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QBism
QBism
	The agent takes action on an external quantum system of finite dimension d. This action is represented by a set of operators {Ei} a positive-operator-valued measure (POVM). Which leads to an outcome that the agent cannot fully predict.The quantum state exists only in the agent’s mind, reflecting their beliefs about the outcomes of their actions, not something in the external world. The measurement devices are seen as extensions of the agent and once the agent chooses an action {Ei}, the particular consequence Ek is the resulting outcome.

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QBism is an interpretation of quantum mechanics that reframes the theory as a tool for an individual agent to assess and update their expectations about the outcomes of their actions on the world. It treats the quantum state not as an objective property of a system, but as a mathematical expression of the agent’s personal degrees of belief. From this perspective, quantum mechanics does not describe an observer-independent reality, but offers a normative framework for decision-making in the face of uncertainty. In QBism, a measurement is regarded as an action initiated by the agent, and each outcome is understood as an experience for that agent and not the discovery of a pre-existing fact, but the result of a specific interaction.

History

QBism began to take shape in the early 2010s, building on work initiated in the early 2000s by Christopher Fuchs and Rüdiger Schack, in collaboration with Carlton Caves.^[2]^[3] While QBism uses personalist probability inspired by de Finetti and Ramsey, it has grown into its own framework, with conceptual commitments far beyond classical Bayesianism. As QBism developed, several early ideas that initially guided its direction were later found to require substantial reinterpretation—a point highlighted by Stacey in 2019.^[4]

Fuchs and Schack continued to develop the interpretation in the years that followed reflecting a distinct shift in emphasis and direction^[5]. QBism is also deeply connected to quantum information theory, which has played a crucial role in shaping its conceptual and technical development^[6]. Over time, QBism has expanded beyond its original scope, exploring whether the nature of the physical world aligns with philosophical perspectives such as pragmatism, pluralism, non-reductionism, and meliorism. QBism is both philosophically grounded and mathematically active. A major thread of research, largely pursued by Fuchs, investigates how quantum theory can be reformulated in explicitly probabilistic terms through symmetric informationally complete (SIC) measurements. In this setting, the Born Rule forms a normative relation among an agent’s probability assignments referred to as the Urgleichung, from the German for primal equation^[6] because of the central role it plays in their reconstruction of quantum theory.THIS IS BLAKE'S, MAKE SURE TO CITE IT CORRECTLY

The Tenets of QBism

Fuchs presents eight key tenets that define QBism's foundational principles, offering a clear framework for understanding how it diverges from other interpretations of quantum mechanics^[7]. These tenets emphasize the role of an agent in shaping quantum theory, rejecting the idea of a universal quantum state in favor of a perspective where reality emerges through an agent's interactions with their external world. QBism presents a profoundly participatory and interactive interpretation in which the universe is not a passive entity governed by fixed laws but an evolving domain shaped by each agent's actions and inquiries.^[8]

1. A Quantum State is an Agent’s Personal Judgment

A quantum state does not describe an intrinsic property of a system but rather reflects an agent’s personal expectations regarding future experiences. The state is assigned by an agent based on their knowledge and is not a universally shared truth. Different agents can assign different quantum states to the same system without contradiction. The key implication is that quantum states are not ontic but epistemic.^[4] This perspective contrasts with interpretations that treat the wave function as an objective physical entity.

2. A Quantum Measurement is an Agent’s Action Upon Their External World

In QBism, a quantum measurement is an agent's interaction with their external world rather than passively observing pre-existing properties. A measurement is an agent's action based on their expectations, not a passive retrieval of pre-existing information.^[1] It is an active gamble, where the outcome is not predetermined but arises through the agent’s interaction with the world. This perspective differs from other interpretations, which often treat measurement as revealing objective features of a system.

