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.

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.

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 Multi-Bloch vector representation of the qutrit

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.

Proposal for dimensionality testing in QPQ

2018 ◽  
Vol 18 (13&14) ◽  
pp. 1125-1142
Author(s):  
Arpita Maitra ◽  
Bibhas Adhikari ◽  
Satyabrata Adhikari
Keyword(s):  
Information Processing ◽  
Quantum Information ◽  
Quantum System ◽  
Quantum State ◽  
Quantum Information Processing ◽  
Quantum States ◽  
Quantum Private Query ◽  
Unfair Advantage ◽  
Security Proofs

Recently, dimensionality testing of a quantum state has received extensive attention (Ac{\'i}n et al. Phys. Rev. Letts. 2006, Scarani et al. Phys. Rev. Letts. 2006). Security proofs of existing quantum information processing protocols rely on the assumption about the dimension of quantum states in which logical bits are encoded. However, removing such assumption may cause security loophole. In the present paper, we show that this is indeed the case. We choose two players' quantum private query protocol by Yang et al. (Quant. Inf. Process. 2014) as an example and show how one player can gain an unfair advantage by changing the dimension of subsystem of a shared quantum system. To resist such attack we propose dimensionality testing in a different way. Our proposal is based on CHSH like game. As we exploit CHSH like game, it can be used to test if the states are product states for which the protocol becomes completely vulnerable.

Abnormal Quantum State Search Based on Parallel Phase Comparison

2021 ◽  
Author(s):  
Guanlei Xu ◽  
Xiaogang Xu ◽  
Xiaotong Wang
Keyword(s):  
Quantum State ◽  
Search Algorithm ◽  
Quantum States ◽  
Quantum Search ◽  
Superposition State ◽  
Quantum Operator ◽  
Abnormal State ◽  
Number Formula ◽  
Speed Up ◽  
Grover Search

We discuss the problem of filtering out abnormal states from a larger number of quantum states. For this type of problem with [Formula: see text] items to be searched, both the traditional search by enumeration and classical Grover search algorithm have the complexity about [Formula: see text]. In this letter a novel quantum search scheme with exponential speed up is proposed for abnormal states. First, a new comprehensive quantum operator is well-designed to extract the superposition state containing all abnormal states with unknown number [Formula: see text] with complexity [Formula: see text] in probability 1 via well-designed parallel phase comparison. Then, every abnormal state is achieved respectively from [Formula: see text] abnormal states via [Formula: see text] times’ measurement. Finally, a numerical example is given to show the efficiency of the proposed scheme.

scholarly journals Quantum Generative Adversarial Networks for learning and loading random distributions

2019 ◽  
Vol 5 (1) ◽  
Author(s):  
Christa Zoufal ◽  
Aurélien Lucchi ◽  
Stefan Woerner
Keyword(s):  
Quantum State ◽  
Quantum Channel ◽  
Quantum Algorithms ◽  
Probability Distributions ◽  
Quantum Algorithm ◽  
Quantum Circuit ◽  
Quantum Simulation ◽  
Quantum States ◽  
Generative Adversarial Networks ◽  
Adversarial Networks

AbstractQuantum algorithms have the potential to outperform their classical counterparts in a variety of tasks. The realization of the advantage often requires the ability to load classical data efficiently into quantum states. However, the best known methods require $${\mathcal{O}}\left({2}^{n}\right)$$O2n gates to load an exact representation of a generic data structure into an $$n$$n-qubit state. This scaling can easily predominate the complexity of a quantum algorithm and, thereby, impair potential quantum advantage. Our work presents a hybrid quantum-classical algorithm for efficient, approximate quantum state loading. More precisely, we use quantum Generative Adversarial Networks (qGANs) to facilitate efficient learning and loading of generic probability distributions - implicitly given by data samples - into quantum states. Through the interplay of a quantum channel, such as a variational quantum circuit, and a classical neural network, the qGAN can learn a representation of the probability distribution underlying the data samples and load it into a quantum state. The loading requires $${\mathcal{O}}\left(poly\left(n\right)\right)$$Opolyn gates and can thus enable the use of potentially advantageous quantum algorithms, such as Quantum Amplitude Estimation. We implement the qGAN distribution learning and loading method with Qiskit and test it using a quantum simulation as well as actual quantum processors provided by the IBM Q Experience. Furthermore, we employ quantum simulation to demonstrate the use of the trained quantum channel in a quantum finance application.

scholarly journals Quantum state space dimension as a quantum resource

2015 ◽  
Vol 13 (06) ◽  
pp. 1550039 ◽  
Author(s):  
A. Plastino ◽  
G. Bellomo ◽  
A. R. Plastino
Keyword(s):  
Quantum Information ◽  
State Space ◽  
Quantum State ◽  
Space Dimension ◽  
Quantum Systems ◽  
Quantum States ◽  
Information Tasks

We argue that the dimensionality of the space of quantum systems’ states should be considered as a legitimate resource for quantum information tasks. The assertion is supported by the fact that quantum states with discord-like capacities can be obtained from classically-correlated states in spaces of dimension large enough. We illustrate things with some simple examples that justify our claim.

High-dimensional quantum state manipulation and tracking

2020 ◽  
pp. 2050045
Author(s):  
Mevludin Licina
Keyword(s):  
Probability Distribution ◽  
Quantum State ◽  
Critical Points ◽  
Theoretical Framework ◽  
Quantum Systems ◽  
Quantum States ◽  
High Dimensional ◽  
Quantum Topology ◽  
Mathematical Representations ◽  
Framework Approach

Dynamical high-dimensional quantum states can be tracked and manipulated in many cases. Using a new theoretical framework approach of manipulating quantum systems, we will show how one can manipulate and introduce parameters that allow tracking and descriptive insight in the dynamics of states. Using quantum topology and other novel mathematical representations, we will show how quantum states behave in critical points when the shift of probability distribution introduces changes.

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