$k$-Uniform states and quantum information masking

Abstract

A pure state of $N$ parties with local dimension $d$ is called a $k$-uniform state if all the reductions to $k$ parties are maximally mixed. Based on the connections among $k$-uniform states, orthogonal arrays and linear codes, we give general constructions for $k$-uniform states. We show that when $d\ge 4k-2$ (resp. $d\ge 2k-1$) is a prime power, there exists a $k$-uniform state for any $N\ge 2k$ (resp. $2k\le N\le d+1$). Specially, we give the existence of $4,5$-uniform states for almost every $N$-qudits. Further, we generalize the concept of quantum information masking in bipartite systems given by [Modi \emph{et al.} {Phys. Rev. Lett. \textbf{120}, 230501 (2018)}] to $k$-uniform quantum information masking in multipartite systems, and we show that $k$-uniform states and quantum error-correcting codes can be used for $k$-uniform quantum information masking.

References in corpus (32)

• How to share a quantum secret
• A Theory of Quantum Error-Correcting Codes
• Optimal Quantum Cloning Machines
• Noncommuting mixed states cannot be broadcast
• Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions
• On optimal quantum codes
• Experimental Quantum Cloning of Single Photons
• Absolute Maximal Entanglement and Quantum Secret Sharing
• Quantum information cannot be completely hidden in correlations: implications for the black-hole information paradox
• How entangled can two couples get?
• Absolutely Maximally Entangled states, combinatorial designs and multi-unitary matrices
• Genuinely multipartite entangled states and orthogonal arrays
• Absolutely maximally entangled states of seven qubits do not exist
• Entanglement and quantum combinatorial designs
• Bounds on absolutely maximally entangled states from shadow inequalities, and the quantum MacWilliams identity
• Masking quantum information is impossible
• Quantum MDS Codes over Small Fields
• Multipartite entanglement in heterogeneous systems
• Masking quantum information in multipartite scenario
• Quantum Codes of Maximal Distance and Highly Entangled Subspaces
• The No-Broadcasting Theorem and its Classical Counterpart
• Experimental Test of Quantum No-Hiding Theorem
• Absolutely Maximally Entangled Qudit Graph States
• Information-theoretic interpretation of quantum error-correcting codes
• Absolutely Maximally Entangled States: Existence and Applications
• Complete characterization of qubit masking
• Entanglement of Subspaces and Error Correcting Codes
• Photonic implementation of quantum information masking
• Impossibility of masking a set of quantum states of nonzero measure
• Quantum multipartite maskers vs quantum error-correcting codes
• Quantum Error-Correcting Codes over Mixed Alphabets
• Constructions of $k$-uniform states from mixed orthogonal arrays

Cited by in corpus (10)

• Strong quantum nonlocality in $N$-partite systems
• Entanglement accelerates quantum simulation
• Quantum cost of dense coding and teleportation
• Quantum information masking of an arbitrary qudit can be realized in multipartite lower dimensional systems
• Multipartite entanglement and quantum error identification in $D$-dimensional cluster states
• Near MDS and near quantum MDS codes via orthogonal arrays
• No-masking theorem for observables
• Entanglement is indispensable for masking arbitrary set of quantum states
• Comment on "Masking quantum information is impossible"
• Scalable and fault-tolerant preparation of encoded k-uniform states