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

Physical Review A

Entanglement swapping for X states demands threshold values

Luis Roa, Ariana S. Muñoz, Gesa Grüning

Published Jun 13, 2014• 22 citations
Publisher

Abstract

The basic entanglement-swapping scheme can be seen as a process which allows one to redistribute the Bell states properties between different pairs of a four-qubit system. We analyze a similar scheme by performing a Bell--von Neumann measurement over two local qubits, each one initially correlated through an $X$ state with a spatially distant qubit. This process swaps the $X$ feature without conditions, whereas the input entanglement is partially distributed in the four possible outcome states under certain conditions. Specifically, we obtain two threshold values for the entanglement of formation of the input $X$ states in order for the outcome states to be nonseparable.

DOI
10.1103/physreva.89.064301

Related papers

Entanglement-swapping for X-states demands threshold values

Ariana S. Muñoz, Gesa Grüning, Luis Roa

The basic entanglement-swapping scheme can be seen as a process which allows to redistribute the Bell states' properties between different pairs of a four qubits system. Achieving the task requires performing a von Neumann measurement, which projects a pair of factorized qubits randomly onto one of the four Bell states. In this work we propose a similar scheme, by performing the same Bell-von Neumann measurement over two local qubits, each one initially being correlated through an X-state with a spatially distant qubit. This process swaps the X-feature without conditions, whereas the input entanglement is partially distributed in the four possible outcome states under certain conditions. Specifically, we obtain two threshold values for the input entanglement in order for the outcome states to be nonseparable. Besides, we find that there are two possible amounts of outcome entanglement, one is greater and the other less than the input entanglement; the probability of obtaining the greatest outcome entanglement is smaller than the probability of achieving the least one. In addition, we illustrate the distribution of the entanglement for some particular and interesting initial X-states.

arXiv:1311.6784•Nov 26, 2013•1 citation

Matching for probabilistic entanglement swapping.

Luis Roa, Torben L. Purz, Ariana S. Muñoz +3 more

The basic entanglement swapping protocol allows to achieve the main aim of deterministically projecting two qubits, which have never interacted, onto a maximally entangled state. For deterministic swapping the key ingredient is the maximal entanglement initially contained in two pairs of qubits and the ability to measure onto a Bell basis. In other words, the basic and deterministic entanglement swapping scheme involves three maximal level of entanglement. In this work we address probabilistic entanglement swapping processes performed with different amounts of initial entanglement. Besides, we suggest a non Bell measuring-basis, thus we introduce a third entanglement level in the process. Additionally, we propose the \emph{unambiguous state extraction} scheme as the local mechanism for probabilistically achieving the main aim. Amalgamating these three elements allows us to design four strategies for performing probabilistic entanglement swapping. Surprisingly, we encountered an twofold entanglement matching effect related to the concurrence of the measuring-basis. Specifically, the maximal probability of accomplishing the main aim becomes a constant for concurrences higher than or equal to the matching entanglement values. Thus, we show that maximal entanglement in the measuring-basis is not required for attaining the main aim with optimal probability.

•Jul 16, 2021•0 citations

The utility of entanglement swapping in quantum communications

Brian T. Kirby, Siddhartha Santra, Vladimir S. Malinovsky +1 more

The nonlocal correlations between quantum states in an entangled system are essential to many quantum communications applications. A basic quantum operation, which permits the distribution of entanglement between two initially uncorrelated systems, is entanglement swapping. Here we present a rigorous formulation of entanglement swapping of any two partially mixed two-qubit states without limiting ourselves to any specific type of state or noise. Further, for two important classes of the input states, Bell diagonal and pure states, we describe how the concurrence of the final state is related to the concurrence of the initial states. First, we consider Bell diagonal states, and find bounds on the concurrence of the final state in terms of the concurrences of the initial states. These bounds are important for communications applications because polarization mode dispersion in fibers produces Bell diagonal states up to a local unitary rotation. Second, we show that swapping pure states occasionally results in a state of higher concurrence than either of the initial states. In addition, we find that two pure states are most likely to be capable of swapping to a state of increased concurrence when the two initial states have similar concurrences. Our analysis offers a completely general framework for investigating the behavior of any pair of two-qubit states when used for entanglement swapping.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Sep 13, 2016•0 citations

A local variable model for entanglement swapping exploiting the detection loophole

Nicolas Gisin, Bernard Gisin

In an entanglement swapping process two initially uncorrelated qubits become entangled, without any direct interaction. We present a model using local variables aiming at reproducing this remarkable process, under the realistic assumption of finite detection efficiencies. The model assumes that the local variables describing the two qubits are initially completely uncorrelated. Nevertheless, we show that once conditioned on the Bell measurement result, the local variables bear enough correlation to simulate quantum measurement results with correlation very close to the quantum prediction. When only a partial Bell measurement is simulated, as carried out is all experiments so far, then the model recovers analytically the quantum prediction.

