We study classical string commitment over quantum channels with limited preshared entanglement. For noninteractive protocols, we determine the commitment capacity of a class of channels with input dimension $d$ that, at each use, sample a pair of classical random variables $(F,Z)$, apply one of the $d^2$ Heisenberg--Weyl operators indexed by $Z$ to the input, and deliver the transformed quantum system together with $F$ to the receiver. If $E$ is the available entanglement rate in bits per channel use, then the capacity is $\min\{H(Z|F),\log_2d+E\}$. This class of channels encompasses quantum erasure and depolarizing channels, as well as families of Pauli channels. Additionally, for interactive protocols, we show that the commitment rate cannot exceed $\log_2d+E$ bits per channel use, so that when $H(Z|F)\geq\log_2d+E$, interactive communication does not increase the capacity. As a consequence, for interactive protocols, we determine the capacity of the quantum erasure channel.
This work derives sample-complexity bounds for estimating entries of the transfer matrix/map to additive accuracy $\epsilon$ with success probability $\ge1-\delta$, under different resources: access to the complex-conjugate channel $\mathcal{E}^*$ and/or parallel access to $c$ copies.
M. Subramanian, Hyukgun Kwon, Liang Jiang· 0 citations
The results demonstrate that quantum superposition cannot efficiently simulate the coordination afforded by public randomness, extending this separation to arbitrary $k, and prove an exact factorization theorem for unambiguous quantum state identification, which may be of independent mathematical interest.
Pedro Montealegre, I. Rapaport, Jorge Valenzuela· 0 citations
It is demonstrated that shared randomness is necessary to achieve the complexity of distributed state certification with limited communication, and an $\Omega$ lower bound in the $\textit{private-coin}$ setting is proved.
Kenny Chen, Mina Doosti, R. Sweke et al.· 1 citation
We introduce a measure of information loss for any quantum process that may be modeled by a prepare-evolve-measure scenario: Alice prepares an ensemble of states that gets sent via a quantum channel to Bob, who then measures the output. As a quantum channel models open system dynamics, our measure of information loss q...
James Fullwood, Wu-Zhong Guo, Bo-Yu Yang· 0 citations
In this work, we define entanglement-assisted quantum locally recoverable codes with availability, in which any set of up to $\delta-1$ erased qudits can be recovered from any one of $t$ local recovery sets, each of size at most $r+\delta-1$, with the recovery sets intersecting exactly in the erased coordinates, where...
Rutuja Kshirsagar, Gretchen L. Matthews, Julia Shapiro· 2 citations· ⚡1
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