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

arXiv:2102.00780 · Physical Review A

Maximum violation of monogamy of entanglement for indistinguishable particles by measures that are monogamous for distinguishable particles

Goutam Paul, Soumya Das, Anindya Banerji

Published Jul 20, 2021• 3 citations
arXivHTMLPDF

Abstract

Two important results of quantum physics are the no-cloning theorem and the monogamy of entanglement. The former forbids the creation of an independent and identical copy of an arbitrary unknown quantum state and the latter restricts the shareability of quantum entanglement among multiple quantum systems. For distinguishable particles, one of these results implies the other. In this Letter, we show that in qubit systems with indistinguishable particles (where each particle cannot be addressed individually) a maximum violation of the monogamy of entanglement is possible by the measures that are monogamous for distinguishable particles. To derive this result, we formulate the degree of freedom trace-out rule for indistinguishable particles corresponding to a spatial location where each degree of freedom might be entangled with the other degrees of freedom. Our result removes the restriction on the shareability of quantum entanglement for indistinguishable particles, without contradicting the no-cloning theorem.

DOI
10.1103/physreva.104.l010402

Related papers

Entanglement monogamy in indistinguishable particle systems

Soumya Das, Goutam Paul, Ritabrata Sengupta

Recently, it has been realized that indistinguishability is a resource for quantum information processing. A new method to represent the indistinguishable particles by Franco et al. (Sci Rep 6:20603, 2016, https://doi.org/10.1038/srep20603 ) and measure the concurrence is developed by Nosrati et al. (npj Quantum Inf 6:39, 2020, https://doi.org/10.1038/s41534-020-0271-7 ). The monogamy property says that quantum entanglement cannot be shared freely between more than two particles. For three distinguishable particles, the monogamy of entanglement was first expressed as an inequality using squared concurrence where each particle has a single degree of freedom (for pure or mixed states). Using multiple degrees of freedom, similar inequality was shown to be held between two distinguishable particles. However, for two indistinguishable particles, where each particle cannot be addressed individually, the monogamy inequality was shown to be violated maximally for a specific state. Thus a question naturally arises: what happens to the monogamy of entanglement in the case of three or more indistinguishable particles? We prove that monogamy holds in this scenario and the inequality becomes equality for all pure indistinguishable states. Further, we provide three major operational meanings of our result. Finally, we present an experimental schematic using photons to observe our result.

Scientific Reports•Dec 11, 2023•2 citations

Aspects of Quantum Entanglement and Indistinguishability

Soumya Das

This thesis investigates the entanglement of distinguishable and indistinguishable particles, introducing a new error model for Hardy's test, experimentally verified using superconducting qubits. We address challenges in implementing quantum protocols based on this test and propose potential solutions and present two performance measures for qubits in superconducting quantum computers. We demonstrate that if quantum particles can create hyper-hybrid entangled states and achieve unit fidelity quantum teleportation, arbitrary state cloning is possible. This leads to two no-go theorems: hyper-hybrid entangled states cannot be formed with distinguishable particles, and unit fidelity quantum teleportation is unattainable with indistinguishable particles. These results establish unique correlations for each particle type, creating a clear distinction between the two domains. We also show that hyper-hybrid entangled states can be formed with indistinguishable fermions and generalize this for both fermions and bosons. We develop a generalized DoF trace-out rule applicable to single or multiple degrees of freedom for both types of particles. This framework allows us to derive expressions for teleportation fidelity and singlet fraction, establishing an upper bound for the generalized singlet fraction. We present an optical circuit that generates entanglement in distinguishable particles. Using our trace-out rule, we show that for two indistinguishable particles with multiple DoFs, the monogamy of entanglement can be maximally violated. We assert that indistinguishability is essential for this violation in qubit systems. For three indistinguishable particles, we confirm that monogamy is upheld using squared concurrence. Finally, we propose a novel entanglement swapping protocol involving two indistinguishable particles, enhancing quantum networks and quantum repeaters.

arXiv:2503.08623•Mar 11, 2025•0 citations

Monogamy of Quantum Entanglement

Xiao-Lan Zong, Hao-Hao Yin, Wei Song +1 more

Unlike classical correlation, quantum entanglement cannot be freely shared among many parties. This restricted shareability of entanglement among multi-party systems is known as monogamy of entanglement, which is one of the most fundamental properties of entanglement. Here, we summarize recent theoretical progress in the field of monogamy of entanglement. We firstly review the standard CKW-type monogamy inequalities in terms of various entanglement measures. In particular, the squashed entanglement and one-way distillable entanglement are monogamous for arbitrary dimensional systems. We then introduce some generalized version of monogamy inequalities which extend and sharpen the traditional ones. We also consider the dual polygamy inequalities for multi-party systems. Moreover, we present two new definitions to define monogamy of entanglement. Finally, some challenges and future directions for monogamy of entanglement are highlighted.

