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Mapping of classical canonical transformations to quantum unitary operators

Fan Hong‐Yi, Jack Vanderlinde

Classical linear transformations in coordinate-momentum phase space are mapped to unitary quantum-mechanical operators in Hilbert space to produce a generalization of squeeze operators. The classical to quantum transition is manifestly apparent in the derivation. The unitary operators are evaluated in the coherent-state representation using the ``integration within ordered products'' technique in the one- and two-mode cases. Application of these operators results in a new generalization of coherent states.Classical linear transformations in coordinate-momentum phase space are mapped to unitary quantum-mechanical operators in Hilbert space to produce a generalization of squeeze operators. The classical to quantum transition is manifestly apparent in the derivation. The unitary operators are evaluated in the coherent-state representation using the ``integration within ordered products'' technique in the one- and two-mode cases. Application of these operators results in a new generalization of coherent states.

Physical Review AMar 1, 198961 citations

UNITARY OPERATORS IN QUANTUM THEORY

IMPERIAL COLLEGE PRESS eBooksSep 1, 19950 citations

Probabilistic unitary quantum channels

Shengjun Wu

Probabilistic unitary maps and probabilistic unitary quantum channels are introduced, many quantum information applications, including (unambiguous) teleportation, can be described as probabilistic unitary quantum channels. Some properties of probabilistic unitary maps and probabilistic unitary quantum channels are derived. The property of a probabilistic unitary quantum channel ensures certain simple form for the measurements involved in realizing the probabilistic unitary quantum channel. The relation between a probabilistic unitary quantum channel and a uniformly entangled state is established. The combined operation of a noisy quantum channel and the error correction operation is a probabilistic unitary channel, from this point of view the condition for the errors to be correctable is easily derived. The condition for the errors caused by a noisy channel to be correctable with any nonzero probability is also obtained. Dense coding with a partially entangled state can also be viewed as a probabilistic unitary quantum channel when all messages are required to be transmitted with equal probability of success, the maximal achievable probability of success is derived and the optimum protocol is also obtained. 1Probabilistic unitary maps and probabilistic unitary quantum channels are introduced, many quantum information applications, including (unambiguous) teleportation, can be described as probabilistic unitary quantum channels. Some properties of probabilistic unitary maps and probabilistic unitary quantum channels are derived. The property of a probabilistic unitary quantum channel ensures certain simple form for the measurements involved in realizing the probabilistic unitary quantum channel. The relation between a probabilistic unitary quantum channel and a uniformly entangled state is established. The combined operation of a noisy quantum channel and the error correction operation is a probabilistic unitary channel, from this point of view the condition for the errors to be correctable is easily derived. The condition for the errors caused by a noisy channel to be correctable with any nonzero probability is also obtained. Dense coding with a partially entangled state can also be viewed as a probabilistic unitary quantum channel when all messages are required to be transmitted with equal probability of success, the maximal achievable probability of success is derived and the optimum protocol is also obtained. 1

Sep 29, 20050 citations

Unitary Operators and Quantum Dynamics

Lev Deych

Springer eBooksJan 1, 20180 citations

A unified approach to Hermitian and Unitary operators

Chandana Roy

Jan 1, 19770 citations

Quantum-Mechanical Unitary Operators Gained via Integrations over a Type of Ket-Bra Operators

Fan Hong-Yi

Applying the technique of integration within ordered product (IWOP) to a type of ket-bra operators which are in integral form in coordinate representation, we derive unitary normally ordered quantum-mechanical images of real symmetric transformations in classical coordinate space, which provide us with a convenient approach to constructing the corresponding coherent states. Some examples showing the physical applications of this kind of unitary images are presented.

Europhysics Letters (EPL)Jan 21, 19922 citations

Some Unitary Operators Derived Using the Quantum State and Its Application

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