A geometrical description of the universal $$1 \rightarrow 2$$ asymmetric quantum cloning region

Nechita, Ion; Pellegrini, Clément; Rochette, Denis

doi:10.1007/s11128-021-03258-y

Cited by 3 publications

(1 citation statement)

References 22 publications

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“…It is well known that the channel

is self-compatible if

[ 26 , 39 ]. The necessary and sufficient condition for the compatibility of two different depolarizing channels

and

were shown in [ 40 , 41 , 42 ]:

…”

Section: Compatibility Of Quantum Channelsmentioning

confidence: 99%

A Fisher Information-Based Incompatibility Criterion for Quantum Channels

Zhang

Nechita

2022

Entropy

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We introduce a new incompatibility criterion for quantum channels based on the notion of (quantum) Fisher information. Our construction is based on a similar criterion for quantum measurements put forward by H. Zhu. We then study the power of the incompatibility criterion in different scenarios. First, we prove the first analytical conditions for the incompatibility of two Schur channels. Then, we study the incompatibility structure of a tuple of depolarizing channels, comparing the newly introduced criterion with the known results from asymmetric quantum cloning.

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“…It is well known that the channel

is self-compatible if

[ 26 , 39 ]. The necessary and sufficient condition for the compatibility of two different depolarizing channels

and

were shown in [ 40 , 41 , 42 ]:

…”

Section: Compatibility Of Quantum Channelsmentioning

confidence: 99%

A Fisher Information-Based Incompatibility Criterion for Quantum Channels

Zhang

Nechita

2022

Entropy

Self Cite

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Linear Programming with Unitary-Equivariant Constraints

Grinko,

Ozols

2024

Commun. Math. Phys.

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Unitary equivariance is a natural symmetry that occurs in many contexts in physics and mathematics. Optimization problems with such symmetry can often be formulated as semidefinite programs for a $$d^{p+q}$$ d p + q -dimensional matrix variable that commutes with $$U^{\otimes p} \otimes {\bar{U}}^{\otimes q}$$ U ⊗ p ⊗ U ¯ ⊗ q , for all $$U \in \textrm{U}(d)$$ U ∈ U ( d ) . Solving such problems naively can be prohibitively expensive even if $$p+q$$ p + q is small but the local dimension d is large. We show that, under additional symmetry assumptions, this problem reduces to a linear program that can be solved in time that does not scale in d, and we provide a general framework to execute this reduction under different types of symmetries. The key ingredient of our method is a compact parametrization of the solution space by linear combinations of walled Brauer algebra diagrams. This parametrization requires the idempotents of a Gelfand–Tsetlin basis, which we obtain by adapting a general method inspired by the Okounkov–Vershik approach. To illustrate potential applications of our framework, we use several examples from quantum information: deciding the principal eigenvalue of a quantum state, quantum majority vote, asymmetric cloning and transformation of a black-box unitary. We also outline a possible route for extending our method to general unitary-equivariant semidefinite programs.

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