scholarly journals Multipartite entanglement in XOR games

2013 ◽  
Vol 13 (3&4) ◽  
pp. 334-360
Author(s):  
Jop Briet ◽  
Harry Buhrman ◽  
Troy Lee ◽  
Thomas Vidick
Keyword(s):  
Communication Complexity ◽  
Constant Factor ◽  
Hardness Of Approximation ◽  
Entangled States ◽  
Multipartite Entanglement ◽  
Ghz States ◽  
Random Strategy ◽  
Grothendieck’S Inequality ◽  
Novel Applications ◽  
Classical Strategy

We study multipartite entanglement in the context of XOR games. In particular, we study the ratio of the entangled and classical \emph{biases}, which measure the maximum advantage of a quantum or classical strategy over a uniformly random strategy. For the case of two-player XOR games, Tsirelson proved that this ratio is upper bounded by the celebrated Grothendieck constant. In contrast, \PG proved the existence of entangled states that give quantum players an unbounded advantage over classical players in a three-player XOR game. We show that the multipartite entangled states that are most often seen in today's literature can only lead to a bias that is a constant factor larger than the classical bias. These states include GHZ states, any state local-unitarily equivalent to combinations of GHZ and maximally entangled states shared between different subsets of the players (e.g., stabilizer states), as well as generalizations of GHZ states of the form $\sum_i \alpha_i \ket{i}\cdots\ket{i}$ for arbitrary amplitudes $\alpha_i$. Our results have the following surprising consequence: \emph{classical} three-player XOR games do not follow an XOR parallel repetition theorem, even a very weak one. Besides this, we discuss implications of our results for communication complexity and hardness of approximation. Our proofs are based on novel applications of extensions of Grothendieck's inequality, due to Blei and Tonge, and Carne, generalizing Tsirelson's use of Grothendieck's inequality to bound the bias of two-player XOR games.

Teleportation and dense coding via a multiparticle quantum channel of the GHZ-class

2002 ◽  
Vol 2 (5) ◽  
pp. 367-378
Author(s):  
V.N. Gorbachev ◽  
A.I. Zhiliba ◽  
A.I. Trubilko ◽  
A.A. Rodichkina
Keyword(s):  
Quantum Channel ◽  
Entangled States ◽  
Dense Coding ◽  
Ghz States ◽  
Classical Capacity ◽  
Coding Schemes ◽  
One To One

A set of protocols for teleportation and dense coding schemes based on a multiparticle quantum channel, represented by the $N$-particle entangled states of the GHZ class, is introduced. Using a found representation for the GHZ states, it was shown that for dense coding schemes enhancement of the classical capacity of the channel due from entanglement is $N/N-1$. Within the context of our schemes it becomes clear that there is no one-to one correspondence between teleportation and dense coding schemes in comparison when the EPR channel is exploited. A set of schemes, for which two additional operations as entanglement and disentanglement are permitted, is considered.

Controlled quantum key agreement based on maximally three-qubit entangled states

2020 ◽  
Vol 34 (18) ◽  
pp. 2050201
Author(s):  
Jie Tang ◽  
Lei Shi ◽  
Jiahua Wei
Keyword(s):  
Performance Analysis ◽  
Key Agreement ◽  
Entangled States ◽  
Quantum Key Agreement ◽  
Ghz States ◽  
Participant Attack ◽  
Significant Change

In this paper, we propose a two-party and a three-party controlled quantum key agreement (QKA) protocols with three-qubit GHZ states and Bell measurements. Compared with previous protocols, the significant change of our schemes is that a supervisor is introduced for controlling the agreement process to improve the controllability. Moreover, our protocols ensure each communication participant contribute equally to the agreement keys, and all participants can negotiate the shared keys without exchanging classical bits between them. The performance analysis shows that our protocols can be immune to outsider and participant attack.

Generation of four-photon polarization entangled states with cross-Kerr nonlinearity

2015 ◽  
Vol 13 (05) ◽  
pp. 1550024 ◽  
Author(s):  
Meiyu Wang ◽  
Fengli Yan
Keyword(s):  
Kerr Nonlinearity ◽  
Entangled States ◽  
Entangled State ◽  
Kerr Medium ◽  
Coherent Light ◽  
Photon Polarization ◽  
Beam Splitters ◽  
Ghz States ◽  
Different Types ◽  
Quantum Optical

We show how to prepare three different types of four-photon polarization entangled states among four modes. The scheme only use cross-Kerr medium, polarization beam splitters and X homodyne measurements on coherent light fields, which can be efficiently implemented in quantum optical laboratories. GHZ states and symmetric Dick states can be generated in deterministic way based on the scheme. With the possible availability of suitable strong Kerr nonlinearity, another type of entangled state called genuine four-photon entangled state can be realized as well.

