arXiv subjects

Sowrabh Sudevan

Publications and source records attributed to Sowrabh Sudevan.

4 recordsLinked to original sources

arXiv2025

Codeword Stabilized Codes from m-Uniform Graph States

An m-uniform quantum state on n qubits is an entangled state in which every m-qubit subsystem is maximally mixed. Starting with an m-uniform state realized as the graph state associated with an m-regular graph, and a classical [n,k,d \ge m+1] binary linear code with certain additional properties, we show that pure [[n,k,m+1]]_2 quantum error-correcting codes (QECCs) can be constructed within the codeword stabilized (CWS) code framework. As illustrations, we construct pure [[2^{2r}-1,2^{2r}-2r-3,3]]_2 and [[(2^{4r}-1)^2, (2^{4r}-1)^2 - 32r-7, 5]]_2 QECCs. We also give measurement-based protocols for encoding into code states and for recovery of logical qubits from code states.

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arXiv2024

Majority-Agreed Key Distribution using Absolutely Maximally Entangled Stabilizer States

In [Phys. Rev. A 77, 060304(R),(2008)], Facchi et al. introduced absolutely maximally entangled (AME) states and also suggested ``majority-agreed key distribution"(MAKD) as a possible application for such states. In MAKD, the qubits of an AME state are distributed one each to many spatially separated parties. AME property makes it necessary that quantum key distribution(QKD) between any two parties can only be performed with the cooperation of a majority of parties. Our contributions to MAKD are, $(1)$ We recognize that stabilizer structure of the shared state is a useful addition to MAKD and prove that the cooperation of any majority of parties(including the two communicants) is necessary and sufficient for QKD between any two parties sharing AME stabilizer states. Considering the rarity of qubit AME states, we extended this result to the qudit case. $(2)$ We generalize to shared graph states that are not necessarily AME. We show that the stabilizer structure of graph states allows for QKD between any inseparable bipartition of qubits. Inseparability in graph states is visually apparent in the connectivity of its underlying mathematical graph. We exploit this connectivity to demonstrate conference keys and multiple independent keys per shared state. Recent experimental and theoretical progress in graph state preparation and self-testing make these protocols feasible in the near future.

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arXiv2023

Multipartite entanglement and quantum error identification in $D$-dimensional cluster states

An entangled state is said to be $m$-uniform if the reduced density matrix of any $m$ qubits is maximally mixed. This is intimately linked to pure quantum error correction codes (QECCs), which allow not only to correct errors, but also to identify their precise nature and location. Here, we show how to create $m$-uniform states using local gates or interactions and elucidate several QECC applications. We first show that $D$-dimensional cluster states are $m$-uniform with $m=2D$. This zero-correlation length cluster state does not have finite size corrections to its $m=2D$ uniformity, which is exact both for infinite and for large enough but finite lattices. Yet at some finite value of the lattice extension in each of the $D$ dimensions, which we bound, the uniformity is degraded due to finite support operators which wind around the system. We also outline how to achieve larger $m$ values using quasi-$D$ dimensional cluster states. This opens the possibility to use cluster states to benchmark errors on quantum computers. We demonstrate this ability on a superconducting quantum computer, focusing on the 1D cluster state which, we show, allows to detect and identify 1-qubit errors, distinguishing $X$, $Y$ and $Z$ errors.

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arXiv2022

$n$-qubit states with maximum entanglement across all bipartitions: A graph state approach

We discuss the construction of $n$-qubit pure states with maximum bipartite entanglement across all possible choices of $k$ vs $n-k$ bi-partitioning, which implies that the Von Neumann entropy of every $k$-qubit reduced density matrix corresponding to this state should be $k \ln 2 $. Such states have been referred to as $k$-uniform, $k$-MM states. We show that a subset of the 'graph states' satisfy this condition, hence providing a recipe for constructing $k$-uniform states. Finding recipes for construction of $k$-uniform states using graph states is useful since every graph state can be constructed starting from a product state using only controlled-$Z$ gates. Though, a priori it is not clear how to construct a graph which corresponds to an arbitrary $k$-uniform state, but in particular, we show that graphs with no isolated vertices are $1$-uniform. Graphs organized as a circular linear chain corresponds to the case of $2$-uniform state, where we show that the minimum number of qubits required to host such a state is $n=5$. $3$-uniform states can be constructed by forming bi-layer graphs with $n/2$ qubits ($n=2\mathbb{Z}$) in each layer, such that each layer forms a fully connected graph while inter-layer connections are such that the vertices in one layer has a one to one connectivity to the other layer. $4$-uniform states can be formed by taking 2D lattice graphs( also referred elsewhere as a 2D cluster Ising state ) with periodic boundary conditions along both dimensions and both dimensions having at least $5$ vertices.

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