Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Mathematical Physics

Dense coding and quantum teleportation using type II1 von Neumann algebras

Siendong Huang

Published Aug 1, 2019• 1 citation
Publisher

Abstract

Quantum states with perfect correlation of continuous variable systems are investigated. On the basis of the property of perfect correlation, the local observable algebras are assumed to be type II1 factor von Neumann algebras. Consequently, finite dimensional matrices may be represented using elements of local observable algebras. Therefore, the dense coding and teleportation processes are identical in performance to those in the finite dimensional cases.

DOI
10.1063/1.5031165

Related papers

Perfect quantum teleportation and dense coding protocols via the 2N-qubit W state

Mei-Yu Wang, Fengli Yan

In this paper, we investigate perfect quantum teleportation and dense coding by using an 2 N -qubit W state channel. In the quantum teleportation scheme, an unknown N -qubit entangled state can be perfectly teleported. One ebit of entanglement and two bits of classical communication are consumed in the teleportation process, just like when using the Bell state channel. While N + 1 bits of classical information can be transmitted by only sending N particles in the dense coding protocol.

Chinese Physics B•Dec 1, 2011•20 citations

Quantum Teleportation and Super-Dense Coding in Operator Algebras

Li Gao, Samuel J Harris, Marius Junge

Abstract We show for any $d,m\ge 2$ with $(d,m)\neq (2,2)$, the matrix-valued generalization of the (tensor product) quantum correlation set of $d$ inputs and $m$ outputs is not closed. Our argument uses a reformulation of super-dense coding and teleportation in terms of $C^*$-algebra isomorphisms. Namely, we prove that for certain actions of cyclic group ${{\mathbb{Z}}}_d$, $$\begin{equation*}M_d(C^*({{\mathbb{F}}}_{d^2}))\cong{{\mathcal{B}}}_d\rtimes{{\mathbb{Z}}}_d\rtimes{{\mathbb{Z}}}_d , M_d({{\mathcal{B}}}_d)\cong C^*({{\mathbb{F}}}_{d^2})\rtimes{{\mathbb{Z}}}_d\rtimes{{\mathbb{Z}}}_d,\end{equation*}$$where ${{\mathcal{B}}}_d$ is the universal unital $C^*$-algebra generated by the elements $u_{jk}, \, 0 \le i, j \le d-1$, satisfying the relations that $[u_{j,k}]$ is a unitary operator, and $C^*({{\mathbb{F}}}_{d^2})$ is the universal $C^*$-algebra of $d^2$ unitaries. These isomorphisms provide a nice connection between the embezzlement of entanglement and the non-closedness of quantum correlation sets.

arXiv:1709.02785•International Mathematics Research Notices•Apr 16, 2019•8 citations

Performance of dense coding and teleportation for random states: Augmentation via preprocessing

Rivu Gupta, Shashank Gupta, Shiladitya Mal +1 more

In order to understand the resourcefulness of a natural quantum system in quantum communication tasks, we study the dense coding capacity (DCC) and teleportation fidelity of Haar uniformly generated random multipartite states of various ranks. We prove that when a rank-2 two-qubit state, a Werner state, and a pure state possess the same amount of entanglement, the DCC of a rank-2 state belongs to the envelope made by pure and Werner states. In a similar way, we obtain an upper bound via the generalized Greenberger-Horne-Zeilinger state for rank-2 three-qubit states when the dense coding with two senders and a single receiver is performed and entanglement is measured in the senders:receiver bipartition. The normalized frequency distributions of DCC for randomly generated two-, three-, and four-qubit density matrices with global as well as local decodings at the receiver's end are reported. The estimation of mean DCC for two-qubit states is found to be in good agreement with the numerical simulations. Universally, we observe that the performance of random states for dense coding as well as teleportation decreases with the increase of the rank of states, which we have shown to be surmounted by the local preprocessing operations performed on the shared states before starting the protocols, irrespective of the rank of the states. The local preprocessing employed here is based on positive operator valued measurements along with classical communication and we show that unlike dense coding with two-qubit random states, the senders' operations are always helpful to probabilistically enhance the capabilities of implementing dense coding as well as teleportation.

arXiv:2012.05865•Physical Review A•Mar 15, 2021•10 citations

Quantum Teleportation: An Operator Algebraic Perspective

Alexandre Conlon

We show that quantum teleportation is intimately connected to Jones' basic construction. This connection leads to generalized, or hybrid teleportation protocols to simultaneously transmit classical and quantum information through finite dimensional von Neumann algebras. We present two operationally concrete teleportation protocols, Hybrid teleportation and our so-called Scaffolding teleportation. Under some mild symmetry assumptions, we establish that any teleportation scheme in the scaffolding framework is equivalent to a teleportation scheme of a special form.

