W-like states are not necessary for totally correct quantum anonymous leader election

2015 ◽  
Vol 15 (7&8) ◽  
pp. 677-684
Author(s):  
Alexander Norton
Keyword(s):  
Quantum State ◽  
Distributed Computation ◽  
Leader Election ◽  
Quantum States ◽  
W State ◽  
Correct Quantum ◽  
Local Quantum ◽  
Symmetric Quantum ◽  
Non Local ◽  
Entangled Quantum States

I show that $W$-like entangled quantum states are not a necessary quantum resource for totally correct anonymous leader election protocols. This is proven by defining a symmetric quantum state that is $n$-partite SLOCC inequivalent to the $W$ state, and then constructing a totally correct anonymous leader election protocol using this state. This result, which contradicts the previous necessity result of D'Hondt and Panangaden, furthers our understanding of how non-local quantum states can be used as a resource for distributed computation.

scholarly journals Designing locally maximally entangled quantum states with arbitrary local symmetries

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 450
Author(s):  
Oskar Słowik ◽  
Adam Sawicki ◽  
Tomasz Maciążek
Keyword(s):  
Quantum State ◽  
Quantum States ◽  
Local Mode ◽  
Trivial Representation ◽  
Tensor Power ◽  
Technical Result ◽  
Combinatorial Objects ◽  
Local Symmetries ◽  
Entangled Quantum States ◽  
Group Of Symmetries

One of the key ingredients of many LOCC protocols in quantum information is a multiparticle (locally) maximally entangled quantum state, aka a critical state, that possesses local symmetries. We show how to design critical states with arbitrarily large local unitary symmetry. We explain that such states can be realised in a quantum system of distinguishable traps with bosons or fermions occupying a finite number of modes. Then, local symmetries of the designed quantum state are equal to the unitary group of local mode operations acting diagonally on all traps. Therefore, such a group of symmetries is naturally protected against errors that occur in a physical realisation of mode operators. We also link our results with the existence of so-called strictly semistable states with particular asymptotic diagonal symmetries. Our main technical result states that the Nth tensor power of any irreducible representation of SU(N) contains a copy of the trivial representation. This is established via a direct combinatorial analysis of Littlewood-Richardson rules utilising certain combinatorial objects which we call telescopes.

scholarly journals Local and Non-Local Invasive Measurements on Two Quantum Spins Coupled via Nanomechanical Oscillations

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1078
Author(s):  
Dimitrios Maroulakos ◽  
Levan Chotorlishvili ◽  
Dominik Schulz ◽  
Jamal Berakdar
Keyword(s):  
Quantum Coherence ◽  
Indirect Measurement ◽  
Quantum Spin ◽  
Quantum States ◽  
Spin Interaction ◽  
First Case ◽  
Composite Quantum System ◽  
Local Quantum ◽  
Non Local ◽  
Quantum Spins

Symmetry plays the central role in the structure of quantum states of bipartite (or many-body) fermionic systems. Typically, symmetry leads to the phenomenon of quantum coherence and correlations (entanglement) inherent to quantum systems only. In the present work, we study the role of symmetry (i.e., quantum correlations) in invasive quantum measurements. We consider the influence of a direct or indirect measurement process on a composite quantum system. We derive explicit analytical expressions for the case of two quantum spins positioned on both sides of the quantum cantilever. The spins are coupled indirectly to each others via their interaction with a magnetic tip deposited on the cantilever. Two types of quantum witnesses can be considered, which quantify the invasiveness of a measurement on the systems’ quantum states: (i) A local quantum witness stands for the consequence on the quantum spin states of a measurement done on the cantilever, meaning we first perform a measurement on the cantilever, and subsequently a measurement on a spin. (ii) The non-local quantum witness signifies the response of one spin if a measurement is done on the other spin. In both cases the disturbance must involve the cantilever. However, in the first case, the spin-cantilever interaction is linear in the coupling constant Ω , where as in the second case, the spin-spin interaction is quadratic in Ω . For both cases, we find and discuss analytical results for the witness.

An anomaly of non-locality

2007 ◽  
Vol 7 (1&2) ◽  
pp. 157-170 ◽  
Author(s):  
A.A. Methot ◽  
V. Scarani
Keyword(s):  
Bell Inequalities ◽  
Present Knowledge ◽  
Quantum States ◽  
Entangled States ◽  
Low Dimensions ◽  
Local Correlations ◽  
Non Local ◽  
Entangled Quantum States ◽  
Maximally Entangled States ◽  
Non Locality

Ever since the work of Bell, it has been known that entangled quantum states can produce non-local correlations between the outcomes of separate measurements. However, for almost forty years, it has been assumed that the most non-local states would be the maximally entangled ones. Surprisingly it is not the case: non-maximally entangled states are generally more non-local than maximally entangled states for all the measures of non-locality proposed to date: Bell inequalities, the Kullback-Leibler distance, entanglement simulation with communication or with non-local boxes, the detection loophole and efficiency of cryptography. In fact, one can even find simple examples in low dimensions, confirming that it is not an artefact of a specifically constructed Hilbert space or topology. This anomaly shows that entanglement and non-locality are not only different concepts, but also truly different resources. We review the present knowledge on this anomaly, point out that Hardy's theorem has the same feature, and discuss the perspectives opened by these discoveries.

