Single photon quantum filtering using non-Markovian embeddings

Abstract

We determine quantum master and filter equations for continuous measurement of systems coupled to input fields in certain non-classical continuous-mode states, specifically single photon states. The quantum filters are shown to be derivable from an embedding into a larger non-Markovian system, and are given by a system of coupled stochastic differential equations.

Quantum continuous measurements: The stochastic Schrödinger equations and the spectrum of the output

“…The quantum trajectory approach can be generalized to introduce also feedback control with delay, coloured noises, various non-Markovian effects [59][60][61][62][63][64]. The simplest nonMarkovian contribution is to take the laser wave to be random [22,25].…”

“…Let us introduce the formal time derivatives I( ) =Ẇ 1 ( ) andÎ( ) =Q( ; ); from (63) and (64) we obtain immediately the expressions of mean function and autocorrelation function:…”

Principles and applications of quantum control engineering

“…The former can now be generated on demand using state-of-the-art experimental techniques, while the latter correspond to the so-called cat states. The filtering problem for these non-classical states turns out to be tractable, see the contribution of Gough et al [42] in this issue, where one employs an ancilla to extend the filter in an appropriate manner. The role of the ancilla may often be easily understood as a preparation device that takes the vacuum input and feeds out the non-classical field into the system of interest.…”

Quantum trajectories for a system interacting with environment in a single-photon state: Counting and diffusive processes

“…About the methods of its generation and application in quantum of computing and communication one can read in [15][16][17][18][19][20][21][22]. The filtering equation for quantum system interacting with the environment prepared in the single photon state was derived in [23][24][25][26]. The authors of the mentioned papers determined the filters with the aid of embedding of the quantum system into a larger Markovian [23,24] or non-Markovian [25,26] systems.…”

“…The filtering equation for quantum system interacting with the environment prepared in the single photon state was derived in [23][24][25][26]. The authors of the mentioned papers determined the filters with the aid of embedding of the quantum system into a larger Markovian [23,24] or non-Markovian [25,26] systems. In [23,24] the authors used the concept of quantum cascaded system [6] and introduced an ancilla being a source of the Bose field in desired non-classical state.…”