•Jan 1, 2022•0 citations

Entanglement-invertible channels

Dominic Verdon

In a well-known result [R. Werner, J. Phys. A: Math. Gen. 34(35), 7081 (2001)], Werner classified all tight quantum teleportation and dense coding schemes, showing that they correspond to unitary error bases. Here tightness is a certain dimensional restriction: the quantum system to be teleported and the entangled resource must be of dimension d, and the measurement must have d2 outcomes. Here we generalise this classification so as to remove the dimensional restriction altogether, thereby resolving an open problem raised in that work. In fact, we classify not just teleportation and dense coding schemes, but entanglement-reversible channels. These are channels between finite-dimensional C*-algebras which are reversible with the aid of an entangled resource state, generalising ordinary reversibility of a channel. We show that such channels correspond to families of linear maps which are bi-isometric with respect to a duality defined by the resource state. In particular, in Werner’s classification, a bijective correspondence between tight teleportation and dense coding schemes was shown: swapping Alice and Bob’s operations turns a teleportation scheme into a dense coding scheme and vice versa. We observe that this property generalises ordinary invertibility of a channel; we call it entanglement-invertibility. We show that entanglement-invertible channels are precisely the quantum bijections previously studied in noncommutative topology [B. Musto et al., J. Math. Phys. 59(8), 081706 (2018)], and therefore admit a classification in terms of Wang’s quantum permutation group [S. Wang, Commun. Math. Phys. 195, 195–211 (1998)].

arXiv:2204.04493•Journal of Mathematical Physics•Jun 1, 2024•0 citations

Local projections on Einstein–Podolsky–Rosen states

Siendong Huang

The nonlocality of Einstein–Podolsky–Rosen (EPR) states is discussed in the framework of Weyl algebras. To include all possible limits of expectation values, the associated canonical cyclic representations of EPR states are considered. The momentum and position operators of individual particles do not exist in such representations, which explains the uncertainty principle in these cases. However, there are still one-to-one correspondences between the local Weyl operators associated with individual particles. The local observable algebras of individual particles are Type II1 von Neumann algebras and have numerous projection operators. The states obtained by applying local projection operations to the EPR states have perfect correlations between local subalgebras. Bell’s inequality is maximally violated by these states. The lack of atomic projections of Type II1 von Neumann algebras implies that the EPR states cannot be disentangled by local projection operations.

