scholarly journals Constant-sized correlations are sufficient to self-test maximally entangled states with unbounded dimension

Quantum ◽  
2022 ◽  
Vol 6 ◽  
pp. 614
Author(s):  
Honghao Fu
Keyword(s):  
Multiplicative Group ◽  
Prime Numbers ◽  
Quarterly Journal ◽  
Entangled States ◽  
Entangled State ◽  
Local Dimension ◽  
Maximally Entangled State ◽  
Self Testing ◽  
Maximally Entangled States ◽  
Self Test

Let p be an odd prime and let r be the smallest generator of the multiplicative group Zp∗. We show that there exists a correlation of size Θ(r2) that self-tests a maximally entangled state of local dimension p−1. The construction of the correlation uses the embedding procedure proposed by Slofstra (Forum of Mathematics, Pi. (2019)). Since there are infinitely many prime numbers whose smallest multiplicative generator is in the set {2,3,5} (D.R. Heath-Brown The Quarterly Journal of Mathematics (1986) and M. Murty The Mathematical Intelligencer (1988)), our result implies that constant-sized correlations are sufficient for self-testing of maximally entangled states with unbounded local dimension.

scholarly journals MAXIMALLY ENTANGLED STATES AND BELL'S INEQUALITY IN RELATIVISTIC REGIME

2009 ◽  
Vol 07 (01) ◽  
pp. 395-401 ◽  
Author(s):  
SHAHPOOR MORADI
Keyword(s):  
Ghz State ◽  
Entangled States ◽  
Entangled State ◽  
Maximally Entangled State ◽  
Expectation Value ◽  
Spin Observables ◽  
Chsh Inequality ◽  
Relativistic Regime ◽  
Maximal Violation ◽  
Maximally Entangled States

In this letter we show that in the relativistic regime, maximally entangled state of two spin-1/2 particles not only gives maximal violation of the Bell-CHSH inequality but also gives the largest violation attainable for any pairs of four spin observables that are noncommuting for both systems. Also, we extend our results to three spin-1/2 particles. We obtain the largest eigenvalue of Bell operator and show that this value is equal to the expectation value of Bell operator on GHZ state.

Generalized three-party sharing of operations on remote single qutrit

2014 ◽  
Vol 12 (03) ◽  
pp. 1450011 ◽  
Author(s):  
Pengfei Xing ◽  
Yimin Liu ◽  
Chuanmei Xie ◽  
Xiansong Liu ◽  
Zhanjun Zhang
Keyword(s):  
Success Probability ◽  
Entangled States ◽  
Entangled State ◽  
Quantum Channels ◽  
Channel State ◽  
Classical Communication ◽  
Maximally Entangled State ◽  
Quantum Operations ◽  
Local Operation ◽  
Maximally Entangled States

Two three-party schemes are put forward for sharing quantum operations on a remote qutrit with local operation and classical communication as well as shared entanglements. The first scheme uses a two-qutrit and three-qutrit non-maximally entangled states as quantum channels, while the second replaces the three-qutrit non-maximally entangled state with a two-qutrit. Both schemes are treated and compared from the four aspects of quantum and classical resource consumption, necessary-operation complexity, success probability and efficiency. It is found that the latter is overall more optimal than the former as far as a restricted set of operations is concerned. In addition, comparisons of both schemes with other four relevant ones are also made to show their two features, including degree generalization and channel-state generalization. Furthermore, some concrete discussions on both schemes are made to expose their important features of security, symmetry and experimental feasibility. Particularly, it is revealed that the success probabilities and intrinsic efficiencies in both schemes are completely determined by the shared entanglement.

Bipartite entanglement of decohered mixed states generated from maximally entangled cluster states

2021 ◽  
Vol 36 (03) ◽  
pp. 2150010
Author(s):  
Mostafa Mansour ◽  
Saeed Haddadi
Keyword(s):  
Mixed State ◽  
Entangled States ◽  
Entangled State ◽  
Mixed States ◽  
Density Matrices ◽  
Bipartite Entanglement ◽  
Cluster States ◽  
Maximally Entangled State ◽  
Qubit System ◽  
Maximally Entangled States

In this work, we investigate the bipartite entanglement of decohered mixed states generated from maximally entangled cluster states of [Formula: see text] qubits physical system. We introduce the disconnected cluster states for an ensemble of [Formula: see text] non-interacting qubits and we give the corresponding separable density matrices. The maximally entangled states can be generated from disconnected cluster states, by assuming that the dynamics of the multi-qubit system is governed by a quadratic Hamiltonian of Ising type. When exposed to a local noisy interaction with the environment, the multi-qubit system evolves from its initial pure maximally entangled state to a decohered mixed state. The decohered mixed states generated from bipartite, tripartite and multipartite maximally entangled cluster states are explicitly expressed and their bipartite entanglements are investigated.

