Observations of quantum systems carried out by finite observers who subsequently communicate their results using classical data structures can be described as “local operations, classical communication” (LOCC) observations. The implementation of LOCC observations by the Hamiltonian dynamics prescribed by minimal quantum mechanics is investigated. It is shown that LOCC observations cannot be described using decoherence considerations alone, but rather require the a priori stipulation of a positive operator-valued measure (POVM) about which communicating observers agree. It is also shown that the transfer of classical information from system to observer can be described in terms of system-observer entanglement, raising the possibility that an apparatus implementing an appropriate POVM can reveal the entangled system-observer states that implement LOCC observations.
This paper considers the use of linear state observers to infer the unknown state (density matrix) of a closed quantum system using generalized quantum measurement—positive operator-valued measures (POVMs). An efficient test for observability is described in terms of two quantum observability matrices. The main contribution of this work is the development of a canonical quantum state observer, which may be utilized to estimate the state of any closed quantum system using POVM measurements. The observer ensures the state estimation error tends to the unobservable space of the system, which is exactly zero when the system is observable. The space of Hermitian matrices is shown to be invariant with respect to the dynamics of the canonical observer, which allows one to project the observer's state onto the space of valid quantum density operators while retaining convergence to the true state.
To observe or control a quantum system, one must interact with it via an interface. This article exhibits simple universal quantum interfaces---quantum input/output ports consisting of a single two-state system or quantum bit that interacts with the system to be observed or controlled. It is shown that under very general conditions the ability to observe and control the quantum bit on its own implies the ability to observe and control the system itself. The interface can also be used as a quantum communication channel, and multiple quantum systems can be connected by interfaces to become an efficient universal quantum computer. Experimental realizations are proposed, and implications for controllability, observability, and quantum information processing are explored.