"What makes an action specifically "quantum" is when it is worth the agent's while to analyze her expectations for its outcomes in terms of the quantum formalism."^[7]
— Christopher A. Fuchs

3. Measurement Outcomes Are Personal to the Agent

In QBism, measurement outcomes are personal events that arise from an agent's interaction with the world rather than objective, pre-existing properties of a system. Unlike traditional interpretations, where measurement outcomes are seen as absolute facts, QBism insists they are specific to the agent who performed the measurement. Fuchs emphasizes that "quantum measurements give rise to new creation within the universe," meaning that outcomes are not merely discovered but brought into existence through the agent's engagement with the system.^[8]

4. The Quantum Formalism is Normative Rather than Descriptive

In QBism, the mathematical framework of quantum mechanics does not describe an objective reality independent of the observer. Instead, it serves as a normative tool, guiding agents in updating their expectations and making decisions when interacting with the world. This is in contrast to descriptive interpretations, which assume that quantum mechanics reveals an agent-independent structure of reality.^[1] The Born rule exemplifies this normative role. Rather than being a law that dictates how nature is, it provides a rule for how an agent should coherently update their probabilities when making predictions about measurement outcomes. In this sense, the quantum formalism functions much like Bayesian probability theory^[9]. It does not uncover "true" properties of a system but instead prescribes how an agent should assign and revise their beliefs to remain internally consistent.^[10] This perspective shifts quantum mechanics' focus from being a theory about the world "as it is" to an agent-centric framework that refines an agent’s expectations. Just as probability theory does not tell us what will happen but only how to reason about uncertainty, quantum mechanics, in QBism, tells agents how to manage their expectations when making choices and taking actions in a world where direct knowledge is limited.

5. Unitary Evolution Expresses an Agent’s Degrees of Belief

In QBism, unitary evolution is not seen as an objective, fixed law of nature but as a subjective tool that agents use to model their expectations about a system's behavior. Just like other elements of quantum mechanics, it reflects the agent's personal beliefs and knowledge rather than representing an ontic property of the system. In traditional quantum mechanics, however, unitary evolution (as described by the Schrödinger equation) is viewed as a fundamental, deterministic law that governs the quantum state of a system over time, independent of the observer.

6. Even Probability-1 Assignments are Judgments

Probability-1 Assignments are judgments without ontic content. In QBism, even when an agent assigns probability 1 to an outcome, this does not mean the event has an absolute existence independent of the agent. It simply reflects the agent's total confidence in their prediction. This is an important distinction from classical realism, where probability 1 is often taken to mean that an event must happen in an objective sense. In QBism, a probability-1 assignment remains part of the agent's subjective belief system and does not imply the existence of predetermined outcomes.

7. Subjective Certainty Does Not Imply Pre-Existing Outcomes

If a measurement is not carried out, then it simply has no outcome—there is no hidden value that existed beforehand. QBism rejects the idea that quantum mechanics describes a pre-existing reality independent of observation. This principle is embedded in the use of the Born rule instead of the classical Law of Total Probability. The Born rule does not allow for the assumption that unperformed measurements have definite results, reinforcing the idea that measurement outcomes are not pre-existing properties of a system but are brought into existence through the act of measurement itself.^[11] This tenet distinguishes QBism from interpretations like Many-Worlds, where all possible outcomes are assumed to exist in parallel. In QBism, unobserved outcomes are simply non-existent.

8. Quantum Theory is a Single-User Theory for Each Agent.

QBism emphasizes that quantum mechanics is inherently subjective. It does not provide a universal, observer-independent account of reality. Instead, it is a framework that each agent uses individually to manage their expectations and make decisions. Every agent assigns their quantum states, performs a measurements, and experiences their own outcomes. While agents can communicate and compare results, their experiences remain fundamentally subjective.^[12]

Foundational Breakthroughs

QBists work with a subjectivist notion of probability, following de Finetti's axioms and emphasizing Dutch-book coherence as a rationality criterion. This demand ensures that one can derive the standard rules for working with probabilities as normative guides for agents placing bets in a non-classical world. QBists developed a formalism that allows them to substitute probability distributions over the outcomes of reference specified by informationally complete measurements. In doing so, they treat probabilities as density matrices and quantum states as expressions of belief. QBists developed a formalism that allows them to substitute probability distributions over the outcomes of reference devices specified by informationally complete measurements. In doing so, they treat probabilities as density matrices and quantum states as expressions of belief. Within this framework, the Born rule is not regarded as a law of nature that dictates which outcomes will occur but rather as a normative rule—a constraint an agent adopts to maintain internal coherence among their personal probabilistic expectations. It relates the agent's probability assignments for the outcomes of an informationally complete reference measurement to their assignments for the outcomes of any other potential measurement.

