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:1801.07927 · Journal of Physics A Mathematical and Theoretical

Entanglement properties of multipartite informationally complete quantum measurements

Jakub Czartowski, Dardo Goyeneche, Karol Życzkowski

Published Jun 1, 2018• 18 citations
arXivHTMLPDF

Abstract

Abstract We analyze tight informationally complete measurements for arbitrarily large multipartite systems and study their configurations of entanglement. We demonstrate that tight measurements cannot be exclusively composed neither of fully separable nor maximally entangled states. We establish an upper bound on the maximal number of fully separable states allowed by tight measurements and investigate the distinguished case in which every measurement operator carries the same amount of entanglement. Furthermore, we introduce the notion of nested tight measurements, i.e. multipartite tight informationally complete measurements such that every reduction to a certain number of parties induces a lower dimensional tight measurement, proving that they exist for any number of parties and internal levels.

DOI
10.1088/1751-8121/aac973

Related papers

Multipartite entanglement for informationally complete quantum measurements

Jakub Czartowski, Dardo Goyeneche, Karol Życzkowski

We present a comprehensible introduction to tight informationally complete measurements for arbitrarily large multipartite systems and study their allowed entanglement configurations, focusing on those requiring simplest possible quantum resources. We demonstrate that tight measurements cannot be exclusively composed neither by fully separable nor maximally entangled states, according to a selected measure of entanglement. We establish an upper bound on the maximal number of fully separable states allowed by tight measurements and we study the distinguished case in which every measurement operator has the same amount of entanglement. Furthermore, we introduce the notion of nested tight measurements, i.e. multipartite tight informationally complete measurements such that every reduction to a certain number of parties induces a lower dimensional tight measurement, proving that they exist for any number of parties and internal levels.

•Jan 24, 2018•0 citations

Multipartite entanglement of superpositions

Daniel Cavalcanti, Marcelo Terra Cunha, Antonio Acín

The entanglement of superpositions [Linden et al., Phys. Rev. Lett. 97, 100502 (2006)]is generalized to the multipartite scenario: an upper bound to the multipartite entanglement of a superposition is given in terms of the entanglement of the superposed states and the superposition coefficients. This bound is proven to be tight for a class of states composed of an arbitrary number of qubits. We also extend the result to a large family of quantifiers, which includes the negativity, the robustness of entanglement, and the best separable approximation measure.

arXiv:0705.2521•Physical Review A•Oct 23, 2007•19 citations

Tight bounds on the distinguishability of quantum states under separable measurements

Somshubhro Bandyopadhyay, Michael Nathanson

One of the many interesting features of quantum nonlocality is that the states of a multipartite quantum system cannot always be distinguished as well by local measurements as they can when all quantum measurements are allowed. In this work, we characterize the distinguishability of sets of multipartite quantum states when restricted to separable measurements, those which contain the class of local measurements but nevertheless are free of entanglement between the component systems. We consider two quantities: the separable fidelity, a truly quantum quantity, which measures how well we can ``clone'' the input state, and the classical probability of success, which simply gives the optimal probability of identifying the state correctly. We obtain lower and upper bounds on the separable fidelity and give several examples in the bipartite and multipartite settings where these bounds are optimal. Moreover the optimal values in these cases can be attained by local measurements. We further show that for distinguishing orthogonal states under separable measurements, a strategy that maximizes the probability of success is also optimal for separable fidelity. We point out that the equality of fidelity and success probability does not depend on an using the optimal strategy, only on the orthogonality of the states. To illustrate this, we present an example where two sets (one consisting of orthogonal states and the other nonorthogonal states) are shown to have the same separable fidelity even though the success probabilities are different.

arXiv:1306.2712•Physical Review A•Nov 12, 2013•23 citations

Maximally Entangled Multipartite States: A Brief Survey

Marco Enríquez, Iwona Wintrowicz, Karol Życzkowski

The problem of identifying maximally entangled quantum states of a composite quantum systems is analyzed. We review some states of multipartite systems distinguished with respect to certain measures of quantum entanglement. Numerical results obtained for 4-qubit pure states illustrate the fact that the notion of maximally entangled state depends on the measure used.

Journal of Physics Conference Series•Mar 1, 2016•54 citations

Genuinely Multipartite Entangled Quantum States with Fully Local Hidden Variable Models and Hidden Multipartite Nonlocality

Joseph Bowles, Jérémie Francfort, Mathieu Fillettaz +2 more

The relation between entanglement and nonlocality is discussed in the case of multipartite quantum systems. We show that, for any number of parties, there exist genuinely multipartite entangled states that admit a fully local hidden variable model, i.e., where all parties are separated. Hence, although these states exhibit the strongest form of multipartite entanglement, they cannot lead to Bell inequality violation considering general nonsequential local measurements. Then, we show that the nonlocality of these states can nevertheless be activated using sequences of local measurements, thus revealing genuine multipartite hidden nonlocality.

