Physical realizations of quantum operations

Abstract

Quantum operations (QO) describe any state change allowed in quantum mechanics, such as the evolution of an open system or the state change due to a measurement. We address the problem of which unitary transformations and which observables can be used to achieve a QO with generally different input and output Hilbert spaces. We classify all unitary extensions of a QO, and give explicit realizations in terms of free-evolution direct-sum dilations and interacting tensor-product dilations. In terms of Hilbert space dimensionality the free-evolution dilations minimize the physical resources needed to realize the QO, and for this case we provide bounds for the dimension of the ancilla space versus the rank of the QO. The interacting dilations, on the other hand, correspond to the customary ancilla-system interaction realization, and for these we derive a majorization relation which selects the allowed unitary interactions between system and ancilla.

8 pages, no figures. Accepted for publication on Phys. Rev. A

References in corpus (2)

• Optimal realization of the transposition maps
• Unitary realizations of the ideal phase measurement

Cited by in corpus (18)

• Quantum stochastic processes and quantum non-Markovian phenomena
• A quantum algorithm for evolving open quantum dynamics on quantum computing devices
• Economical Phase-Covariant Cloning of Qudits
• Equivalence between divisibility and monotonic decrease of information in classical and quantum stochastic processes
• The modern tools of quantum mechanics (A tutorial on quantum states, measurements, and operations)
• Covariant quantum measurements which maximize the likelihood
• Implementation of quantum operations on single photon qudits
• On the minimum number of unitaries needed to describe a random-unitary channel
• A general approach to physical realization of unambiguous quantum-state discrimination
• Interpreting quantum coherence through a quantum measurement process
• Convex approximations of quantum channels
• Universal and phase covariant superbroadcasting for mixed qubit states
• Phase-covariant cloning of coherent states
• Protecting quantum correlations in presence of generalised amplitude damping channel: the two-qubit case
• Ancilla models for quantum operations: For what unitaries does the ancilla state have to be physical?
• Economical realization of phase covariant devices in arbitrary dimensions
• Optimal Time-Reversal of Multi-phase Equatorial States
• Quantum State Preparation and Non-Unitary Evolution with Diagonal Operators