•Jan 1, 2002•9 citations

Activation of entanglement in generalized entanglement swapping

Pratapaditya Bej, Abhishek Banerjee

We study entanglement activation in a generalized entanglement swapping process involving two Bell pairs and generalized measurements. The conventional understanding posits entangled measurements as both necessary and sufficient for establishing entanglement between distant parties. In this study, we reassess the role of measurement operators in entanglement generation within a generalized entanglement swapping process. We focus on maximally entangled two-qubit initial states and generalized measurements, investigating the necessity and sufficiency conditions for entangled measurement operators. By utilizing two Bell pairs, (1, 2) shared between Alice and Bob, and (3, 4) shared between Bob and Charlie, we demonstrate that while entangled measurements are sufficient, they are not indispensable for establishing entanglement between spatially separated observers. Through a sequential approach, if Bob performs an initial measurement which is not able to establish entanglement then followed by another measurement after postprocessing the first measurement it is possible to establish entanglement. We identify specific criteria for different measurement operators that enable the potential for performing a second measurement to establish entanglement. Our findings highlight the feasibility of generating entanglement between distant parties through a combination of measurements, shedding light on entanglement distribution in quantum networks. Additionally, we showcase through illustrative examples how successive measurements enhance entanglement compared to single measurements, underscoring the practical benefits of our approach in enhancing entanglement. Moreover, our protocol extends beyond bipartite qubit states to higher-dimensional maximally entangled states, emphasizing its versatility and applicability.

arXiv:2403.06518•Physical Review A•May 23, 2024•2 citations

Entanglement swapping of two arbitrarily degraded entangled states

Brian T. Kirby, Siddhartha Santra, Vladimir S. Malinovsky +1 more

We consider entanglement swapping, a key component of quantum network operations and entanglement distribution. Pure entangled states, which are the desired input to the swapping protocol, are typically mixed by environmental interactions, causing a reduction in their degree of entanglement. Thus an understanding of entanglement swapping with partially mixed states is of importance. Here we present a general analytical solution for entanglement swapping of arbitrary two-qubit states. Our result provides a comprehensive method for analyzing entanglement swapping in quantum networks. First, we show that the concurrence of a partially mixed state is conserved when this state is swapped with a Bell state. Then, we find upper and lower bounds on the concurrence of the state resulting from entanglement swapping for various classes of input states. Finally, we determine a general relationship between the ranks of the initial states and the rank of the final state after swapping.