Activation of the Violation of Svetlichny Inequality for a Broad Class of States

2016 ◽  
Vol 23 (04) ◽  
pp. 1650018 ◽  
Author(s):  
Paweł Caban ◽  
Andrzej Molenda ◽  
Kamila Trzcińska
Keyword(s):  
Quantum Mechanics ◽  
Quantum State ◽  
Broad Class ◽  
Quantum States ◽  
Quantum Nonlocality ◽  
Research Results ◽  
Nonlocal Correlation ◽  
Local Quantum ◽  
First Time

The fact that several copies of a local quantum state — when processed together — can generate a nonlocal correlation, i.e. the superactivation of quantum nonlocality, is a well-known feature of quantum mechanics. Most of research results focused strongly on the bipartite scenario. In this paper we show that the activation of violation of Svetlichny inequality, reported for the first time in our previous paper, is not an exceptional phenomenon but holds for a broad class of quantum states as well for pure as for mixed, noisy ones.

“Non-locality”

2017 ◽  
Author(s):  
Richard Healey
Keyword(s):  
Quantum Theory ◽  
Quantum Entanglement ◽  
Quantum States ◽  
Entangled States ◽  
Entangled Quantum States ◽  
Action At A Distance ◽  
Insight Into ◽  
Non Locality

Quantum entanglement is popularly believed to give rise to spooky action at a distance of a kind that Einstein decisively rejected. Indeed, important recent experiments on systems assigned entangled states have been claimed to refute Einstein by exhibiting such spooky action. After reviewing two considerations in favor of this view I argue that quantum theory can be used to explain puzzling correlations correctly predicted by assignment of entangled quantum states with no such instantaneous action at a distance. We owe both considerations in favor of the view to arguments of John Bell. I present simplified forms of these arguments as well as a game that provides insight into the situation. The argument I give in response turns on a prescriptive view of quantum states that differs both from Dirac’s (as stated in Chapter 2) and Einstein’s.

scholarly journals Gaussian quantum states can be disentangled using symplectic rotations

2021 ◽  
Vol 111 (3) ◽  
Author(s):  
Maurice A. de Gosson
Keyword(s):  
Quantum State ◽  
Covariance Matrices ◽  
Quantum States ◽  
Weyl Quantization ◽  
Symplectic Transformation ◽  
Metaplectic Operator

AbstractWe show that every Gaussian mixed quantum state can be disentangled by conjugation with a passive symplectic transformation, that is a metaplectic operator associated with a symplectic rotation. The main tools we use are the Werner–Wolf condition on covariance matrices and the symplectic covariance of Weyl quantization. Our result therefore complements a recent study by Lami, Serafini, and Adesso.

scholarly journals Purification and redistribution of entanglement via single local filtering

2014 ◽  
Vol 12 (01) ◽  
pp. 1450004 ◽  
Author(s):  
K. O. Yashodamma ◽  
P. J. Geetha ◽  
Sudha
Keyword(s):  
Quantum State ◽  
The State ◽  
Quantum States ◽  
Local Action ◽  
Entanglement Transfer ◽  
Local Filtering

The effect of filtering operation with respect to purification and concentration of entanglement in quantum states are discussed in this paper. It is shown, through examples, that the local action of the filtering operator on a part of the composite quantum state allows for purification of the remaining part of the state. The redistribution of entanglement in the subsystems of a noise affected state is shown to be due to the action of local filtering on the non-decohering part of the system. The varying effects of the filtering parameter, on the entanglement transfer between the subsystems, depending on the choice of the initial quantum state is illustrated.

Introduction, generation and entanglement of entangled displaced even and odd squeezed states

2021 ◽  
pp. 2050047
Author(s):  
Amir Karimi
Keyword(s):  
Quantum States ◽  
Entangled States ◽  
Squeezed States ◽  
Displacement Operator ◽  
Text Type ◽  
Level Atom ◽  
Displacement Parameter ◽  
Entangled Quantum States ◽  
Quantized Field ◽  
Classical Fields

In this paper, first, we introduce special types of entangled quantum states named “entangled displaced even and odd squeezed states” by using displaced even and odd squeezed states which are constructed via the action of displacement operator on the even and odd squeezed states, respectively. Next, we present a theoretical scheme to generate the introduced entangled states. This scheme is based on the interaction between a [Formula: see text]-type three-level atom and a two-mode quantized field in the presence of two strong classical fields. In the continuation, we consider the entanglement feature of the introduced entangled states by evaluating concurrence. Moreover, we study the influence of the displacement parameter on the entanglement degree of the introduced entangled states and compare the results. It will be observed that the concurrence of the “entangled displaced odd squeezed states” has less decrement with respect to the “entangled displaced even squeezed states” by increasing the displacement parameter.

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.

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