Designing locally maximally entangled quantum states with arbitrary local 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.

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

Quantum Information and Computation ◽

10.26421/qic15.7-8-8 ◽

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.

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“Non-locality”

10.1093/oso/9780198714057.003.0004 ◽

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.

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Gaussian quantum states can be disentangled using symplectic rotations

Letters in Mathematical Physics ◽

10.1007/s11005-021-01410-4 ◽

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.

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Purification and redistribution of entanglement via single local filtering

International Journal of Quantum Information ◽

10.1142/s021974991450004x ◽

2014 ◽

Vol 12 (01) ◽

pp. 1450004 ◽

Cited By ~ 5

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.

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Adaptive quantum state estimation for dynamic quantum states

2017 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) ◽

10.1109/cleoe-eqec.2017.8087436 ◽

2017 ◽

Author(s):

Saki Nohara ◽

Ryo Okamoto ◽

Akio Fujiwara ◽

Shigeki Takeuchi

Keyword(s):

State Estimation ◽

Quantum State ◽

Quantum States ◽

Quantum State Estimation

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

International Journal of Quantum Information ◽

10.1142/s0219749920500471 ◽

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.

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MULTIPARTY REMOTELY PREPARING MULTIPARTITE EQUATORIAL ENTANGLED STATES IN HIGH DIMENSIONS

International Journal of Quantum Information ◽

10.1142/s0219749911008088 ◽

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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Multi-Bloch vector representation of the qutrit

Quantum Information and Computation ◽

10.26421/qic11.5-6-1 ◽

2011 ◽

Vol 11 (5&6) ◽

pp. 361-373

Author(s):

Pawel Kurzynski

Keyword(s):

Quantum State ◽

Quantum Systems ◽

Quantum States ◽

The Other ◽

Two Dimensional ◽

Bloch Vector ◽

Vector Representation ◽

Alternative Approach ◽

Complete Set

An ability to describe quantum states directly by average values of measurement outcomes is provided by the Bloch vector. For an informationally complete set of measurements one can construct unique Bloch vector for any quantum state. However, not every Bloch vector corresponds to a quantum state. It seems that only for two-dimensional quantum systems it is easy to distinguish proper Bloch vectors from improper ones, i.e. the ones corresponding to quantum states from the other ones. I propose an alternative approach to the problem in which more than one vector is used. In particular, I show that a state of the qutrit can be described by the three qubit-like Bloch vectors.

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