Failure of Standard Quantum Mechanics for the Description of Compound Quantum Entities

Aerts, Diederik; Valckenborgh, Frank

doi:10.1023/b:ijtp.0000028862.91652.98

Cited by 7 publications

(4 citation statements)

References 21 publications

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“…For the compound system in the quantum limit tests along non orthogonal measurement directions are always compatible but not separable. Therefore, these tests and a fortiori the subsystems are not separated, which is in agreement with previous results stating that separated quantum entities cannot be described in quantum theory [1,2,4,23,24,25]. For intermediate values of the parameter we found that all tests are compatible, but they are only separable if θ u1u2 = π 2 .…”

Section: Discussionsupporting

confidence: 91%

“…For the example of the connected vessels of water it is clear that the considered tests cannot be separated because of the clear physical connection between the two vessels. For entangled quantum systems we encounter non-separated tests in a natural way (actually it is not possible to describe a compound system of two separated quantum systems within the formalism of quantum theory [1,2,4,23,24,25]), but the origin of this quantum non-separability is still a matter of debate for physicists and philosophers alike. To shed more light on this issue, we discuss in the next section a macroscopic model of a compound system of two entangled spin 1/2 in the singlet state, in which tests are defined by a parameter reflecting randomness in the measurement such that we obtain a continuous transition from a quantum system to a classical system, and check what happens with separability and compatibility for these systems.…”

Section: Classicalitymentioning

confidence: 99%

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Compatibility and Separability for Classical and Quantum Entanglement

Aerts

Ronde

D’Hooghe

2011

Worldviews, Science and Us

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We study the concepts of compatibility and separability and their implications for quantum and classical systems. These concepts are illustrated on a macroscopic model for the singlet state of a quantum system of two entangled spin 1/2 with a parameter reflecting indeterminism in the measurement procedure. By varying this parameter we describe situations from quantum, intermediate to classical and study which tests are compatible or separated. We prove that for classical deterministic systems the concepts of separability and compatibility coincide, but for quantum systems and intermediate systems these concepts are generally different.

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Section: Discussionsupporting

confidence: 91%

Section: Classicalitymentioning

confidence: 99%

Compatibility and Separability for Classical and Quantum Entanglement

Aerts

Ronde

D’Hooghe

2011

Worldviews, Science and Us

Self Cite

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“…the quantum axioms are violated. 15,16 This also sheds new light on the claims of EPR, namely that quantum mechanics is incomplete. This is true, but in a slightly different way: if separated quantum systems do exist, then the corresponding compound system cannot be described by quantum mechanics.…”

Section: When Quantum Axioms Break Down I: Separated Quantum Entitiesmentioning

confidence: 88%

On the Orthocomplementation of State-Property-Systems of Contextual Systems

D’Hooghe

2014

Probing the Meaning of Quantum Mechanics

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We describe a model in which the maximal change of state of the system due to interaction with the measurement context is controlled by a parameter which corresponds with the number N of possible outcomes in an experiment. In the limit N = 2 the system reduces to a model for the spin measurements on a quantum spin-1 2 particle. This model fits in the hidden measurement approach to quantum mechanics in which quantum probabilities are explained as due to an uncontrollable fluctuation in the measurement process. In the limit N → ∞ the system is classical, i.e. the experiments are deterministic and its set of properties is a Boolean lattice. For intermediate situations the change of state due to measurement is neither 'maximal' (i.e. quantum) nor 'zero' (i.e. classical). We show that two of the axioms used in Piron's representation theorem for quantum mechanics are violated, namely the covering law and weak modularity. Next, we discuss a modified version of the model for which it is even impossible to define an orthocomplementation on the set of properties. Another interesting feature for the intermediate situations of this model is that the probability of a state transition in general not only depends on the angular distance between the two states but also on the measurement context which induces the state transition. Therefore our models also shed new light on Gleason's theorem and suggest that transition probability maybe is not a secondary concept which can be derived from the structure on the set of states and properties, but instead should be regarded as a primitive concept by its own right for which the measurement context is crucial.

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“…It is important to notice that the result of this theorem points at a failure of standard quantum mechanics, and is not just a characteristic of the axiomatic approach itself. Indeed, one can show that the structure on the set of states and set of properties of a compound system of two separated systems does not fit in Hilbert space, i.e., the quantum axioms are violated [25,26]. This also sheds new light on the claims of EPR, namely that quantum mechanics is incomplete.…”

Section: Two Entangled Qubits 51 Description Of Compound Systemsmentioning

confidence: 99%

Macroscopic models for quantum systems and computers

Aerts

Czachor

Dehaene

et al. 2007

J. Phys.: Conf. Ser.

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We present examples of macroscopic systems entailing a quantum mechanical structure. One of our examples has a structure which is isomorphic to the spin structure for a spin 1/2 and another system entails a structure isomorphic to the structure of two spin 1/2 in the entangled singlet state. We elaborate this system by showing that an arbitrary tensor product state representing two entangled qubits can be described in a complete way by a specific internal constraint between the ray or density states of the two qubits, which describes the behavior of the state of one of the spins if measurements are executed on the other spin. Since any n-qubit unitary operation can be decomposed into 2-qubit gates and unary operations, we argue that our representation of 2-qubit entanglement contributes to a better understanding of the role of n-qubit entanglement in quantum computation. We illustrate our approach on two 2-qubit algorithms proposed by Deutsch, respectively Arvind et al. One of the advantages of the 2-qubit case besides its relative simplicity is that it allows for a nice geometrical representation of entanglement, which contributes to a more intuitive grasp of what is going on in a 2-qubit quantum computation.

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Failure of Standard Quantum Mechanics for the Description of Compound Quantum Entities

Cited by 7 publications

References 21 publications

Compatibility and Separability for Classical and Quantum Entanglement

Compatibility and Separability for Classical and Quantum Entanglement

On the Orthocomplementation of State-Property-Systems of Contextual Systems

Macroscopic models for quantum systems and computers

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