scholarly journals Sign-rank Can Increase under Intersection

2021 ◽  
Vol 13 (4) ◽  
pp. 1-17
Author(s):  
Mark Bun ◽  
Nikhil S. Mande ◽  
Justin Thaler
Keyword(s):  
Communication Complexity ◽  
Function Class ◽  
Time Algorithm ◽  
Constant Factor ◽  
Pac Learning ◽  
New Techniques ◽  
Know How ◽  
Communication Problem ◽  
Analytic Complexity ◽  
Class Of Functions

The communication class UPP cc is a communication analog of the Turing Machine complexity class PP . It is characterized by a matrix-analytic complexity measure called sign-rank (also called dimension complexity), and is essentially the most powerful communication class against which we know how to prove lower bounds. For a communication problem f , let f ∧ f denote the function that evaluates f on two disjoint inputs and outputs the AND of the results. We exhibit a communication problem f with UPP cc ( f ) = O (log n ), and UPP cc ( f ∧ f ) = Θ (log 2 n ). This is the first result showing that UPP communication complexity can increase by more than a constant factor under intersection. We view this as a first step toward showing that UPP cc , the class of problems with polylogarithmic-cost UPP communication protocols, is not closed under intersection. Our result shows that the function class consisting of intersections of two majorities on n bits has dimension complexity n Omega Ω(log n ) . This matches an upper bound of (Klivans, O’Donnell, and Servedio, FOCS 2002), who used it to give a quasipolynomial time algorithm for PAC learning intersections of polylogarithmically many majorities. Hence, fundamentally new techniques will be needed to learn this class of functions in polynomial time.

scholarly journals Necessary and sufficient criterion for k-separability of N-qubit noisy GHZ states

2018 ◽  
Vol 16 (04) ◽  
pp. 1850037 ◽  
Author(s):  
Xiao-Yu Chen ◽  
Li-Zhen Jiang ◽  
Zhu-An Xu
Keyword(s):  
White Noise ◽  
Sufficient Conditions ◽  
Ghz State ◽  
Entangled State ◽  
Multipartite Entanglement ◽  
Quantum Code ◽  
Sufficient Criterion ◽  
Output State ◽  
Ghz States ◽  
Necessary And Sufficient

A Multipartite entangled state has many different kinds of entanglements specified by the number of partitions. The most essential example of multipartite entanglement is the entanglement of multi-qubit Greenberger–Horne–Zeilinger (GHZ) state in white noise. We explicitly construct the entanglement witnesses for these states with stabilizer generators of the GHZ states. For an [Formula: see text] qubit GHZ state in white noise, we demonstrate the necessary and sufficient criterion of separability when it is divided into [Formula: see text] parties with [Formula: see text] for arbitrary [Formula: see text] and [Formula: see text]. The criterion covers more than a half of all kinds of partial entanglements for [Formula: see text]-qubit GHZ states in white noise. For the rest of multipartite entanglement problems, we present a method to obtain the sufficient conditions of separability. As an application, we consider [Formula: see text] qubit GHZ state as a codeword of the degenerate quantum code passing through depolarizing channel. We find that the output state is neither genuinely entangled nor fully separable when the quantum channel capacity reduces from positive to zero.

An Improved Ping-Pong Protocol Using Three-Qubit Nonmaximally Nonorthogonal Entangled States

2019 ◽  
Vol 74 (9) ◽  
pp. 799-811
Author(s):  
Hargeet Kaur ◽  
Atul Kumar
Keyword(s):  
Information Transfer ◽  
Orthogonal Basis ◽  
Basis Set ◽  
Entangled States ◽  
Ghz States ◽  
Ping Pong ◽  
Orthogonal Set ◽  
Qubit States ◽  
Single Receiver ◽  
Qubit Efficiency

AbstractWe analyse the ping-pong (PP) protocol [K. Bostrom and T. Felbinger, Phys. Rev. Lett. 89, 187902 (2002)] using different sets of partially entangled three-qubit states. Interestingly, our results show that the partially entangled nonorthogonal three-qubit states are more useful as resources in comparison to three-qubit maximally entangled Greenberger–Horne–Zeilinger (GHZ) states. The properties of orthogonal set of partially entangled states as resources for PP protocol, however, are similar to that of maximally entangled GHZ states – both the states are not preferable due to the vulnerability towards eavesdropping. On the other hand, partially entangled nonorthogonal basis set holds importance for transferring two-bit information, one each from a sender, to a single receiver. The protocol is further analysed for various eavesdropping attacks, and the results are compared with the use of two shared Bell pairs for two-bit information transfer. Surprisingly, the use of partially entangled nonorthogonal set of states is found to offer better qubit efficiency and increased security, as against the use of two separate maximally entangled Bell states with orthogonal basis. In addition, we also propose a mixed-state sharing protocol to further enhance the security of the PP protocol.

