Discrete coherent and squeezed states of many-qudit systems

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

doi:10.1103/physreva.80.043836

Cited by 35 publications

(42 citation statements)

References 76 publications

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“…There are other proposals of discrete bases for finite-dimensional phase spaces in literature, with convenient inherent mathematical properties, which can also be applied in analogous quantum systems [5]. In particular, Klimov and co-workers [22,25] proposed equivalent mathematical expressions of discrete bases for finite state spaces, where they basically showed that discrete Wigner functions depend on the specific phase choice for such bases. So, in Appendix A we present certain interesting aspects of those aforementioned discrete bases and their consequences on the different definitions of discrete Wigner functions.…”

Section: Finite-dimensional Discrete Phase Spacesmentioning

confidence: 99%

On the discrete Wigner function for $\mathrm{SU(N)}$

Marchiolli¹,

Galetti²

2019

J. Phys. A: Math. Theor.

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We present a self-consistent theoretical framework for finite-dimensional discrete phase spaces that leads us to establish a well-grounded mapping scheme between Schwinger unitary operators and generators of the special unitary group SU(N). This general mathematical construction provides a sound pathway to the formulation of a genuinely discrete Wigner function for arbitrary quantum systems described by finite-dimensional state vector spaces. To illustrate our results, we obtain a general discrete Wigner function for the group SU(3) and apply this to the study of a particular three-level system. Moreover, we also discuss possible extensions to the discrete Husimi and Glauber-Sudarshan functions, as well as future investigations on multipartite quantum states.

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Section: Finite-dimensional Discrete Phase Spacesmentioning

confidence: 99%

On the discrete Wigner function for $\mathrm{SU(N)}$

Marchiolli¹,

Galetti²

2019

J. Phys. A: Math. Theor.

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“…In order to create a closed phase space path via displacements on a spin coherent state, it is necessary to take into account the curvature of the phase space as quantified by Eq. (42). However, this is not possible when there are multiple qubits entangled with either quadrature as then different parts of the spin coherent state superposition are different distances from the phase space origin (the north pole).…”

Section: B the Computational Modelmentioning

confidence: 99%

Quantum computation mediated by ancillary qudits and spin coherent states

2015

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Publisher's copyright statement:Reprinted with permission from the American Physical Society: Physical Review A 91, 012308 c (2015) by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modied, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Models of universal quantum computation in which the required interactions between register (computational) qubits are mediated by some ancillary system are highly relevant to experimental realizations of a quantum computer. We introduce such a universal model that employs a d-dimensional ancillary qudit. The ancilla-register interactions take the form of controlled displacements operators, with a displacement operator defined on the periodic and discrete lattice phase space of a qudit. We show that these interactions can implement controlled phase gates on the register by utilizing geometric phases that are created when closed loops are traversed in this phase space. The extra degrees of freedom of the ancilla can be harnessed to reduce the number of operations required for certain gate sequences. In particular, we see that the computational advantages of the quantum bus (qubus) architecture, which employs a field-mode ancilla, are also applicable to this model. We then explore an alternative ancilla-mediated model which employs a spin ensemble as the ancillary system and again the interactions with the register qubits are via controlled displacement operators, with a displacement operator defined on the Bloch sphere phase space of the spin coherent states of the ensemble. We discuss the computational advantages of this model and its relationship with the qubus architecture.

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“…Additional applications to more general dynamical groups have also appeared in the literature [33][34][35][36]. Moreover, the basic notions have been successfully extended to discrete qudits, where the phase space is a finite grid [37][38][39][40][41][42][43].…”

Section: Introductionmentioning

confidence: 99%

Wigner function for SU(1,1)

Seyfarth

Klimov

Guise

et al. 2020

Quantum

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In spite of their potential usefulness, Wigner functions for systems with SU(1,1) symmetry have not been explored thus far. We address this problem from a physically-motivated perspective, with an eye towards applications in modern metrology. Starting from two independent modes, and after getting rid of the irrelevant degrees of freedom, we derive in a consistent way a Wigner distribution for SU(1,1). This distribution appears as the expectation value of the displaced parity operator, which suggests a direct way to experimentally sample it. We show how this formalism works in some relevant examples.Dedication: While this manuscript was under review, we learnt with great sadness of the untimely passing of our colleague and friend Jonathan Dowling. Through his outstanding scientific work, his kind attitude, and his inimitable humor, he leaves behind a rich legacy for all of us. Our work on SU(1,1) came as a result of long conversations during his frequent visits to Erlangen. We dedicate this paper to his memory.

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Discrete coherent and squeezed states of many-qudit systems

Cited by 35 publications

References 76 publications

On the discrete Wigner function for $\mathrm{SU(N)}$

On the discrete Wigner function for $\mathrm{SU(N)}$

Quantum computation mediated by ancillary qudits and spin coherent states

Wigner function for SU(1,1)

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