Concentration of entanglement in collective-rotating decoherence-free subspace

2020 ◽  
Vol 34 (05) ◽  
pp. 2050067
Author(s):  
Yan-Jie Zhang ◽  
Cai-Peng Shen ◽  
Zhi-Feng Pan ◽  
Ya Gao ◽  
Shi-Lei Su ◽  
...  
Keyword(s):  
Distinctive Feature ◽  
Kerr Nonlinearity ◽  
Entangled States ◽  
Entangled State ◽  
Maximally Entangled State ◽  
Maximal Entanglement ◽  
Measurement Devices ◽  
Maximally Entangled States ◽  
Partially Entangled States ◽  
Decoherence Free Subspace

An entanglement concentration protocol in photonic collective-rotating decoherence-free subspace (CRDFS) is proposed. To accomplish the scheme, two methods to construct parity measurement devices in CRDFS are presented by exploiting the cross-Kerr nonlinearity, through which partially entangled states are converted to maximally entangled states. The performance of the protocol can be improved by iteration method. Fidelity in consideration of dissipation is discussed, which demonstrates good robustness. In contrast to the conventional protocols, the present one has distinctive feature since it can not only get maximally entangled state from less entangled state, but also maintain the maximal entanglement in collective-rotating noise environment.

scholarly journals Self-testing quantum systems of arbitrary local dimension with minimal number of measurements

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Shubhayan Sarkar ◽  
Debashis Saha ◽  
Jędrzej Kaniewski ◽  
Remigiusz Augusiak
Keyword(s):  
Bell Inequality ◽  
Quantum Systems ◽  
Entangled State ◽  
Local Dimension ◽  
Maximally Entangled State ◽  
Testing Protocol ◽  
Self Testing ◽  
Minimum Number ◽  
Bell Nonlocality ◽  
Testing Protocols

AbstractBell nonlocality as a resource for device-independent certification schemes has been studied extensively in recent years. The strongest form of device-independent certification is referred to as self-testing, which given a device, certifies the promised quantum state as well as quantum measurements performed on it without any knowledge of the internal workings of the device. In spite of various results on self-testing protocols, it remains a highly nontrivial problem to propose a certification scheme of qudit–qudit entangled states based on violation of a single d-outcome Bell inequality. Here we address this problem and propose a self-testing protocol for the maximally entangled state of any local dimension using the minimum number of measurements possible, i.e., two per subsystem. Our self-testing result can be used to establish unbounded randomness expansion, $${{{\mathrm{log}}}\,}_{2}d$$ log 2 d perfect random bits, while it requires only one random bit to encode the measurement choice.

Unbounded entanglement in nonlocal games

2015 ◽  
Vol 15 (15&16) ◽  
pp. 1317-1332
Author(s):  
Laura Mančinska ◽  
Thomas Vidick
Keyword(s):  
Quantum Entanglement ◽  
Finite Length ◽  
Success Probability ◽  
The Other ◽  
Entangled States ◽  
Entangled State ◽  
Local Dimension ◽  
Hardy's Paradox ◽  
First Time ◽  
Quantum Strategies

Quantum entanglement is known to provide a strong advantage in many two-party distributed tasks. We investigate the question of how much entanglement is needed to reach optimal performance. For the first time we show that there exists a purely classical scenario for which no finite amount of entanglement suffices. To this end we introduce a simple two-party nonlocal game H, inspired by Lucien Hardy’s paradox. In our game each player has only two possible questions and can provide bit strings of any finite length as answer. We exhibit a sequence of strategies which use entangled states in increasing dimension d and succeed with probability 1 − O(d−c ) for some c ≥ 0.13. On the other hand, we show that any strategy using an entangled state of local dimension d has success probability at most 1 − Ω(d−2 ). In addition, we show that any strategy restricted to producing answers in a set of cardinality at most d has success probability at most 1 − Ω(d−2 ). Finally, we generalize our construction to derive similar results starting from any game G with two questions per player and finite answers sets in which quantum strategies have an advantage.