arXiv:1512.06093•Physical Review A•Jul 20, 2016•49 citations
The basic entanglement-swapping scheme can be seen as a process which allows one to redistribute the Bell states properties between different pairs of a four-qubit system. We analyze a similar scheme by performing a Bell--von Neumann measurement over two local qubits, each one initially correlated through an XXX state with a spatially distant qubit. This process swaps the XXX feature without conditions, whereas the input entanglement is partially distributed in the four possible outcome states under certain conditions. Specifically, we obtain two threshold values for the entanglement of formation of the input XXX states in order for the outcome states to be nonseparable.
The basic entanglement-swapping scheme can be seen as a process which allows to redistribute the Bell states' properties between different pairs of a four qubits system. Achieving the task requires performing a von Neumann measurement, which projects a pair of factorized qubits randomly onto one of the four Bell states. In this work we propose a similar scheme, by performing the same Bell-von Neumann measurement over two local qubits, each one initially being correlated through an X-state with a spatially distant qubit. This process swaps the X-feature without conditions, whereas the input entanglement is partially distributed in the four possible outcome states under certain conditions. Specifically, we obtain two threshold values for the input entanglement in order for the outcome states to be nonseparable. Besides, we find that there are two possible amounts of outcome entanglement, one is greater and the other less than the input entanglement; the probability of obtaining the greatest outcome entanglement is smaller than the probability of achieving the least one. In addition, we illustrate the distribution of the entanglement for some particular and interesting initial X-states.
The basic entanglement swapping protocol allows to achieve the main aim of deterministically projecting two qubits, which have never interacted, onto a maximally entangled state. For deterministic swapping the key ingredient is the maximal entanglement initially contained in two pairs of qubits and the ability to measure onto a Bell basis. In other words, the basic and deterministic entanglement swapping scheme involves three maximal level of entanglement. In this work we address probabilistic entanglement swapping processes performed with different amounts of initial entanglement. Besides, we suggest a non Bell measuring-basis, thus we introduce a third entanglement level in the process. Additionally, we propose the \emph{unambiguous state extraction} scheme as the local mechanism for probabilistically achieving the main aim. Amalgamating these three elements allows us to design four strategies for performing probabilistic entanglement swapping. Surprisingly, we encountered an twofold entanglement matching effect related to the concurrence of the measuring-basis. Specifically, the maximal probability of accomplishing the main aim becomes a constant for concurrences higher than or equal to the matching entanglement values. Thus, we show that maximal entanglement in the measuring-basis is not required for attaining the main aim with optimal probability.
The nonlocal correlations between quantum states in an entangled system are essential to many quantum communications applications. A basic quantum operation, which permits the distribution of entanglement between two initially uncorrelated systems, is entanglement swapping. Here we present a rigorous formulation of entanglement swapping of any two partially mixed two-qubit states without limiting ourselves to any specific type of state or noise. Further, for two important classes of the input states, Bell diagonal and pure states, we describe how the concurrence of the final state is related to the concurrence of the initial states. First, we consider Bell diagonal states, and find bounds on the concurrence of the final state in terms of the concurrences of the initial states. These bounds are important for communications applications because polarization mode dispersion in fibers produces Bell diagonal states up to a local unitary rotation. Second, we show that swapping pure states occasionally results in a state of higher concurrence than either of the initial states. In addition, we find that two pure states are most likely to be capable of swapping to a state of increased concurrence when the two initial states have similar concurrences. Our analysis offers a completely general framework for investigating the behavior of any pair of two-qubit states when used for entanglement swapping.
In an entanglement swapping process two initially uncorrelated qubits become entangled, without any direct interaction. We present a model using local variables aiming at reproducing this remarkable process, under the realistic assumption of finite detection efficiencies. The model assumes that the local variables describing the two qubits are initially completely uncorrelated. Nevertheless, we show that once conditioned on the Bell measurement result, the local variables bear enough correlation to simulate quantum measurement results with correlation very close to the quantum prediction. When only a partial Bell measurement is simulated, as carried out is all experiments so far, then the model recovers analytically the quantum prediction.
We study entanglement activation in a generalized entanglement swapping process involving two Bell pairs and generalized measurements. The conventional understanding posits entangled measurements as both necessary and sufficient for establishing entanglement between distant parties. In this study, we reassess the role of measurement operators in entanglement generation within a generalized entanglement swapping process. We focus on maximally entangled two-qubit initial states and generalized measurements, investigating the necessity and sufficiency conditions for entangled measurement operators. By utilizing two Bell pairs, (1, 2) shared between Alice and Bob, and (3, 4) shared between Bob and Charlie, we demonstrate that while entangled measurements are sufficient, they are not indispensable for establishing entanglement between spatially separated observers. Through a sequential approach, if Bob performs an initial measurement which is not able to establish entanglement then followed by another measurement after postprocessing the first measurement it is possible to establish entanglement. We identify specific criteria for different measurement operators that enable the potential for performing a second measurement to establish entanglement. Our findings highlight the feasibility of generating entanglement between distant parties through a combination of measurements, shedding light on entanglement distribution in quantum networks. Additionally, we showcase through illustrative examples how successive measurements enhance entanglement compared to single measurements, underscoring the practical benefits of our approach in enhancing entanglement. Moreover, our protocol extends beyond bipartite qubit states to higher-dimensional maximally entangled states, emphasizing its versatility and applicability.
We consider entanglement swapping, a key component of quantum network operations and entanglement distribution. Pure entangled states, which are the desired input to the swapping protocol, are typically mixed by environmental interactions, causing a reduction in their degree of entanglement. Thus an understanding of entanglement swapping with partially mixed states is of importance. Here we present a general analytical solution for entanglement swapping of arbitrary two-qubit states. Our result provides a comprehensive method for analyzing entanglement swapping in quantum networks. First, we show that the concurrence of a partially mixed state is conserved when this state is swapped with a Bell state. Then, we find upper and lower bounds on the concurrence of the state resulting from entanglement swapping for various classes of input states. Finally, we determine a general relationship between the ranks of the initial states and the rank of the final state after swapping.