Quantum Encoding and Entanglement in Terms of Phase Operators Associated with Harmonic Oscillator

• Published in: International journal of theoretical physics Vol. 55; no. 10; pp. 4393 - 4405
• Main Authors: Singh, Manu Pratap, Rajput, B. S.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.10.2016; Springer Nature B.V
• Subjects: Anomalies; Coding; Elementary Particles; Mathematical and Computational Physics; Operators; Oscillators; Physics; Physics and Astronomy; Quantum entanglement; Quantum Field Theory; Quantum Physics; Quantum theory; Representations; Theoretical; Transformations; Qudit quantum computation; Semi-Unitary Transformation (SUT); Analytic index; Quantum anomalies; Phase operators; Maximally Entangled States (MES); Harmonic oscillator
• ISSN: 0020-7748; 1572-9575
• DOI: 10.1007/s10773-016-3062-3

Realization of qudit quantum computation has been presented in terms of number operator and phase operators associated with one-dimensional harmonic oscillator and it has been demonstrated that the representations of generalized Pauli group, viewed in harmonic oscillator operators, allow the qudits to be explicitly encoded in such systems. The non-Hermitian quantum phase operators contained in decomposition of the annihilation and creation operators associated with harmonic oscillator have been analysed in terms of semi unitary transformations (SUT) and it has been shown that the non-vanishing analytic index for harmonic oscillator leads to an alternative class of quantum anomalies. Choosing unitary transformation and the Hermitian phase operator free from quantum anomalies, the truncated annihilation and creation operators have been obtained for harmonic oscillator and it has been demonstrated that any attempt of removal of quantum anomalies leads to absence of minimum uncertainty.