Unitary quantum gates, perfect entanglers, and unistochastic maps

Musz, Marcin; Kuś, Marek; Życzkowski, Karol

doi:10.1103/physreva.87.022111

Cited by 45 publications

(53 citation statements)

References 57 publications

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“…Altough this set is not convex, it is star-shaped. Since this set contains unistochastic channels [26], which correspond to the coupling with a one-qubit environment initially in the maximally mixed state [23], we conclude that every map accessible through the continuous semigroup is unitarily equivalent to a unistochastic channel.…”

Section: Discussionmentioning

confidence: 83%

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Pauli semigroups and unistochastic quantum channels

2019

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We adopt the perspective of similarity equivalence, in gate set tomography called the gauge, to analyze various properties of quantum operations belonging to a semigroup, Φ = e Lt , and therefore given through the Lindblad operator. We first observe that the non unital part of the channel decouples from the time evolution. Focusing on unital operations we restrict our attention to the single-qubit case, showing that the semigroup embedded inside the tetrahedron of Pauli channels is bounded by the surface composed of product probability vectors and includes the identity map together with the maximally depolarizing channel. Consequently, every member of the Pauli semigroup is unitarily equivalent to a unistochastic map, describing a coupling with one-qubit environment initially in the maximally mixed state, determined by a unitary matrix of order four. * Electronic address: z.puchala@iitis.pl

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Section: Discussionmentioning

confidence: 83%

“…Consider a unistochastic channel Φ U determined by a unitary U ∈ U (4). The corresponding Choi matrix can be written with use of the reshuffled matrix, D U = 1 2 U R (U R ) † , so that the superoperator reads [26],…”

Section: Dynamical Semigroups and Unistochastic Mapsmentioning

confidence: 99%

Pauli semigroups and unistochastic quantum channels

2019

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“…The operator exp(i π 4 σ x 1 σ x 2 ) is the Cartan form of a controlled-NOT (CNOT) gate [25,26]. Thus we can represent and implement quite simply the evolution operator as a quantum circuit composed of CNOT gates and one-qubit gates Z i = e −i π 4 σ z i , as shown in Fig.…”

Section: Modelmentioning

confidence: 99%

Protocol using kicked Ising dynamics for generating states with maximal multipartite entanglement

Mishra

Lakshminarayan²,

Subrahmanyam³

2015

Phys. Rev. A

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We present a solvable model of iterating cluster state protocols that lead to entanglement production, between contiguous blocks, of 1 ebit per iteration. This continues until the blocks are maximally entangled, at which stage an unravelling begins at the same rate until the blocks are unentangled. The model is a variant of the transverse-field Ising model and can be implemented with controlled-NOT and single-qubit gates. The interqubit entanglement as measured by the concurrence is shown to be zero for periodic chain realizations, while for open boundaries there are very specific instances at which these can develop. Thus we introduce a class of simply produced states with very large multipartite entanglement content of potential use in measurement-based quantum computing.

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“…One can reshape the U i to make it transformed into a vector with d 2 components as that made in [17]. If d reshaped U i vectors span a κ -dimensional subspace in the d 2 -dimensional Hilbert-Schmidt space, the upper bounds of EC E and EC l for the uniformly controlled-U gate (7) are log 2 κ and 1 − 1/κ , respectively, for both with and without ancillas.…”

Section: Preliminary and Upper Bound For Ec Of Two-qudit Gatesmentioning

confidence: 99%

“…Entanglement states can be generated from disentangled states by the action of a nonlocal quantum operation (i.e., quantum gate). Consequently, considerable efforts have been made to characterize the efficacy of quantum gate to generate entanglement [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Of particular importance is the maximum amount of entanglement that a quantum gate can generate for some set of initial states.…”

Section: Introductionmentioning

confidence: 99%

Entangling capability of multivalued bipartite gates and optimal preparation of multivalued bipartite quantum states

Wei

Cao

et al. 2015

Quantum Inf Process

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We investigate the entangling capability of various types of two-qudit gates in both the no-ancilla case and the ancilla-assisted case. The investigation involves controlled U gates, uniformly controlled U gates and some high-rank two-qudit gates. The optimal input states for these gates to generate entanglement are also given. By comparison of some important two-qudit gates, the generalized controlled X (GCX) gate shows the excellent properties. Based on the GCX gate, we study the preparation of arbitrary two-qudit quantum states and the transformation of such states. Any twoqudit state with Schmidt number k can be prepared from a product state by using k − 1 GCX gates, and any two-qudit state can be transformed into any other by using at most d − 1 GCX gates. The result reveals that using multivalued quantum systems has obviously advantages over the binary systems in these respects. The best known result for a four-qubit state preparation is that it needs at most nine CNOT gates. A two-ququart state (d = 4) corresponds to a four-qubit state; its preparation and transformation only need at most three GCX gates. Using other gates as the two-qudit elementary gate of multivalued quantum computing, the advantages no longer hold. This once again illustrates that it is reasonable to choose the GCX gate as the two-qudit elementary gate of multivalued quantum computing.

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Unitary quantum gates, perfect entanglers, and unistochastic maps

Cited by 45 publications

References 57 publications

Pauli semigroups and unistochastic quantum channels

Pauli semigroups and unistochastic quantum channels

Protocol using kicked Ising dynamics for generating states with maximal multipartite entanglement

Entangling capability of multivalued bipartite gates and optimal preparation of multivalued bipartite quantum states

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