arXiv:1511.08401•Physical Review Letters•Mar 30, 2016•67 citations

Simplex of bound entangled multipartite qubit states

Beatrix C. Hiesmayr, Florian Hipp, Marcus Huber +2 more

We construct a simplex for multipartite qubit states of even number $n$ of qubits, which has the same geometry concerning separability, mixedness, kind of entanglement, amount of entanglement, and nonlocality as the bipartite qubit states. We derive the entanglement of the class of states which can be described by only three real parameters with the help of a multipartite measure for all discrete systems. We prove that the bounds on this measure are optimal for the whole class of states and that it reveals that the states possess only $n$-partite entanglement and not, e.g., bipartite entanglement. We then show that this $n$-partite entanglement can be increased by stochastic local operations and classical communication to the purest maximal entangled states. However, pure $n$-partite entanglement cannot be distilled; consequently all entangled states in the simplex are $n$-partite bound entangled. We study also Bell inequalities and find the same geometry as for bipartite qubits. Moreover, we show how the (hidden) nonlocality for all $n$-partite bound entangled states can be revealed.

arXiv:0807.4842•Physical Review A•Oct 24, 2008•11 citations
Abstract We analyze tight informationally complete measurements for arbitrarily large multipartite systems and study their configurations of entanglement. We demonstrate that tight measurements cannot be exclusively composed neither of fully separable nor maximally entangled states. We establish an upper bound on the maximal number of fully separable states allowed by tight measurements and investigate the distinguished case in which every measurement operator carries the same amount of entanglement. Furthermore, we introduce the notion of nested tight measurements, i.e. multipartite tight informationally complete measurements such that every reduction to a certain number of parties induces a lower dimensional tight measurement, proving that they exist for any number of parties and internal levels.
We present a comprehensible introduction to tight informationally complete measurements for arbitrarily large multipartite systems and study their allowed entanglement configurations, focusing on those requiring simplest possible quantum resources. We demonstrate that tight measurements cannot be exclusively composed neither by fully separable nor maximally entangled states, according to a selected measure of entanglement. We establish an upper bound on the maximal number of fully separable states allowed by tight measurements and we study the distinguished case in which every measurement operator has the same amount of entanglement. Furthermore, we introduce the notion of nested tight measurements, i.e. multipartite tight informationally complete measurements such that every reduction to a certain number of parties induces a lower dimensional tight measurement, proving that they exist for any number of parties and internal levels.
The entanglement of superpositions [Linden et al., Phys. Rev. Lett. 97, 100502 (2006)]is generalized to the multipartite scenario: an upper bound to the multipartite entanglement of a superposition is given in terms of the entanglement of the superposed states and the superposition coefficients. This bound is proven to be tight for a class of states composed of an arbitrary number of qubits. We also extend the result to a large family of quantifiers, which includes the negativity, the robustness of entanglement, and the best separable approximation measure.
One of the many interesting features of quantum nonlocality is that the states of a multipartite quantum system cannot always be distinguished as well by local measurements as they can when all quantum measurements are allowed. In this work, we characterize the distinguishability of sets of multipartite quantum states when restricted to separable measurements, those which contain the class of local measurements but nevertheless are free of entanglement between the component systems. We consider two quantities: the separable fidelity, a truly quantum quantity, which measures how well we can ``clone'' the input state, and the classical probability of success, which simply gives the optimal probability of identifying the state correctly. We obtain lower and upper bounds on the separable fidelity and give several examples in the bipartite and multipartite settings where these bounds are optimal. Moreover the optimal values in these cases can be attained by local measurements. We further show that for distinguishing orthogonal states under separable measurements, a strategy that maximizes the probability of success is also optimal for separable fidelity. We point out that the equality of fidelity and success probability does not depend on an using the optimal strategy, only on the orthogonality of the states. To illustrate this, we present an example where two sets (one consisting of orthogonal states and the other nonorthogonal states) are shown to have the same separable fidelity even though the success probabilities are different.
The relation between entanglement and nonlocality is discussed in the case of multipartite quantum systems. We show that, for any number of parties, there exist genuinely multipartite entangled states that admit a fully local hidden variable model, i.e., where all parties are separated. Hence, although these states exhibit the strongest form of multipartite entanglement, they cannot lead to Bell inequality violation considering general nonsequential local measurements. Then, we show that the nonlocality of these states can nevertheless be activated using sequences of local measurements, thus revealing genuine multipartite hidden nonlocality.
We construct a simplex for multipartite qubit states of even number nnn of qubits, which has the same geometry concerning separability, mixedness, kind of entanglement, amount of entanglement, and nonlocality as the bipartite qubit states. We derive the entanglement of the class of states which can be described by only three real parameters with the help of a multipartite measure for all discrete systems. We prove that the bounds on this measure are optimal for the whole class of states and that it reveals that the states possess only nnn-partite entanglement and not, e.g., bipartite entanglement. We then show that this nnn-partite entanglement can be increased by stochastic local operations and classical communication to the purest maximal entangled states. However, pure nnn-partite entanglement cannot be distilled; consequently all entangled states in the simplex are nnn-partite bound entangled. We study also Bell inequalities and find the same geometry as for bipartite qubits. Moreover, we show how the (hidden) nonlocality for all nnn-partite bound entangled states can be revealed.