Simulating a single-qubit channel using a mixed-state environment

Narang, Geetu; Arvind, .

doi:10.1103/physreva.75.032305

Cited by 18 publications

(33 citation statements)

References 21 publications

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“…A number of explicit counterexamples have subsequently disproved the validity of this conjecture [23,24,25]. Interestingly, we find that a version of the above conjecture does hold true, provided that additional classical randomization resources, as well as non-deterministic channel constructions, are allowed (Section 3.3).…”

Section: Arxiv:170401486v1 [Quant-ph] 5 Apr 2017mentioning

confidence: 79%

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Quantum and classical resources for unitary design of open-system evolutions

Ticozzi

Viola

2017

Quantum Sci. Technol.

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Abstract. A variety of tasks in quantum control, ranging from purification and cooling, to quantum stabilization and open-system simulation, rely on the ability to implement a target quantum channel over a specified time interval within prescribed accuracy. This can be achieved by engineering a suitable unitary dynamics of the system of interest along with its environment -which, depending on the available level of control, is fully or partly exploited as a coherent quantum controller. After formalizing a controllability framework for completely positive trace-preserving quantum dynamics, we provide sufficient conditions on the environment state and dimension that allow for the realization of relevant classes of quantum channelsincluding extreme channels, stochastic unitaries, or simply any channel. The results hinge on generalizations of Stinespring's dilation via a subsystem principle. In the process, we show that a conjecture by Lloyd on the minimal dimension of the environment required for arbitrary open-system simulation, albeit formally disproved, can in fact be salvaged -provided that classical randomization is included among the available resources. Existing measurement-based feedback protocols for universal simulation, dynamical decoupling, and dissipative state preparation are recast within the proposed coherent framework as concrete applications, and the resources they employ discussed in the light of the general results.

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Section: Arxiv:170401486v1 [Quant-ph] 5 Apr 2017mentioning

confidence: 79%

“…However, this conjecture has been proven wrong in Refs. [23,24,25]: one may explicitly identify CPTP maps that need a larger (at least d S + 1 dimensional) ancilla in order to be implemented via unitary design as in Eq. (3).…”

Section: Probabilistic Unitary Designmentioning

confidence: 99%

Quantum and classical resources for unitary design of open-system evolutions

Ticozzi

Viola

2017

Quantum Sci. Technol.

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“…The set of unistochastic maps, denoted by U Q N , forms a proper subset of the set B Q N of bistochastic maps. In the one-qubit case, the set of bistochastic maps forms the tetrahedron of Pauli channels Φ ⃗ p , while U Q 2 , forms its non-convex subset, bounded by ruled surfaces [19,42] and called Steinhaus tetrahedron [43] -see Fig. 1 and ref.…”

Section: Bistochastic Quantum Maps and Classical Bistochastic Matricesmentioning

confidence: 99%

Log-Convex set of Lindblad semigroups acting on $N$-level system

Shahbeigi,

Amaro-Alcalá,

Puchała

et al. 2020

Preprint

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We analyze the set A Q N of mixed unitary channels represented in the Weyl basis and accessible by a Lindblad semigroup acting on an N -level quantum system. General necessary and sufficient conditions for a mixed Weyl quantum channel of an arbitrary dimension to be accessible by a semigroup are established. The set A Q N is shown to be log-convex and star-shaped with respect to the completely depolarizing channel. A decoherence supermap acting in the space of Lindblad operators transforms them into the space of Kolmogorov generators of classical semigroups. We show that for mixed Weyl channels the hyper-decoherence commutes with the dynamics, so that decohering a quantum accessible channel we obtain a bistochastic matrix form the set A C N of classical maps accessible by a semigroup. Focusing on 3-level systems we investigate the geometry of the sets of quantum accessible maps, its classical counterpart and the support of their spectra. We demonstrate that the set A Q 3 is not included in the set U Q 3 of quantum unistochastic channels, although an analogous relation holds for N = 2. The set of transition matrices obtained by hyper-decoherence of unistochastic channels of order N ≥ 3 is shown to be larger than the set of unistochastic matrices of this order, and yields a motivation to introduce the larger sets of k-unistochastic matrices.

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“…Furthermore, recently, Ref. [16] has shown that only 3/8 of the generalized depolarizing channels can be simulated by the one-qubit mixedstate environment.…”

Section: Introductionmentioning

confidence: 99%

Amplitude damping for single-qubit system with single-qubit mixed-state environment

Jung

Hwang

et al. 2008

J. Phys. A: Math. Theor.

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We study a generalized amplitude damping channel when environment is initially in the singlequbit mixed state. Representing the affine transformation of the generalized amplitude damping by a three-dimensional volume, we plot explicitly the volume occupied by the channels simulatable by a single-qubit mixed-state environment. As expected, this volume is embedded in the total volume by the channels which is simulated by two-qubit enviroment. The volume ratio is approximately 0.08 which is much smaller than 3/8, the volume ratio for generalized depolarizing channels.

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Simulating a single-qubit channel using a mixed-state environment

Cited by 18 publications

References 21 publications

Quantum and classical resources for unitary design of open-system evolutions

Quantum and classical resources for unitary design of open-system evolutions

Log-Convex set of Lindblad semigroups acting on $N$-level system

Amplitude damping for single-qubit system with single-qubit mixed-state environment

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