Law of Total Probability in Quantum Theory and Its Application in Wigner’s Friend Scenario

Yang, Jianhao M.

doi:10.3390/e24070903

Cited by 3 publications

(3 citation statements)

References 37 publications

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“…Another issue of the no-go theorems is that there may exist logical loophole related to the law of total probability. By introducing two-time conditional probability, Yang [29] claimed that the violation of the inequalities may be derived from the invalidity of the law of total probability or the law of marginal probability in quantum theory. In our opinion, the law of total probability will be valid condition on the assumption of 'observer-independent facts' or 'absoluteness of observed events', i.e.…”

Section: Discussion and Summarymentioning

confidence: 99%

Tripartite Wigner’s friend scenario and its test

Ding

Wang

et al. 2023

Phys. Scr.

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Wigner’s friend thought experiment is intended to reveal the inherent tension between unitary evolution and measurement collapse. Inspired by the Wigner’s friend experiment, Brukner derives a no-go theorem for observer-independent facts, focusing on two entangled observers in their respective laboratories. We construct an extended Wigner’s friend scenario, including three laboratories, namely, Alice’s laboratory, Bob’s laboratory and Charlie’s laboratory, where Alice, Bob and Charlie are standing outside the laboratories while their friends are placed inside their own laboratories. To realize this scenario, we create a universal quantum circuit, especially the circuit realization of the state evolution and measurement inside each laboratory, simple but novel. We carry out experiments on the IBM quantum computers to test the primary circuits, i.e., state preparation, state evolution and measurement inside the laboratory. Furthermore, we perform the simulation of the quantum circuit via Q# quantum programming on a classical computer.

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Section: Discussion and Summarymentioning

confidence: 99%

Tripartite Wigner’s friend scenario and its test

Ding

Wang

et al. 2023

Phys. Scr.

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“…Such an intuitive representation of a complex phenomenon was proposed by Erwin Schrödinger in 1926 and later refined by Max Born (Born & Wiener, 1926). Since and denote probabilities, they are subject to the law of total probability and must fulfill the following requirement: Yang, 2022). Physically, the qubit can be realized by any system that is quantum and has two different basis states, e.g.…”

Section: Principles Of Quantum Computing: Qubit Superposition and Ent...mentioning

confidence: 99%

On quantum computing for artificial superintelligence

Grabowska,

Gunia

2024

Euro Jnl Phil Sci

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Artificial intelligence algorithms, fueled by continuous technological development and increased computing power, have proven effective across a variety of tasks. Concurrently, quantum computers have shown promise in solving problems beyond the reach of classical computers. These advancements have contributed to a misconception that quantum computers enable hypercomputation, sparking speculation about quantum supremacy leading to an intelligence explosion and the creation of superintelligent agents. We challenge this notion, arguing that current evidence does not support the idea that quantum technologies enable hypercomputation. Fundamental limitations on information storage within finite spaces and the accessibility of information from quantum states constrain quantum computers from surpassing the Turing computing barrier. While quantum technologies may offer exponential speed-ups in specific computing cases, there is insufficient evidence to suggest that focusing solely on quantum-related problems will lead to technological singularity and the emergence of superintelligence. Subsequently, there is no premise suggesting that general intelligence depends on quantum effects or that accelerating existing algorithms through quantum means will replicate true intelligence. We propose that if superintelligence is to be achieved, it will not be solely through quantum technologies. Instead, the attainment of superintelligence remains a conceptual challenge that humanity has yet to overcome, with quantum technologies showing no clear path toward its resolution.

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“…Most importantly, it involves assigning a joint probability distribution to sets of variables that can be inferred to have simultaneously well-defined values, given the premise of Absoluteness of Observed Events [16]. In a recently published work [17] it was argued that this could leave open a loophole by which one may take the result as indicating the failure of law of total probability in quantum mechanics, as opposed to the failure of one of the LF assumptions. Regardless of the merit of that argument, one may wonder whether it is possible to formulate a probability-free version of the LF no-go theorem, analogous to the Hardy and GHZ theorems, to which no such critique could apply.…”

Section: Introductionmentioning

confidence: 99%

A possibilistic no-go theorem on the Wigner’s friend paradox

Haddara,

Cavalcanti

2023

New J. Phys.

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The famous "Wigner's friend" paradox highlights the difficulty of modelling the evolution of quantum systems under measurement in situations where observers themselves are considered to be subject to the laws of quantum mechanics. In recent years, variations of the original Wigner's friend paradox have been recognized as fruitful arenas for probing the foundations of quantum theory. In particular Bong et al. [Nature Physics 16, 1199 (2020)] demonstrated a contradiction between a set of intuitive assumptions called "Local Friendliness" (LF) and certain quantum phenomena on an extended version of the Wigner's friend paradox. The LF assumptions can be understood as the conjunction of two independent assumptions: Absoluteness of Observed Events requires that any event observed by any observer has an absolute, rather than relative, value; Local Agency is the assumption that an intervention cannot be correlated with relevant events outside its future light cone. These assumptions are weaker than the assumptions that lead to Bell's theorem, and thus while the Local Friendliness result may be considered to be conceptually comparable to Bell's result, its implications are even deeper. The proof of the LF no-go theorem, however, relies on probability theory, and a fundamental question remained whether or not LF is an inherently statistical concept. Here we present a probability-free version of the Local Friendliness theorem, building upon Hardy's no-go theorem for local hidden variables. The argument is phrased in the language of possibilities, which we make formal by using a modal logical approach. It relies on a weaker version of Local Agency, which we call "Possibilistic Local Agency": the assumption that an intervention cannot affect the possibilities of events outside its future light cone.

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Law of Total Probability in Quantum Theory and Its Application in Wigner’s Friend Scenario

Cited by 3 publications

References 37 publications

Tripartite Wigner’s friend scenario and its test

Tripartite Wigner’s friend scenario and its test

On quantum computing for artificial superintelligence

A possibilistic no-go theorem on the Wigner’s friend paradox

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