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 A two-player dimension witness based on embezzlement, and an elementary proof of the non-closure of the set of quantum correlations

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 282 ◽  
Author(s):  
Andrea Coladangelo
Keyword(s):  
Optimal Strategy ◽  
Elementary Proof ◽  
Quantum Correlations ◽  
Entangled State ◽  
Finitely Presented Groups ◽  
Self Testing ◽  
Question And Answer ◽  
Questions And Answers ◽  
Non Local ◽  
Finitely Presented

We describe a two-player non-local game, with a fixed small number of questions and answers, such that an ϵ-close to optimal strategy requires an entangled state of dimension 2Ω(ϵ−1/8). Our non-local game is inspired by the three-player non-local game of Ji, Leung and Vidick \cite{ji2018three}. It reduces the number of players from three to two, as well as the question and answer set sizes. Moreover, it provides an (arguably) elementary proof of the non-closure of the set of quantum correlations, based on embezzlement and self-testing. In contrast, previous proofs \cite{slofstra2019set, dykema2017non, musat2018non} involved representation theoretic machinery for finitely-presented groups and C∗-algebras.

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.

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.

The influence of excitation number of photon-added coherent state field on the entanglement swapping process

2017 ◽  
Vol 31 (27) ◽  
pp. 1750198 ◽  
Author(s):  
M. Soltani ◽  
M. K. Tavassoly ◽  
R. Pakniat
Keyword(s):  
Coherent State ◽  
Quantum Electrodynamics ◽  
Coherent States ◽  
Success Probability ◽  
Entanglement Swapping ◽  
Cavity Quantum Electrodynamics ◽  
Linear Entropy ◽  
Entangled State ◽  
Maximally Entangled State ◽  
Coherent Field

In this paper, we outline a scheme for the entanglement swapping procedure based on cavity quantum electrodynamics using the Jaynes–Cummings model consisting of the coherent and photon-added coherent states. In particular, utilizing the photon-added coherent states ([Formula: see text][Formula: see text][Formula: see text][Formula: see text], where [Formula: see text] is the Glauber coherent state) in the scheme, enables us to investigate the effect of [Formula: see text], i.e., the number of excitations corresponding to the photon-added coherent field on the entanglement swapping process. In the scheme, two two-level atoms [Formula: see text] and [Formula: see text] are initially entangled together, and distinctly two exploited cavity fields [Formula: see text] and [Formula: see text] are prepared in an entangled state (a combination of coherent and photon-added coherent states). Interacting the atom [Formula: see text] with field [Formula: see text] (via the Jaynes–Cummings model) and then making detection on them, transfers the entanglement from the two atoms [Formula: see text], [Formula: see text] and the two fields [Formula: see text], [Formula: see text] to the atom-field “[Formula: see text]-[Formula: see text]”, i.e., entanglement swapping occurs. In the continuation, we pay our attention to the evaluation of the fidelity of the swapped entangled state relative to a suitable maximally entangled state, success probability of the performed detections and linear entropy as the degree of entanglement of the swapped entangled state. It is demonstrated that, an increase in the number of excitations, [Formula: see text], leads to the increment of fidelity as well as the amount of entanglement. According to our numerical results, the maximum values of fidelity (linear entropy) 0.98 (0.46) is obtained for [Formula: see text], however, the maximum value of success probability does not significantly change by increasing [Formula: see text].

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.

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.

scholarly journals Path identity as a source of high-dimensional entanglement

2020 ◽  
Vol 117 (42) ◽  
pp. 26118-26122
Author(s):  
Jaroslav Kysela ◽  
Manuel Erhard ◽  
Armin Hochrainer ◽  
Mario Krenn ◽  
Anton Zeilinger
Keyword(s):  
Angular Momentum ◽  
Degrees Of Freedom ◽  
General Scheme ◽  
Higher Dimensions ◽  
High Dimensional ◽  
Entangled States ◽  
Entangled State ◽  
Experimental Demonstration ◽  
Entanglement Generation ◽  
High Degree

We present an experimental demonstration of a general entanglement-generation framework, where the form of the entangled state is independent of the physical process used to produce the particles. It is the indistinguishability of multiple generation processes and the geometry of the setup that give rise to the entanglement. Such a framework, termed entanglement by path identity, exhibits a high degree of customizability. We employ one class of such geometries to build a modular source of photon pairs that are high-dimensionally entangled in their orbital angular momentum. We demonstrate the creation of three-dimensionally entangled states and show how to incrementally increase the dimensionality of entanglement. The generated states retain their quality even in higher dimensions. In addition, the design of our source allows for its generalization to various degrees of freedom and even for the implementation in integrated compact devices. The concept of entanglement by path identity itself is a general scheme and allows for construction of sources producing also customized states of multiple photons. We therefore expect that future quantum technologies and fundamental tests of nature in higher dimensions will benefit from this approach.

scholarly journals A SUFFICIENT AND NECESSARY CONDITION FOR SUPERDENSE CODING OF QUANTUM STATES

2008 ◽  
Vol 06 (05) ◽  
pp. 1115-1125 ◽  
Author(s):  
DAOWEN QIU
Keyword(s):  
Lower Bound ◽  
Success Probability ◽  
Quantum States ◽  
Entangled States ◽  
Necessary Condition ◽  
Entangled State ◽  
Maximally Entangled State ◽  
High Success Probability ◽  
Sufficient And Necessary Condition ◽  
Arbitrary Quantum

Recently, Harrow et al. [Phys. Rev. Lett.92 (2004) 187901] gave a method for preparing an arbitrary quantum state with high success probability by physically transmitting some qubits, and by consuming a maximally entangled state, together with exhausting some shared random bits. In this paper, we discover that some states are impossible to be perfectly prepared by Alice and Bob initially sharing some entangled states. In particular, we present a sufficient and necessary condition for the states being enabled to be exactly prepared with probability equal to unity, in terms of the initial entangled states (maybe nonmaximally). In contrast, if the initially shared entanglement is maximal, then the probabilities for preparing these quantum states are smaller than unity. Furthermore, the lower bound on the probability for preparing some states are derived.

scholarly journals Groups with one defining relator

1964 ◽  
Vol 4 (4) ◽  
pp. 385-392 ◽  
Author(s):  
Gilbert Baumslag
Keyword(s):  
Finite Number ◽  
Algebraic Theory ◽  
Late Nineteenth Century ◽  
Simple Type ◽  
Modern Theory ◽  
Infinite Groups ◽  
Finitely Presented Groups ◽  
Late Nineteenth ◽  
Finitely Presented ◽  
Finitely Related

The present day theory of finite groups might be regarded as the outgrowth of the algebraic theory of equations. In much the same way one might consider the modern theory of infinite groups as stemming from late nineteenth century topology. The groups that crop up in topology are of a particularly simple type in that they are both finitely generated and finitely related. This means that every element in such a group can be expressed in terms of a finite number of elements and their inverses and every relation is an algebraic consequence of a finite number of relations between these elements. In other words the legacy of topology to group theory is the estate of finitely presented groups. This talk is concerned with the seemingly simplest of the finitely presented groups, the so-called groups with a single defining relator.

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