arXiv:2201.00366•Frontiers in Physics•Jun 9, 2022•13 citations

Monogamy of Particle Statistics in Tripartite Systems Simulating Bosons and Fermions

Marcin Karczewski, Dagomir Kaszlikowski, Paweł Kurzyński

In the quantum world, correlations can take the form of entanglement which is known to be monogamous. In this Letter we show that another type of correlation, indistinguishability, is also restricted by some form of monogamy. Namely, if particles A and B simulate bosons, then A and C cannot perfectly imitate fermions. Our main result consists in demonstrating to what extent it is possible.

arXiv:1802.02404•Physical Review Letters•Aug 31, 2018•14 citations

Monogamy of correlations versus monogamy of entanglement

M. P. Seevinck

A fruitful way of studying physical theories is via the question whether the possible physical states and different kinds of correlations in each theory can be shared to different parties. Over the past few years it has become clear that both quantum entanglement and non-locality (i.e., correlations that violate Bell-type inequalities) have limited shareability properties and can sometimes even be monogamous. We give a self-contained review of these results and present new results on the shareability of different kinds of correlations, including local, quantum and no-signalling correlations. This includes an alternative simpler proof of the Toner-Verstraete monogamy inequality for quantum correlations, as well as a strengthening thereof. Further, the relationship between sharing non-local quantum correlations and sharing mixed entangled states is investigated, and already for the simplest case of bi-partite correlations and qubits this is shown to be non-trivial. Also, a recently proposed new interpretation of Bell’s theorem by Schumacher in terms of shareability of correlations is critically assessed. Finally, the relevance of monogamy of non-local correlations for secure quantum key distribution is pointed out, and in this regard it is stressed that not all non-local correlations are monogamous.

arXiv:0908.1867•Quantum Information Processing•Jan 15, 2010•82 citations

Monogamy of entanglement of formation

Thiago Rodrigues de Oliveira, Marcio F. Cornelio, F. F. Fanchini

It is well known that a particle cannot freely share entanglement with two or more particles. This restriction is generally called monogamy. However the formal quantification of such restriction is only known for some measures of entanglement and for two-level systems. The first and broadly known monogamy relation was established by Coffman, Kundu, and Wootters for the square of the concurrence. Since then, it is usually said that the entanglement of formation is not monogamous, as it does not obey the same relation. We show here that despite that, the entanglement of formation cannot be freely shared and therefore should be said to be monogamous. Furthermore, the square of the entanglement of formation does obey the same relation of the squared concurrence, a fact recently noted for three particles and extended here for N particles. Therefore the entanglement of formation is as monogamous as the concurrence. We also numerically study how the entanglement is distributed in pure states of three qubits and the relation between the sum of the bipartite entanglement and the classical correlation.

