscopically visible motion of the measuring pointer. Its essence is exemplified and examined in the concrete model of the Stern-Gerlach experiment for spin measurement, where the Helgason duality controlling the Radon transform is seen to play essential roles.

scholarly journals Statistics of the Bifurcation in Quantum Measurement

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 834 ◽  
Author(s):  
Karl-Erik Eriksson ◽  
Kristian Lindgren
Keyword(s):  
Field Theory ◽  
Quantum Measurement ◽  
Measurement Process ◽  
Quantum Field ◽  
Born Rule ◽  
Level System ◽  
Measurement Device ◽  
Final State ◽  
Initial States ◽  
Quantum Measurement Process

We model quantum measurement of a two-level system μ . Previous obstacles for understanding the measurement process are removed by basing the analysis of the interaction between μ and the measurement device on quantum field theory. This formulation shows how inverse processes take part in the interaction and introduce a non-linearity, necessary for the bifurcation of quantum measurement. A statistical analysis of the ensemble of initial states of the measurement device shows how microscopic details can influence the transition to a final state. We find that initial states that are efficient in leading to a transition to a final state result in either of the expected eigenstates for μ , with ensemble averages that are identical to the probabilities of the Born rule. Thus, the proposed scheme serves as a candidate mechanism for the quantum measurement process.

The Collapse of the Quantum State

2019 ◽  
pp. 118-142
Author(s):  
Jeffrey A. Barrett
Keyword(s):  
Quantum Mechanics ◽  
Quantum State ◽  
Quantum Measurement ◽  
Measurement Problem ◽  
Primitive Ontology ◽  
Quantum Measurement Problem

We consider Wigner’s proposal for solving the quantum measurement problem. His solution involves a strong mind-body dualism, but it is also possible to provide a purely physical collapse solution to the quantum measurement problem. To this end, we consider the GRW formulation of quantum mechanics and three ways one might interpret it: GRWr, GRWm, and GRWf. These ways of interpreting the theory differ in the metaphysical commitments one makes and, hence, in how one explains one’s measurement records and hence one’s experience. This provides an introduction to the notions of an empirical ontology and a primitive ontology. We consider some of the comparative virtues and vices of the GRW formulation of quantum mechanics.

scholarly journals Computational Collapse of Quantum State with Application to Oblivious Transfer

2003 ◽  
Vol 10 (37) ◽  
Author(s):  
Claude Crépeau ◽  
Paul Dumais ◽  
Dominic Mayers ◽  
Louis Salvail
Keyword(s):  
Quantum State ◽  
Polynomial Time ◽  
Quantum Measurement ◽  
Oblivious Transfer ◽  
Black Box ◽  
The State ◽  
Natural Question ◽  
Full Information ◽  
Classical Counterpart ◽  
Commitment Scheme

Quantum 2-party cryptography differs from its classical counterpart in at least one important way: Given black-box access to a perfect commitment scheme there exists a secure 1-2 <em>quantum</em> oblivious transfer. This reduction proposed by Crépeau and Kilian was proved secure against any receiver by Yao, in the case where perfect commitments are used. However, quantum commitments would normally be based on computational assumptions. A natural question therefore arises: What happens to the security of the above reduction when computationally secure commitments are used instead of perfect ones?<br /> <br />In this paper, we address the security of 1-2 QOT when computationally binding string commitments are available. In particular, we analyse the security of a primitive called <em>Quantum Measurement Commitment</em> when it is constructed from unconditionally concealing but computationally binding commitments. As measuring a quantum state induces an irreversible collapse, we describe a QMC as an instance of ``computational collapse of a quantum state''. In a QMC a state appears to be collapsed to a polynomial time observer who cannot extract full information about the state without breaking a computational assumption.<br /> <br />We reduce the security of QMC to a <em>weak</em> binding criteria for the string commitment. We also show that <em>secure</em> QMCs implies QOT using a straightforward variant of the reduction above.

Competition of Continuous and Projective Measurements in Filtering Processes

2016 ◽  
Vol 23 (04) ◽  
pp. 1650021 ◽  
Author(s):  
Benedetto Militello
Keyword(s):  
Quantum System ◽  
Quantum State ◽  
Numerical Results ◽  
Unitary Evolution ◽  
Theoretical Predictions ◽  
Measured System ◽  
Projective Measurements ◽  
Specific Quantum

A quantum system interacting with a repeatedly measured one turns out to be subjected to a non-unitary evolution which can force the former to a specific quantum state. It is shown that in the case where the repeatedly measured system is subjected to the action of its environment, the occurrence of a competition between the dissipation and the measurements can reduce the influence of the decay on the filtering process. Both theoretical predictions and numerical results are presented.

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