Christopher Fuchs began exploring the conceptual and mathematical significance of symmetric informationally complete positive operator-valued measures (SIC-POVMs) well before their formal introduction in 2004.^[13] His early work into SICs emerged in a broader effort to recast quantum theory in explicitly probabilistic terms, an approach that would later define the QBist research program. Building on these initial reflections, a 2004 ^[14] collaboration with Joseph Renes, Robin Blume-Kohout, and A. Scott, which provided a formal mathematical treatment of SIC-POVMs and introduced them more broadly to the quantum information community. This early work played a crucial role in establishing the mathematical structure of SIC-POVMs and drawing attention to their foundational implications for quantum theory. It helped motivate a research program in which quantum states are represented through probability assignments associated with a chosen SIC-POVM, enabling the Born rule to be reformulated within QBism as a normative constraint on an agent's expectations. Ongoing research continues to expand the role of SICs, both in exploring the conceptual foundations of quantum mechanics and in addressing open mathematical questions related to their existence and structure.

SIC-POVM

SICs (Symmetric Informationally Complete quantum measurements) play a fundamental role in QBism^[15]. They provide a way to formulate quantum mechanics that fully aligns with the interpretation's emphasis on subjective probabilities while preserving the formal mathematical structure of the theory.^[7]

That is, if one expresses a density matrix as a probability distribution over the outcomes of a SIC-POVM experiment, one can reproduce all the statistical predictions implied by the density matrix from the SIC-POVM probabilities instead. The Born rule then takes the role of relating one valid probability distribution to another, rather than of deriving probabilities from something apparently more fundamental. Fuchs, Schack, and others have taken to calling this restatement of the Born rule the urgleichung, from the German for "primal equation" (see Ur- prefix), because of the central role it plays in their reconstruction of quantum theory.this is Blakes quote Cite it correctly

Comparisons with Other Interpretations

Copenhagen Interpretation

QBism builds on the role of measurement but makes observer-dependence explicit. INCOMPLETE!!!

Relational Quantum Mechanics

QBism and Relational Quantum Mechanics (RQM)^[16] are often compared as interpretations that rethink the foundations of quantum mechanics. However, despite some superficial similarities, their ontological principles diverge significantly. Comparisons between them are often drawn to highlight the fact that both interpretations reject a universal wave function, emphasize measurement outcomes as an active process, and neither treat quantum states as intrinsic properties of a system. However, despite this similarities, there are ontological subtleties that need to be considered. These similarities have been taken loosely, and through a broad approach to both interpretations.

RQM adopts a relational ontology in which quantum states and measurement outcomes are facts—definite outcomes relative to a given system. QBism rejects the idea that quantum mechanics describes external reality. Instead, QBism interprets quantum mechanics with a normative approach, taking it as a manual for guiding an agent's experiences in the world without assuming that measurement outcomes exist independently of the agent experiencing them.^[7] For QBism, measurements are actions made by an agent, and its outcome is an experience personal to that agent, not a pre-existing fact revealed by an interaction. This contrast extends to quantum states. RQM treats them as informational tools—epistemic but intersubjective, conditioned by prior interactions.^[10] QBism radicalizes the epistemic view by treating quantum states as personal degrees of belief, reflecting an agent's expectations about their own actions.

In this framework, QBism takes a co-creational approach, an agent is defined as an entity capable of experiencing and updating its beliefs in response to new information, a criterion that excludes inanimate objects like electrons or rocks.^[10] In contrast, RQM considers interactions between any two physical systems, treating all measurement events as relational facts, regardless of whether the interacting systems have any notion of experience or belief. While both interpretations challenge classical objectivity, QBism uniquely emphasizes the participatory role of the agent in shaping their reality, making measurement an act of creation rather than revelation.^[17]

Many-Worlds Interpretation

QBism rejects the need for branching universes. While agents can communicate and compare results, their experiences remain fundamentally subjective, Contrasting with interpretations like the Many-Worlds or objective-collapse theories, which treat the wave function as a universal, observer-independent entity. INCOMPLETE!!!

Bohmian Mechanics

Unlike Bohmian mechanics, QBism does not rely on hidden variables. INCOMPLETE!!!

Criticism

INCOMPLETE BUT DO WE REALLY WANT THIS?!?!

Notes

YEAH I DON'T KNOW WHAT HAPPEND HERE...