arXiv:1312.7287•Physical Review A•Mar 24, 2014•94 citations
Two important results of quantum physics are the no-cloning theorem and the monogamy of entanglement. The former forbids the creation of an independent and identical copy of an arbitrary unknown quantum state and the latter restricts the shareability of quantum entanglement among multiple quantum systems. For distinguishable particles, one of these results implies the other. In this Letter, we show that in qubit systems with indistinguishable particles (where each particle cannot be addressed individually) a maximum violation of the monogamy of entanglement is possible by the measures that are monogamous for distinguishable particles. To derive this result, we formulate the degree of freedom trace-out rule for indistinguishable particles corresponding to a spatial location where each degree of freedom might be entangled with the other degrees of freedom. Our result removes the restriction on the shareability of quantum entanglement for indistinguishable particles, without contradicting the no-cloning theorem.
Recently, it has been realized that indistinguishability is a resource for quantum information processing. A new method to represent the indistinguishable particles by Franco et al. (Sci Rep 6:20603, 2016, https://doi.org/10.1038/srep20603 ) and measure the concurrence is developed by Nosrati et al. (npj Quantum Inf 6:39, 2020, https://doi.org/10.1038/s41534-020-0271-7 ). The monogamy property says that quantum entanglement cannot be shared freely between more than two particles. For three distinguishable particles, the monogamy of entanglement was first expressed as an inequality using squared concurrence where each particle has a single degree of freedom (for pure or mixed states). Using multiple degrees of freedom, similar inequality was shown to be held between two distinguishable particles. However, for two indistinguishable particles, where each particle cannot be addressed individually, the monogamy inequality was shown to be violated maximally for a specific state. Thus a question naturally arises: what happens to the monogamy of entanglement in the case of three or more indistinguishable particles? We prove that monogamy holds in this scenario and the inequality becomes equality for all pure indistinguishable states. Further, we provide three major operational meanings of our result. Finally, we present an experimental schematic using photons to observe our result.
This thesis investigates the entanglement of distinguishable and indistinguishable particles, introducing a new error model for Hardy's test, experimentally verified using superconducting qubits. We address challenges in implementing quantum protocols based on this test and propose potential solutions and present two performance measures for qubits in superconducting quantum computers. We demonstrate that if quantum particles can create hyper-hybrid entangled states and achieve unit fidelity quantum teleportation, arbitrary state cloning is possible. This leads to two no-go theorems: hyper-hybrid entangled states cannot be formed with distinguishable particles, and unit fidelity quantum teleportation is unattainable with indistinguishable particles. These results establish unique correlations for each particle type, creating a clear distinction between the two domains. We also show that hyper-hybrid entangled states can be formed with indistinguishable fermions and generalize this for both fermions and bosons. We develop a generalized DoF trace-out rule applicable to single or multiple degrees of freedom for both types of particles. This framework allows us to derive expressions for teleportation fidelity and singlet fraction, establishing an upper bound for the generalized singlet fraction. We present an optical circuit that generates entanglement in distinguishable particles. Using our trace-out rule, we show that for two indistinguishable particles with multiple DoFs, the monogamy of entanglement can be maximally violated. We assert that indistinguishability is essential for this violation in qubit systems. For three indistinguishable particles, we confirm that monogamy is upheld using squared concurrence. Finally, we propose a novel entanglement swapping protocol involving two indistinguishable particles, enhancing quantum networks and quantum repeaters.
Unlike classical correlation, quantum entanglement cannot be freely shared among many parties. This restricted shareability of entanglement among multi-party systems is known as monogamy of entanglement, which is one of the most fundamental properties of entanglement. Here, we summarize recent theoretical progress in the field of monogamy of entanglement. We firstly review the standard CKW-type monogamy inequalities in terms of various entanglement measures. In particular, the squashed entanglement and one-way distillable entanglement are monogamous for arbitrary dimensional systems. We then introduce some generalized version of monogamy inequalities which extend and sharpen the traditional ones. We also consider the dual polygamy inequalities for multi-party systems. Moreover, we present two new definitions to define monogamy of entanglement. Finally, some challenges and future directions for monogamy of entanglement are highlighted.
A fruitful way of studying physical theories is via the question whether the possible physical states and different kinds of correlations in each theory can be shared to different parties. Over the past few years it has become clear that both quantum entanglement and non-locality (i.e., correlations that violate Bell-type inequalities) have limited shareability properties and can sometimes even be monogamous. We give a self-contained review of these results and present new results on the shareability of different kinds of correlations, including local, quantum and no-signalling correlations. This includes an alternative simpler proof of the Toner-Verstraete monogamy inequality for quantum correlations, as well as a strengthening thereof. Further, the relationship between sharing non-local quantum correlations and sharing mixed entangled states is investigated, and already for the simplest case of bi-partite correlations and qubits this is shown to be non-trivial. Also, a recently proposed new interpretation of Bell’s theorem by Schumacher in terms of shareability of correlations is critically assessed. Finally, the relevance of monogamy of non-local correlations for secure quantum key distribution is pointed out, and in this regard it is stressed that not all non-local correlations are monogamous.
It is well known that a particle cannot freely share entanglement with two or more particles. This restriction is generally called monogamy. However the formal quantification of such restriction is only known for some measures of entanglement and for two-level systems. The first and broadly known monogamy relation was established by Coffman, Kundu, and Wootters for the square of the concurrence. Since then, it is usually said that the entanglement of formation is not monogamous, as it does not obey the same relation. We show here that despite that, the entanglement of formation cannot be freely shared and therefore should be said to be monogamous. Furthermore, the square of the entanglement of formation does obey the same relation of the squared concurrence, a fact recently noted for three particles and extended here for N particles. Therefore the entanglement of formation is as monogamous as the concurrence. We also numerically study how the entanglement is distributed in pure states of three qubits and the relation between the sum of the bipartite entanglement and the classical correlation.