Quantum Markov channels for qubits

Daffer, Sonja; Wódkiewicz, K.; McIver, John K.

doi:10.1103/physreva.67.062312

Cited by 61 publications

(72 citation statements)

References 24 publications

(33 reference statements)

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“…The Schrödinger picture equivalent of this model was introduced by Bowen and Mancini in [19] and has been shown to encompass channels with Markovian correlated noise discussed previously in [10,11,14,20]. As advertised in the Introduction, in Section IV we will show that this model is sufficiently general to describe all causal quantum channel, which was left as an open problem in [19].…”

Section: A the Constructive Approachmentioning

confidence: 99%

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Quantum channels with memory

2005

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We present a general model for quantum channels with memory, and show that it is sufficiently general to encompass all causal automata: any quantum process in which outputs up to some time t do not depend on inputs at times t ′ > t can be decomposed into a concatenated memory channel. We then examine and present different physical setups in which channels with memory may be operated for the transfer of (private) classical and quantum information. These include setups in which either the receiver or a malicious third party have control of the initializing memory. We introduce classical and quantum channel capacities for these settings, and give several examples to show that they may or may not coincide. Entropic upper bounds on the various channel capacities are given. For forgetful quantum channels, in which the effect of the initializing memory dies out as time increases, coding theorems are presented to show that these bounds may be saturated. Forgetful quantum channels are shown to be open and dense in the set of quantum memory channels.

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Section: A the Constructive Approachmentioning

confidence: 99%

“…[18,19] and references therein). A Lindbladian approach to memory channels has been taken by Daffer et al [20,21]. Upper bounds on the classical capacity for a more general class of channels have been given recently by Bowen et al [22].…”

Section: B Model Systems and Related Workmentioning

confidence: 99%

Quantum channels with memory

2005

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“…Using damping basis methods [48,49] (details can be found in Appendix A) we find, as per (11)- (13), that the affine map representation M of T (θ k ) t is given by…”

Section: Simulation Of Constituent Semigroupsmentioning

confidence: 99%

“…In order to obtain this convex decomposition we proceed via the following steps: Firstly, we utilise the damping basis [48,49] in order to find the affine map representation of T (θ k ) t . From this affine map representation it is then easy to construct the Jamiolkowski state, from which it is possible to obtain the desired convex decomposition [45].…”

Section: Simulation Of Constituent Semigroupsmentioning

confidence: 99%

Simulation of single-qubit open quantum systems

2014

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A quantum algorithm is presented for the simulation of arbitrary Markovian dynamics of a qubit, described by a semigroup of single qubit quantum channels {Tt} specified by a generator L. This algorithm requires only O (||L|| (1→1) t) 3/2 / 1/2 single qubit and CNOT gates and approximates the channel Tt = e tL up to chosen accuracy . Inspired by developments in Hamiltonian simulation, a decomposition and recombination technique is utilised which allows for the exploitation of recently developed methods for the approximation of arbitrary single-qubit channels. In particular, as a result of these methods the algorithm requires only a single ancilla qubit, the minimal possible dilation for a non-unitary single-qubit quantum channel.

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“…This, in qubit case, corresponds to the choice of representation of the qubit state density operator: the basis of Pauli matrices σ i [1,5] …”

Section: State Descriptionmentioning

confidence: 99%