Journal of Mathematical Physics•Sep 1, 2023•0 citations
Quantum states with perfect correlation of continuous variable systems are investigated. On the basis of the property of perfect correlation, the local observable algebras are assumed to be type II1 factor von Neumann algebras. Consequently, finite dimensional matrices may be represented using elements of local observable algebras. Therefore, the dense coding and teleportation processes are identical in performance to those in the finite dimensional cases.
Abstract We show for any d,m≥2d,m\ge 2d,m≥2 with (d,m)≠(2,2)(d,m)\neq (2,2)(d,m)=(2,2), the matrix-valued generalization of the (tensor product) quantum correlation set of ddd inputs and mmm outputs is not closed. Our argument uses a reformulation of super-dense coding and teleportation in terms of C∗C^*C∗-algebra isomorphisms. Namely, we prove that for certain actions of cyclic group Zd{{\mathbb{Z}}}_dZd​, $$\begin{equation*}M_d(C^*({{\mathbb{F}}}_{d^2}))\cong{{\mathcal{B}}}_d\rtimes{{\mathbb{Z}}}_d\rtimes{{\mathbb{Z}}}_d , M_d({{\mathcal{B}}}_d)\cong C^*({{\mathbb{F}}}_{d^2})\rtimes{{\mathbb{Z}}}_d\rtimes{{\mathbb{Z}}}_d,\end{equation*}$$where Bd{{\mathcal{B}}}_dBd​ is the universal unital C∗C^*C∗-algebra generated by the elements ujk, 0≤i,j≤d−1u_{jk}, \, 0 \le i, j \le d-1ujk​,0≤i,j≤d−1, satisfying the relations that [uj,k][u_{j,k}][uj,k​] is a unitary operator, and C∗(Fd2)C^*({{\mathbb{F}}}_{d^2})C∗(Fd2​) is the universal C∗C^*C∗-algebra of d2d^2d2 unitaries. These isomorphisms provide a nice connection between the embezzlement of entanglement and the non-closedness of quantum correlation sets.
In order to understand the resourcefulness of a natural quantum system in quantum communication tasks, we study the dense coding capacity (DCC) and teleportation fidelity of Haar uniformly generated random multipartite states of various ranks. We prove that when a rank-2 two-qubit state, a Werner state, and a pure state possess the same amount of entanglement, the DCC of a rank-2 state belongs to the envelope made by pure and Werner states. In a similar way, we obtain an upper bound via the generalized Greenberger-Horne-Zeilinger state for rank-2 three-qubit states when the dense coding with two senders and a single receiver is performed and entanglement is measured in the senders:receiver bipartition. The normalized frequency distributions of DCC for randomly generated two-, three-, and four-qubit density matrices with global as well as local decodings at the receiver's end are reported. The estimation of mean DCC for two-qubit states is found to be in good agreement with the numerical simulations. Universally, we observe that the performance of random states for dense coding as well as teleportation decreases with the increase of the rank of states, which we have shown to be surmounted by the local preprocessing operations performed on the shared states before starting the protocols, irrespective of the rank of the states. The local preprocessing employed here is based on positive operator valued measurements along with classical communication and we show that unlike dense coding with two-qubit random states, the senders' operations are always helpful to probabilistically enhance the capabilities of implementing dense coding as well as teleportation.
We show that quantum teleportation is intimately connected to Jones' basic construction. This connection leads to generalized, or hybrid teleportation protocols to simultaneously transmit classical and quantum information through finite dimensional von Neumann algebras. We present two operationally concrete teleportation protocols, Hybrid teleportation and our so-called Scaffolding teleportation. Under some mild symmetry assumptions, we establish that any teleportation scheme in the scaffolding framework is equivalent to a teleportation scheme of a special form.
In a well-known result [R. Werner, J. Phys. A: Math. Gen. 34(35), 7081 (2001)], Werner classified all tight quantum teleportation and dense coding schemes, showing that they correspond to unitary error bases. Here tightness is a certain dimensional restriction: the quantum system to be teleported and the entangled resource must be of dimension d, and the measurement must have d2 outcomes. Here we generalise this classification so as to remove the dimensional restriction altogether, thereby resolving an open problem raised in that work. In fact, we classify not just teleportation and dense coding schemes, but entanglement-reversible channels. These are channels between finite-dimensional C*-algebras which are reversible with the aid of an entangled resource state, generalising ordinary reversibility of a channel. We show that such channels correspond to families of linear maps which are bi-isometric with respect to a duality defined by the resource state. In particular, in Werner’s classification, a bijective correspondence between tight teleportation and dense coding schemes was shown: swapping Alice and Bob’s operations turns a teleportation scheme into a dense coding scheme and vice versa. We observe that this property generalises ordinary invertibility of a channel; we call it entanglement-invertibility. We show that entanglement-invertible channels are precisely the quantum bijections previously studied in noncommutative topology [B. Musto et al., J. Math. Phys. 59(8), 081706 (2018)], and therefore admit a classification in terms of Wang’s quantum permutation group [S. Wang, Commun. Math. Phys. 195, 195–211 (1998)].
The nonlocality of Einstein–Podolsky–Rosen (EPR) states is discussed in the framework of Weyl algebras. To include all possible limits of expectation values, the associated canonical cyclic representations of EPR states are considered. The momentum and position operators of individual particles do not exist in such representations, which explains the uncertainty principle in these cases. However, there are still one-to-one correspondences between the local Weyl operators associated with individual particles. The local observable algebras of individual particles are Type II1 von Neumann algebras and have numerous projection operators. The states obtained by applying local projection operations to the EPR states have perfect correlations between local subalgebras. Bell’s inequality is maximally violated by these states. The lack of atomic projections of Type II1 von Neumann algebras implies that the EPR states cannot be disentangled by local projection operations.