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References

^ ^a ^b ^c ^d Fuchs, Christopher A.; Stacey, Blake C. (2016). "QBism: Quantum Theory as a Hero's Handbook". arXiv preprint. arXiv:1612.07308.
^ ^a ^b Caves, C. M.; Fuchs, C. A.; Schack, R. (2001). "Quantum probabilities as Bayesian probabilities". arXiv:quant-ph/0106133.
^ ^a ^b Fuchs, Christopher A.; Schack, Rüdiger (2019). "Quantum Bayesianism (QBism)". Stanford Encyclopedia of Philosophy. The Metaphysics Research Lab, Stanford University. Retrieved 2025-03-17.
^ ^a ^b ^c Stacey, B. C. (2019). "Ideas Abandoned en Route to QBism". arXiv preprint. arXiv:1911.07386.
^ ^a ^b Mermin, N. D. (2014). "Why QBism is not the Copenhagen interpretation and what John Bell might have thought of it". arXiv preprint. arXiv:1409.2454.
^ ^a ^b ^c Fuchs, C. A.; Schack, R. (2009). "A Quantum-Bayesian Route to Quantum-State Space". arXiv:0912.4252. A bot will complete this citation soon. Click here to jump the queue
^ ^a ^b ^c ^d ^e Fuchs, C. A. (2023). "QBism, Where Next?". arXiv preprint. arXiv:2303.01446.
^ ^a ^b ^c Fuchs, C. A. (2016). "On Participatory Realism". arXiv preprint. arXiv:1601.04360.
^ ^a ^b Stacey, B. C. (2022). "The Status of the Bayes Rule in QBism". arXiv:2210.10757. A bot will complete this citation soon. Click here to jump the queue
^ ^a ^b ^c ^d Pienaar, J. L. (2021). "QBism and Relational Quantum Mechanics compared". arXiv preprint. arXiv:2108.13977.
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^ ^a ^b Schack, R. (2023). "When will two agents agree on a quantum measurement outcome? Intersubjective agreement in QBism". arXiv preprint. arXiv:2312.07728.
^ ^a ^b Fuchs, C. A. (2002). "Quantum Mechanics as Quantum Information (and only a little more)". arXiv:quant-ph/0205039.
^ ^a ^b Renes, J. M.; Blume-Kohout, R.; Scott, A. J.; Fuchs, C. A. (2004). "Symmetric Informationally Complete Quantum Measurements". arXiv:quant-ph/0310075.
^ ^a ^b Stacey, Blake C. (2021). A First Course in the Sporadic SICs. Springer. ISBN 978-3-030-76103-5.
^ ^a ^b Rovelli, Carlo (1996). "Relational Quantum Mechanics". arXiv preprint. arXiv:quant-ph/9609002.
^ ^a ^b Pienaar, J. L. (2021). "A quintet of quandaries: five no-go theorems for Relational Quantum Mechanics". arXiv preprint. arXiv:2107.00670.
^ DeBrota, J. B.; Fuchs, C. A.; Schack, R. (2024). "Quantum Dynamics Happens Only on Paper: QBism's Account of Decoherence". arXiv preprint. arXiv:2312.14112.
^ Fuchs, C. A.; Olshanii, M.; Weiss, M. B. (2022). "Quantum mechanics? It's all fun and games until someone loses an i". arXiv preprint. arXiv:2206.15343.
^ Piera, R. S.; DeBrota, J. B.; Weiss, M. B.; Lemos, G. B.; Araújo, J. S.; Aguilar, G. H.; Pienaar, J. L. (2024). "Synthesizing the Born rule with reinforcement learning". arXiv preprint. arXiv:2404.19011.
^ Stacey, B. C. (2019). "Sporadic SICs and Exceptional Lie Algebras". arXiv:1911.05809. A bot will complete this citation soon. Click here to jump the queue
^ Fuchs, C. A.; Stacey, B. C. (2020). "QBians Do Not Exist". arXiv:2012.14375. A bot will complete this citation soon. Click here to jump the queue
^ Fuchs, Christopher A. (2015). Blake C. Stacey (ed.). My Struggles with the Block Universe: Selected Correspondence, January 2001 – May 2011 (PDF). Self-published manuscript, available via the author’s homepage and institutional repositories.