scholarly journals Volume of the space of qubit-qubit channels and state transformations under random quantum channels

2018 ◽  
Vol 30 (10) ◽  
pp. 1850019 ◽  
Author(s):  
Attila Lovas ◽  
Attila Andai
Keyword(s):  
Lebesgue Measure ◽  
Quantum Channel ◽  
Probability Distributions ◽  
Building Blocks ◽  
The State ◽  
Quantum States ◽  
Qubit State ◽  
Quantum Channels ◽  
State Transformation ◽  
Explicit Formulas

The simplest building blocks for quantum computations are the qubit-qubit quantum channels. In this paper, we analyze the structure of these channels via their Choi representation. The restriction of a quantum channel to the space of classical states (i.e. probability distributions) is called the underlying classical channel. The structure of quantum channels over a fixed classical channel is studied, the volume of the general and unital qubit channels with respect to the Lebesgue measure is computed and explicit formulas are presented for the distribution of the volume of quantum channels over given classical channels. We study the state transformation under uniformly random quantum channels. If one applies a uniformly random quantum channel (general or unital) to a given qubit state, the distribution of the resulted quantum states is presented.

scholarly journals Probabilistic Resumable Quantum Teleportation of a Two-Qubit Entangled State

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 352 ◽  
Author(s):  
Zhan-Yun Wang ◽  
Yi-Tao Gou ◽  
Jin-Xing Hou ◽  
Li-Ke Cao ◽  
Xiao-Hui Wang
Keyword(s):  
Quantum Channel ◽  
Quantum Teleportation ◽  
The State ◽  
Entangled States ◽  
Entangled State ◽  
Quantum Channels ◽  
Unknown State ◽  
Optimal Probability

We explicitly present a generalized quantum teleportation of a two-qubit entangled state protocol, which uses two pairs of partially entangled particles as quantum channel. We verify that the optimal probability of successful teleportation is determined by the smallest superposition coefficient of these partially entangled particles. However, the two-qubit entangled state to be teleported will be destroyed if teleportation fails. To solve this problem, we show a more sophisticated probabilistic resumable quantum teleportation scheme of a two-qubit entangled state, where the state to be teleported can be recovered by the sender when teleportation fails. Thus the information of the unknown state is retained during the process. Accordingly, we can repeat the teleportion process as many times as one has available quantum channels. Therefore, the quantum channels with weak entanglement can also be used to teleport unknown two-qubit entangled states successfully with a high number of repetitions, and for channels with strong entanglement only a small number of repetitions are required to guarantee successful teleportation.

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.

TELEPORTATION OF UNKNOWN STATE BY QUTRITS

2008 ◽  
Vol 06 (02) ◽  
pp. 369-378 ◽  
Author(s):  
ARTI CHAMOLI ◽  
C. M. BHANDARI
Keyword(s):  
Quantum Entanglement ◽  
Quantum State ◽  
Quantum Channel ◽  
The State ◽  
Quantum Channels ◽  
Unknown State ◽  
Different Types

Quantum entanglement, like other resources, is now considered to be a resource. It can be produced, concentrated if required, swapped, transported and consumed. During recent years, various schemes of quantum state teleportation have been proposed using different types of quantum channels. Not restricting to qubit based systems, qutrit states and channels have also been of considerable interest. In the present paper, we investigate the teleportation of an unknown single qutrit state, as well as a two qutrit state through a three qutrit quantum channel, along with the required operations to recover the state. This is further generalized to the case of teleportation of an n-qutrit system.

A SCHEME FOR TELEPORTING A GENERAL N-QUBIT STATE THROUGH NONMAXIMALLY ENTANGLED QUANTUM CHANNELS

2009 ◽  
Vol 23 (18) ◽  
pp. 2261-2267 ◽  
Author(s):  
XIU-LAO TIAN ◽  
XIAO-QIANG XI
Keyword(s):  
Tensor Product ◽  
Quantum Channel ◽  
Transformation Matrix ◽  
Inverse Matrix ◽  
Qubit State ◽  
Quantum Channels ◽  
Decomposition Matrix

We propose a scheme for teleporting an arbitrary unknown N-qubit state through nonmaximally entangled quantum channels by using the method of general Bell base decomposition, and give the universal decomposition matrix of the N-qubit. Using the decomposition matrix, one can easily obtain the collapsed state at the receiver's site. The inverse matrix of the decomposition matrix is just the transformation matrix that the receiver can manipulate. The decomposition matrix is a function of the parameters of the quantum channel. After defining the submatrix of the quantum channel, we find that the decomposition matrix is a tensor product of the submatrices.

TRANSFORMATION MATRIX OF NETWORK-CONTROLLED TELEPORTATION

2009 ◽  
Vol 23 (30) ◽  
pp. 3609-3619 ◽  
Author(s):  
XIU-LAO TIAN
Keyword(s):  
Quantum State ◽  
Quantum Channel ◽  
Ghz State ◽  
Transformation Matrix ◽  
Qubit State ◽  
Controlled Teleportation ◽  
Quantum Channels ◽  
Hadamard Operation

According to the collapse principle of quantum state when being measured, we present a method of directly writing out transformation matrix by looking at the figure of a network-controlled quantum channel. We find the rule of constructing transformation matrix in network-controlled teleportation. Based on this method, we gain transformation matrix of two-qubit state teleportation in which two GHZ state act as controlled quantum channels. We further proposed a scheme of one-qubit teleportation by a series-controlled quantum channel and teleportation of three-qubit via a typical network controlled quantum channel, in which two-qubit state instead of GHZ state act as quantum channel. So, Hadamard operation is not necessary in our scheme.