scholarly journals Multipartite entanglement and few-body Hamiltonians

2014 ◽  
Vol 12 (02) ◽  
pp. 1461003
Author(s):  
Francesco V. Pepe
Keyword(s):  
Short Range ◽  
Ghz State ◽  
Entangled States ◽  
Entangled State ◽  
Multipartite Entanglement ◽  
Multipartite Entangled State ◽  
Coupled Qubits

We investigate the possibility to obtain higly multipartite-entangled states as non-degenerate eigenstates of Hamiltonians that involve only short-range and few-body interactions. We study small-size systems (with a number of qubits ranging from three to five) and search for Hamiltonians with a maximally multipartite entangled state (MMES) as a non-degenerate eigenstate. We then find conditions, including bounds on the number of coupled qubits, to build a Hamiltonian with a Greenberger–Horne–Zeilinger (GHZ) state as a non-degenerate eigenstate. We finally comment on possible applications.

scholarly journals Efficient and effective quantum compiling for entanglement-based machine learning on IBM Q devices

2018 ◽  
Vol 16 (08) ◽  
pp. 1840006 ◽  
Author(s):  
Davide Ferrari ◽  
Michele Amoretti
Keyword(s):  
Machine Learning ◽  
Quantum Algorithms ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Entangled States ◽  
Hard Problem ◽  
Practical Applications ◽  
Ghz States ◽  
Quantum Machine Learning ◽  
Uniform Quantum

Quantum compiling means fast, device-aware implementation of quantum algorithms (i.e. quantum circuits, in the quantum circuit model of computation). In this paper, we present a strategy for compiling IBM Q-aware, low-depth quantum circuits that generate Greenberger–Horne–Zeilinger (GHZ) entangled states. The resulting compiler can replace the QISKit compiler for the specific purpose of obtaining improved GHZ circuits. It is well known that GHZ states have several practical applications, including quantum machine learning. We illustrate our experience in implementing and querying a uniform quantum example oracle based on the GHZ circuit, for solving the classically hard problem of learning parity with noise.

Absolutely maximally entangled states from phase states

2019 ◽  
Vol 17 (01) ◽  
pp. 1950009 ◽  
Author(s):  
M. Mansour ◽  
M. Daoud ◽  
L. Bouhouch
Keyword(s):  
Entangled States ◽  
Multipartite Entanglement ◽  
Finite Dimensional ◽  
Heisenberg Type ◽  
Maximally Entangled States ◽  
Phase Operators

We derive absolutely maximally entangled (AME) states from phase states for a multi-qudit system whose dynamics is governed by a two-qudit interaction Hamiltonian of Heisenberg type. AME states are characterized by being maximally entangled for all bipartitions of the multi-qudit system and present absolute multipartite entanglement. The key ingredient of this approach is the theory of phase states for finite-dimensional systems (qudits). We define further the unitary phase operators of [Formula: see text]-qudit systems and we give next the corresponding separable phase states. Using a qudit–qudit Hamiltonian acting as entangling operator on separable phase states, we generate entangled phase states. Finally, from the labeled entangled phase states, we derive the absolutely maximally entangled states.

scholarly journals Creation of Greenberger-Horne-Zeilinger states with thousands of atoms by entanglement amplification

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Yajuan Zhao ◽  
Rui Zhang ◽  
Wenlan Chen ◽  
Xiang-Bin Wang ◽  
Jiazhong Hu
Keyword(s):  
Hilbert Space ◽  
Spin State ◽  
Optical Cavity ◽  
Single Frequency ◽  
Entangled States ◽  
Quantum Metrology ◽  
Atom Number ◽  
Ghz States ◽  
High Finesse ◽  
Coherent Spin

AbstractWe propose an entanglement-creation scheme in a multi-atom ensemble trapped in an optical cavity, named entanglement amplification, converting unentangled states into entangled states and amplifying less-entangled ones to maximally entangled Greenberger-Horne-Zeilinger (GHZ) states whose fidelity is logarithmically dependent on the atom number and robust against common experimental noises. The scheme starts with a multi-atom ensemble initialized in a coherent spin state. By shifting the energy of a particular Dicke state, we break the Hilbert space of the ensemble into two isolated subspaces to tear the coherent spin state into two components so that entanglement is introduced. After that, we utilize the isolated subspaces to further enhance the entanglement by coherently separating the two components. By single-particle Rabi drivings on atoms in a high-finesse optical cavity illuminated by a single-frequency light, 2000-atom GHZ states can be created with a fidelity above 80% in an experimentally achievable system, making resources of ensembles at Heisenberg limit practically available for quantum metrology.

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