Discrete phase-space structures and Wigner functions for N qubits

Muñoz, Claudio; Klimov, A. B.; Sánchez-Soto, Luis L.

doi:10.1007/s11128-017-1607-x

Cited by 6 publications

(4 citation statements)

References 43 publications

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“…In view of the term in the matrix element of the Weyl operator (16) and the term with the Dirac delta-function in (17), after integrating in (15) over variable y , we arrive at the result…”

Section: Quantum State Description By Probability Distribution For Thmentioning

confidence: 99%

“…The tomographic probability distributions of spin states were discussed in [14][15][16]. We point out that different representations-like the Wigner function representation for the system states with discrete variables based on using the formalism of the quantizer operators-were studied in [17][18][19][20]. Gauge invariance of quantum mechanics in the probability representation was studied in [21].…”

Section: Introductionmentioning

confidence: 99%

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Probability Representation of Quantum Mechanics Where System States Are Identified with Probability Distributions

2020

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The probability representation of quantum mechanics where the system states are identified with fair probability distributions is reviewed for systems with continuous variables (the example of the oscillator) and discrete variables (the example of the qubit). The relation for the evolution of the probability distributions which determine quantum states with the Feynman path integral is found. The time-dependent phase of the wave function is related to the time-dependent probability distribution which determines the density matrix. The formal classical-like random variables associated with quantum observables for qubit systems are considered, and the connection of the statistics of the quantum observables with the classical statistics of the random variables is discussed.

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“…In view of the term in the matrix element of the Weyl operator (16) and the term with the Dirac delta-function in (17), after integrating in (15) over variable y , we arrive at the result…”

Section: Quantum State Description By Probability Distribution For Thmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Probability Representation of Quantum Mechanics Where System States Are Identified with Probability Distributions

2020

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“…However, this property breaks down in the case of qubit systems [19,20,30]. The main reason for the loss of tomographic universality in n-qubit systems is the inequivalence among Wigner maps based on different sets of stabilizers [28,32]. This leads to the following question: is it possible for the DWF of an element of a stabilizer basis to take on the form of a delta function if that basis is not used for the construction of a Wigner map?…”

Section: Introductionmentioning

confidence: 99%

Tomographic Universality of the Discrete Wigner Function

Sainz,

Camacho,

García

et al. 2024

Quantum Reports

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We observe that the discrete Wigner functions (DWFs) of n-partite systems with odd local dimensions are tomographically universal, as reflected in the delta function form of the DWF for any stabilizer. However, in the n-qubit case, this property does not hold due to the non-factorization of the mapping kernel, the explicit form of which depends on a particular partition of the discrete phase space. Nonetheless, it turns out that the DWF for some specific stabilizers, not included in the set used for the construction of the Wigner map, takes on the form of a delta function. This implies that the possibility of classical simulations of Pauli measurements in a given stabilizer state for qubit systems is closely tied to the experimental setup.

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“…The idea of the phase-space formalism can be extended to finite dimensional quantum systems used in quantum information processing. Finding either a complete, continuous Wigner function [22][23][24] or discrete Wigner functions having the same essential properties as their continuous counterparts [25][26][27][28][29][30][31][32][33] for such systems is still a subject of investigations.…”

Section: Introductionmentioning

confidence: 99%

Star Product Formalism for Probability and Mean Value Representations of Qudits

Ádám¹,

Andreev²,

Man’ko³

et al. 2019

Preprint

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The quantizer-dequantizer formalism is developed for mean value and probability representation of qubits and qutrits. We derive the star-product kernels providing the possibility to derive explicit expressions of the associative product of the symbols of the density operators and quantum observables for qubits. We discuss an extension of the quantizer-dequantizer formalism associated with the probability and observable mean-value descriptions of quantum states for qudits.

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Discrete phase-space structures and Wigner functions for N qubits

Cited by 6 publications

References 43 publications

Probability Representation of Quantum Mechanics Where System States Are Identified with Probability Distributions

Probability Representation of Quantum Mechanics Where System States Are Identified with Probability Distributions

Tomographic Universality of the Discrete Wigner Function

Star Product Formalism for Probability and Mean Value Representations of Qudits

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