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.

MULTIPARTY REMOTELY PREPARING MULTIPARTITE EQUATORIAL ENTANGLED STATES IN HIGH DIMENSIONS

2011 ◽  
Vol 09 (06) ◽  
pp. 1437-1448
Author(s):  
YI-BAO LI ◽  
KUI HOU ◽  
SHOU-HUA SHI
Keyword(s):  
Quantum State ◽  
Quantum Channel ◽  
Success Probability ◽  
Quantum States ◽  
Remote State Preparation ◽  
Entangled States ◽  
Entangled State ◽  
High Dimensions ◽  
Original State ◽  
State Preparation

We propose two kinds of schemes for multiparty remote state preparation (MRSP) of the multiparticle d-dimensional equatorial quantum states by using partial entangled state as the quantum channel. Unlike more remote state preparation scheme which only one sender knows the original state to be remotely prepared, the quantum state is shared by two-party or multiparty in this scheme. We show that if and only if all the senders agree to collaborate with each other, the receiver can recover the original state with certain probability. It is found that the total success probability of MRSP is only by means of the smaller coefficients of the quantum channel and the dimension d.

Bidirectional quantum teleportation and cyclic quantum teleportation of multi-qubit entangled states via G-state

2020 ◽  
Vol 34 (28) ◽  
pp. 2050261
Author(s):  
Vikram Verma
Keyword(s):  
Quantum Channel ◽  
Quantum Teleportation ◽  
The Other ◽  
Entangled States ◽  
Entangled State ◽  
Bidirectional Quantum Teleportation

We propose a novel scheme for faithful bidirectional quantum teleportation (BQT) in which Alice can transmit an unknown N-qubit entangled state to Bob and at the same time Bob can transmit an unknown M-qubit entangled state to Alice by using a four-qubit entangled G-state as a quantum channel. We also propose a new scheme for cyclic QT of multi-qubit entangled states by using two G-states as a quantum channel. The advantage of our schemes is that it seems to be much simpler and requires reduced number of qubits in quantum channel as compared with the other proposed schemes.

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.

QUANTUM CORRELATIONS IN THE ENTANGLEMENT DISTILLATION PROTOCOLS

2013 ◽  
Vol 11 (03) ◽  
pp. 1350029
Author(s):  
SHAO-XIONG WU ◽  
JUN ZHANG ◽  
CHANG-SHUI YU ◽  
HE-SHAN SONG
Keyword(s):  
Quantum Entanglement ◽  
Quantum Correlation ◽  
Quantum Discord ◽  
Quantum Correlations ◽  
The Other ◽  
Entangled States ◽  
Entanglement Distillation

We study the quantum correlations between source and target pairs in different protocols of entanglement distillation of one kind of entangled states. We find that there does not exist any quantum correlation in the standard recurrence distillation protocol, while quantum discord and even quantum entanglement are always present in the other two cases of the improved distillation protocols. In the three cases, the distillation efficiency improved with the quantum correlations enhanced.

scholarly journals Test for a large amount of entanglement, using few measurements

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 92 ◽  
Author(s):  
Rui Chao ◽  
Ben W. Reichardt ◽  
Chris Sutherland ◽  
Thomas Vidick
Keyword(s):  
Quantum Entanglement ◽  
Bell Inequality ◽  
Success Probability ◽  
The Other ◽  
Simple Test ◽  
Two Systems

Bell-inequality violations establish that two systems share some quantum entanglement. We give a simple test to certify that two systems share an asymptotically large amount of entanglement,nEPR states. The test is efficient: unlike earlier tests that play many games, in sequence or in parallel, our test requires only one or two CHSH games. One system is directed to play a CHSH game on a random specified qubiti, and the other is told to play games on qubits{i,j}, without knowing which index isi.The test is robust: a success probability withinδof optimal guarantees distanceO(n5/2δ)fromnEPR states. However, the test does not tolerate constantδ; it breaks down forδ=Ω~(1/n). We give an adversarial strategy that succeeds within delta of the optimum probability using onlyO~(δ−2)EPR states.

scholarly journals A three-player coherent state embezzlement game

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 349
Author(s):  
Zhengfeng Ji ◽  
Debbie Leung ◽  
Thomas Vidick
Keyword(s):  
Representation Theory ◽  
Coherent State ◽  
Finite Number ◽  
Success Probability ◽  
High Dimensional ◽  
Entangled States ◽  
Entangled State ◽  
Finitely Presented Groups ◽  
Questions And Answers ◽  
Finitely Presented