Deterministic Local Conversion of Incomparable States by Collective LOCC

2005 ◽  
Vol 5 (3) ◽  
pp. 247-257
Author(s):  
I. Chattopadhyay ◽  
D. Sarkar
Keyword(s):  
General Theory ◽  
Finite Number ◽  
Entangled States ◽  
Entangled State ◽  
Input State ◽  
Schmidt Rank ◽  
Maximally Entangled States ◽  
The Given ◽  
Lower Dimensional

Incomparability of pure bipartite entangled states under deterministic LOCC is a very strange phenomena. We find two possible ways of getting our desired pure entangled state which is incomparable with the given input state, by collective LOCC with certainty. The first one is by providing some pure entanglement through the lower dimensional maximally-entangled states or using further less amount of entanglement and the next one is by collective operation on two pairs which are individually incomparable. It is quite surprising that we are able to achieve maximally entangled states of any Schmidt rank from a finite number of 2x2 pure entangled states only by deterministic LOCC. We provide general theory for the case of 3x3 system of incomparable states by the above processes where incomparability seems to be the most hardest one.

Analysing the Efficiencies of Partially Entangled Three-Qubit States for Quantum Information Processing Under Real Conditions

2019 ◽  
Vol 74 (6) ◽  
pp. 523-537
Author(s):  
Jyoti Faujdar ◽  
Atul Kumar
Keyword(s):  
Quantum Information Processing ◽  
Weak Measurement ◽  
Entangled States ◽  
Entangled State ◽  
Maximally Entangled State ◽  
Prepared State ◽  
Noisy Conditions ◽  
Partially Entangled States ◽  
Robust To Noise ◽  
Qubit States

AbstractIn this article, we revisit the question of analysing the efficiencies of partially entangled states in three-qubit classes under real conditions. Our results show some interesting observations regarding the efficiencies and correlations of partially entangled states. Surprisingly, we find that the efficiencies of many three-qubit partially entangled states exceed that of maximally entangled three-qubit states under real noisy conditions and applications of weak measurements. Our analysis, therefore, suggests that the efficiencies of partially entangled states are much more robust to noise than those of maximally entangled states at least for the GHZ (Greenberger–Horne–Zeilinger) class states, for certain protocols; i.e. less correlations in the initially prepared state may also lead to better efficiency and hence one need not always consider starting with a maximally entangled state with maximum correlations between the qubits. For a set of partially entangled states, we find that the efficiency is optimal, independent of the decoherence and state parameters, if the value of weak measurement parameter is very large. For other values of the weak measurement parameter, the robustness of the states depends on the decoherence and state parameters. Moreover, we further show that one can achieve higher efficiencies in a protocol by using non-optimal weak measurement strengths instead of optimal weak measurement strengths.

scholarly journals EFFICIENT QUANTUM CIRCUITS FOR PERFECT AND CONTROLLED TELEPORTATION OF n-QUBIT NON-MAXIMALLY ENTANGLED STATES OF GENERALIZED BELL-TYPE

2011 ◽  
Vol 09 (supp01) ◽  
pp. 389-403 ◽  
Author(s):  
ANIRBAN PATHAK ◽  
ANINDITA BANERJEE
Keyword(s):  
Quantum Channel ◽  
Quantum Teleportation ◽  
Bell State ◽  
Ghz State ◽  
Quantum Circuits ◽  
Controlled Teleportation ◽  
Entangled State ◽  
Maximally Entangled State ◽  
Tripartite Entangled State ◽  
Maximally Entangled States

An efficient and economical scheme is proposed for the perfect quantum teleportation of n-qubit non-maximally entangled state of generalized Bell-type. A Bell state is used as the quantum channel in the proposed scheme. It is also shown that the controlled teleportation of this n-qubit state can be achieved by using a GHZ state or a GHZ-like state as quantum channel. The proposed schemes are economical because for the perfect and controlled teleportation of n-qubit non-maximally entangled state of generalized Bell-type, we only need a Bell state and a tripartite entangled state respectively. It is also established that there exists a family of 12 orthogonal tripartite GHZ-like states which can be used as quantum channel for controlled teleportation. The proposed protocols are critically compared with the existing protocols.

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