arXiv subjects

Shayan Roofeh

Publications and source records attributed to Shayan Roofeh.

4 recordsLinked to original sources

arXiv2025

Exact Quantum Capacity of Decohering Channels in Arbitrary Dimensions

We derive exact analytical expressions for the quantum capacity of a broad subclasses of generalized dephasing channels of the form $\Lambda(\rho)=(1-x)\rho + x D(\rho)$, where $D(\rho)$ represents a structured decoherence process. These channels are degradable for all noise parameters and in arbitrary dimensions, yielding closed-form, single-letter capacity formulas. Our analysis includes fully decohering, block-decohering, and weakly decohering channels, the latter involving coherence preservation within overlapping subspaces. Surprisingly, even under maximal decoherence, the channel may retain nonzero capacity due to residual coherence structure. These results provide quantitative role for decoherence-free and partially coherent subspaces in preserving quantum information, offering guidance for encoding strategies in quantum memories and fault-tolerant quantum communication systems.

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arXiv2024

Construction of channels which in every dimension anti-degrade the depolarizing channel

We consider the depolarizing channel in $d$ dimension defined as $D_x(\rho)=(1-x)\rho+x\: \textit{tr}({\rho}) \frac{I}{d}$, and explicitly find a quantum channel ${\cal N}_x$ which anti-degrades this, when $x\geq\frac{1}{2}$. This proves that the depolarizing channel $D_x$ has zero capacity when $x\geq\frac{1}{2}$. As a corollary, this implies that any quantum channel when contaminated by white noise stronger than this value loses its capacity completely. Although by arguments based on symmetric-extendibiliy of the Choi matrix, it is known that the channel is anti-degradable when $x\geq \frac{d}{2(d+1)}$, the explicit form of the anti-degrading channel in this larger interval is not known. We also calculate in closed form the capacity of the complenetary channel ${\cal D}_x^c$ in the region $x\geq \frac{1}{2}$. This adds to the existing list of quantum channels for which the quantum capacity has been calculated in closed form.

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arXiv2024

Capacities of a two-parameter family of noisy Werner-Holevo channels

In $d=2j+1$ dimensions, the Landau-Streater quantum channel is defined on the basis of spin $j$ representation of the $su(2)$ algebra. Only for $j=1$, this channel is equivalent to the Werner-Holevo channel and enjoys covariance properties with respect to the group $SU(3)$. We extend this class of channels to higher dimensions in a way which is based on the Lie algebra $so(d)$ and $su(d)$. As a result it retains its equivalence to the Werner-Holevo channel in arbitrary dimensions. The resulting channel is covariant with respect to the unitary group $SU(d)$. We then modify this channel in a way which can act as a noisy channel on qudits. The resulting modified channel now interpolates between the identity channel and the Werner-Holevo channel and its covariance is reduced to the subgroup of orthogonal matrices $SO(d)$. We then investigate some of the propeties of the resulting two-parameter family of channels, including their spectrum, their regions of lack of indivisibility, their Holevo quantity, entanglement-assisted capacity and the closed form of their complement channel and a possible lower bound for their quantum capacity.

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arXiv2023

The noisy Werner-Holevo channel and its properties

The interest in the Werner-Holevo channel $\Lambda_{1} (\rho)=\frac{1}{2}(\text{tr}(\rho)I-\rho^T)$ has been mainly due to its abstract mathematical properties. We show that in three dimensions and with a slight modification, this channel can be realized as the rotation of qutrit states in random directions by random angles. Our modification takes the form $\Lambda_x(\rho)=(1-x)\rho+x\Lambda_1(\rho)$. Therefore and in view of the potential use of qutrits in quantum processing tasks and their realization in many different platforms, the modified Werner-Holevo channel can be used as a very simple and realistic noise model, in the same way that the depolarizing channel is for qubits. We will make a detailed study of this channel and derive its various properties. In particular, we will use the recently proposed flag extension and other techniques to derive analytical expressions and bounds for the different capacities of this channel. The role of symmetry is revealed in these derivations. We also rigorously prove that the channel $\Lambda_x$ is anti-degradable and hence has zero quantum capacity, in the region $\frac{4}{7}\leq x\leq 1.$

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