We introduce a three-player nonlocal game, with a finite number of classical questions and answers, such that the optimal success probability of 1 in the game can only be achieved in the limit of strategies using arbitrarily high-dimensional entangled states. Precisely, there exists a constant 0<c≤1 such that to succeed with probability 1−ε in the game it is necessary to use an entangled state of at least Ω(ε−c) qubits, and it is sufficient to use a state of at most O(ε−1) qubits. The game is based on the coherent state exchange game of Leung et al.\ (CJTCS 2013). In our game, the task of the quantum verifier is delegated to a third player by a classical referee. Our results complement those of Slofstra (arXiv:1703.08618) and Dykema et al.\ (arXiv:1709.05032), who obtained two-player games with similar (though quantitatively weaker) properties based on the representation theory of finitely presented groups and C∗-algebras respectively.

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&#x2217;. We show that there exists a correlation of size &#x0398;(r2) that self-tests a maximally entangled state of local dimension p&#x2212;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.

FOUR-MODE EPR CONTINUOUS-VARIABLE ENTANGLED STATE AND ITS GENERATION

2002 ◽  
Vol 16 (22) ◽  
pp. 861-869 ◽  
Author(s):  
HONGYI FAN ◽  
XIANTING LIANG ◽  
JUNHUA CHEN
Keyword(s):  
Quantum Entanglement ◽  
Fock Space ◽  
Continuous Variable ◽  
Entangled States ◽  
Entangled State ◽  
Continuous Variables ◽  
Property A ◽  
Set Up

Based on Einstein, Podolsky and Rosen (EPR) quantum entanglement, we construct a new kind of four-mode entangled states of continuous variables in Fock space and examine its complete property and partly non-orthonormal property. A set-up of one beamsplitter and two polarizers can generate such a four-mode entangled state. The discussion can also be extended to constructing more particles' entangled states.

scholarly journals Experimental creation of multi-photon high-dimensional layered quantum states

2020 ◽  
Vol 6 (1) ◽  
Author(s):  
Xiao-Min Hu ◽  
Wen-Bo Xing ◽  
Chao Zhang ◽  
Bi-Heng Liu ◽  
Matej Pivoluska ◽  
...  
Keyword(s):  
Quantum Information ◽  
Quantum Entanglement ◽  
Quantum State ◽  
Quantum States ◽  
High Dimensional ◽  
Entangled States ◽  
Entangled State ◽  
Quantum Network ◽  
Quantum Networks ◽  
Qubit States

Abstract Quantum entanglement is one of the most important resources in quantum information. In recent years, the research of quantum entanglement mainly focused on the increase in the number of entangled qubits or the high-dimensional entanglement of two particles. Compared with qubit states, multipartite high-dimensional entangled states have beneficial properties and are powerful for constructing quantum networks. However, there are few studies on multipartite high-dimensional quantum entanglement due to the difficulty of creating such states. In this paper, we experimentally prepared a multipartite high-dimensional state $$\left|{\Psi }_{442}\right\rangle =\frac{1}{2}(\left|000\right\rangle +\left|110\right\rangle +\left|221\right\rangle +\left|331\right\rangle )$$ Ψ 442 = 1 2 ( 000 + 110 + 221 + 331 ) by using the path mode of photons. We obtain the fidelity F = 0.854 ± 0.007 of the quantum state, which proves a real multipartite high-dimensional entangled state. Finally, we use this quantum state to demonstrate a layered quantum network in principle. Our work highlights another route toward complex quantum networks.

What is Quantum Entanglement?

2020 ◽  
pp. 109-119
Author(s):  
Gershon Kurizki ◽  
Goren Gordon
Keyword(s):  
Quantum Entanglement ◽  
The State ◽  
The Other ◽  
Entangled State ◽  
Quantum Objects ◽  
The Common ◽  
The Universe ◽  
Non Locality

In this adventure, two quantum characters interact, because Henry has constructed a quantum suit for his cat, Schred. Henry and Schred end up in a quantum-entangled state. Remarkably, by measuring one of two entangled systems, the state of the other system is immediately collapsed, even if they are far apart. This bizarre feature of entanglement implies non-locality—synchronization or “collusion” between quantum objects, regardless of their distance. Cosmology provides an explanation: the universe emerged from a unified state describable as a quantum-entangled “hologram”. This notion resonates with the ancient Hindu view that the common essence of all things, the Brahman, can be revealed at every level of the natural hierarchy. The appendix to this chapter discusses operators that create entanglement.

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