Quantum two-state sharing

2021 ◽  
pp. 2150292
Author(s):  
Peng-Cheng Ma ◽  
Gui-Bin Chen ◽  
Xiao-Wei Li ◽  
You-Bang Zhan
Keyword(s):  
Quantum Channel ◽  
Success Probability ◽  
The State ◽  
Quantum States ◽  
Entangled State ◽  
Single Qubit ◽  
Unit Success Probability

In this paper, we propose a novel scheme for quantum two-state sharing (QTSS) by using a five-qubit entangled state as the quantum channel. In this scheme, a dealer Alice has two unknown quantum states and wants her three agents to share the quantum states. After the dealer performs a four-qubit measurement on her qubits, and the controller employs a single-qubit measurement on his own qubit, the state receivers can reconstruct the original states by using the appropriate unitary operations. It is shown that, only if all agents collaborate with each other, the QTSS can be completed with unit success probability.

Multi-hop teleportation of N-qubit state via Bell states

2021 ◽  
Vol 36 (08) ◽  
pp. 2150053
Author(s):  
Negin Fatahi
Keyword(s):  
Quantum Teleportation ◽  
Large Scale ◽  
Quantum States ◽  
Qubit State ◽  
Bell States ◽  
Quantum Channels ◽  
Single Qubit ◽  
Qubit States

Multi-hop teleportation is a quantum teleportation scheme for transferring quantum states on a large scale. In this paper, a new multi-hop teleportation protocol is investigated for transferring arbitrary N-qubit states between M-neighbor nodes. In this scheme, intermediate nodes are connected with each other by symmetric entangled Bell states as quantum channels. First, one-hop teleportation of single-qubit, two-qubit and N-qubit states are introduced, then this method is generalized to two-hop and multi-hop teleportation for N-qubit. Also, we calculate the efficiency of this scheme.

scholarly journals Tensorization of the strong data processing inequality for quantum chi-square divergences

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 199
Author(s):  
Yu Cao ◽  
Jianfeng Lu
Keyword(s):  
Data Processing ◽  
Relative Entropy ◽  
Quantum Channel ◽  
Quantum States ◽  
Quantum Channels ◽  
Chi Square ◽  
Quantum Regime ◽  
Quantum Relative Entropy ◽  
Data Processing Inequality ◽  
Arbitrary Quantum

It is well-known that any quantum channel E satisfies the data processing inequality (DPI), with respect to various divergences, e.g., quantum χκ2 divergences and quantum relative entropy. More specifically, the data processing inequality states that the divergence between two arbitrary quantum states ρ and σ does not increase under the action of any quantum channel E. For a fixed channel E and a state σ, the divergence between output states E(ρ) and E(σ) might be strictly smaller than the divergence between input states ρ and σ, which is characterized by the strong data processing inequality (SDPI). Among various input states ρ, the largest value of the rate of contraction is known as the SDPI constant. An important and widely studied property for classical channels is that SDPI constants tensorize. In this paper, we extend the tensorization property to the quantum regime: we establish the tensorization of SDPIs for the quantum χκ1/22 divergence for arbitrary quantum channels and also for a family of χκ2 divergences (with κ≥κ1/2) for arbitrary quantum-classical channels.

scholarly journals Quantum Controlled Teleportation of Arbitrary Two-Qubit State via Entangled States

2018 ◽  
Vol 2018 ◽  
pp. 1-4 ◽  
Author(s):  
Lei Shi ◽  
Kaihang Zhou ◽  
Jiahua Wei ◽  
Yu Zhu ◽  
Qiuli Zhu
Keyword(s):  
Quantum Channel ◽  
Quantum States ◽  
Qubit State ◽  
Entangled States ◽  
Controlled Teleportation ◽  
Entangled State ◽  
Classical Information ◽  
Implementation Processes ◽  
Successful Probability

We put forward an efficient quantum controlled teleportation scheme, in which arbitrary two-qubit state is transmitted from the sender to the remote receiver via two entangled states under the control of the supervisor. In this paper, we use the combination of one two-qubit entangled state and one three-qubit entangled state as quantum channel for achieving the transmission of unknown quantum states. We present the concrete implementation processes of this scheme. Furthermore, we calculate the successful probability and the amount of classical information of our protocol.

scholarly journals INFORMATION TRANSMISSION VIA ENTANGLED QUANTUM STATES IN GAUSSIAN CHANNELS WITH MEMORY

2006 ◽  
Vol 04 (03) ◽  
pp. 439-452 ◽  
Author(s):  
NICOLAS J. CERF ◽  
JULIEN CLAVAREAU ◽  
JÉRÉMIE ROLAND ◽  
CHIARA MACCHIAVELLO
Keyword(s):  
Quantum Channel ◽  
Quantum States ◽  
Gaussian Channel ◽  
Hard Problem ◽  
Quantum Channels ◽  
Classical Capacity ◽  
Gaussian Channels ◽  
Memoryless Channels ◽  
Entangled Quantum States ◽  
With Memory

Gaussian quantum channels have recently attracted a growing interest, since they may lead to a tractable approach to the generally hard problem of evaluating quantum channel capacities. However, the analysis performed so far has always been restricted to memoryless channels. Here, we consider the case of a bosonic Gaussian channel with memory, and show that the classical capacity can be significantly enhanced by employing entangled input symbols instead of product symbols.

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