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.

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.

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.

scholarly journals The learnability of quantum states

2007 ◽  
Vol 463 (2088) ◽  
pp. 3089-3114 ◽  
Author(s):  
Scott Aaronson
Keyword(s):  
Quantum Computing ◽  
Probability Distribution ◽  
Quantum State ◽  
Learning Theory ◽  
Communication Protocols ◽  
Computational Learning Theory ◽  
Quantum States ◽  
Computational Learning ◽  
State Tomography ◽  
Long Vectors

Traditional quantum state tomography requires a number of measurements that grows exponentially with the number of qubits n . But using ideas from computational learning theory, we show that one can do exponentially better in a statistical setting. In particular, to predict the outcomes of most measurements drawn from an arbitrary probability distribution, one needs only a number of sample measurements that grows linearly with n . This theorem has the conceptual implication that quantum states, despite being exponentially long vectors, are nevertheless ‘reasonable’ in a learning theory sense. The theorem also has two applications to quantum computing: first, a new simulation of quantum one-way communication protocols and second, the use of trusted classical advice to verify untrusted quantum advice.

scholarly journals Engineering two-photon high-dimensional states through quantum interference

2016 ◽  
Vol 2 (2) ◽  
pp. e1501165 ◽  
Author(s):  
Yingwen Zhang ◽  
Filippus S. Roux ◽  
Thomas Konrad ◽  
Megan Agnew ◽  
Jonathan Leach ◽  
...  
Keyword(s):  
Quantum State ◽  
Quantum Interference ◽  
Large Scale ◽  
Quantum States ◽  
High Dimensional ◽  
Initial State ◽  
Two Photon ◽  
Before And After ◽  
Antisymmetric Component ◽  
Quantum Science

Many protocols in quantum science, for example, linear optical quantum computing, require access to large-scale entangled quantum states. Such systems can be realized through many-particle qubits, but this approach often suffers from scalability problems. An alternative strategy is to consider a lesser number of particles that exist in high-dimensional states. The spatial modes of light are one such candidate that provides access to high-dimensional quantum states, and thus they increase the storage and processing potential of quantum information systems. We demonstrate the controlled engineering of two-photon high-dimensional states entangled in their orbital angular momentum through Hong-Ou-Mandel interference. We prepare a large range of high-dimensional entangled states and implement precise quantum state filtering. We characterize the full quantum state before and after the filter, and are thus able to determine that only the antisymmetric component of the initial state remains. This work paves the way for high-dimensional processing and communication of multiphoton quantum states, for example, in teleportation beyond qubits.

scholarly journals Experimental creation of multi-photon high-dimensional layered quantum states

2020 ◽  
Vol 6 (1) ◽  
Author(s):  
Xiao-Min Hu ◽  
Wen-Bo Xing ◽  
Chao Zhang ◽  
Bi-Heng Liu ◽  
Matej Pivoluska ◽  
...  
Keyword(s):  
Quantum Information ◽  
Quantum Entanglement ◽  
Quantum State ◽  
Quantum States ◽  
High Dimensional ◽  
Entangled States ◽  
Entangled State ◽  
Quantum Network ◽  
Quantum Networks ◽  
Qubit States

Abstract Quantum entanglement is one of the most important resources in quantum information. In recent years, the research of quantum entanglement mainly focused on the increase in the number of entangled qubits or the high-dimensional entanglement of two particles. Compared with qubit states, multipartite high-dimensional entangled states have beneficial properties and are powerful for constructing quantum networks. However, there are few studies on multipartite high-dimensional quantum entanglement due to the difficulty of creating such states. In this paper, we experimentally prepared a multipartite high-dimensional state $$\left|{\Psi }_{442}\right\rangle =\frac{1}{2}(\left|000\right\rangle +\left|110\right\rangle +\left|221\right\rangle +\left|331\right\rangle )$$ Ψ 442 = 1 2 ( 000 + 110 + 221 + 331 ) by using the path mode of photons. We obtain the fidelity F = 0.854 ± 0.007 of the quantum state, which proves a real multipartite high-dimensional entangled state. Finally, we use this quantum state to demonstrate a layered quantum network in principle. Our work highlights another route toward complex quantum networks.

scholarly journals On the Non-Uniqueness of Statistical Ensembles Defining a Density Operator and a Class of Mixed Quantum States with Integrable Wigner Distribution

2021 ◽  
Vol 3 (3) ◽  
pp. 473-481
Author(s):  
Charlyne de Gosson ◽  
Maurice de Gosson
Keyword(s):  
Probability Distribution ◽  
Quantum State ◽  
Density Operator ◽  
Wigner Distribution ◽  
Quantum States ◽  
Modulation Spaces ◽  
Statistical Ensemble ◽  
Integrable Functions ◽  
Statistical Ensembles ◽  
Square Integrable Functions

It is standard to assume that the Wigner distribution of a mixed quantum state consisting of square-integrable functions is a quasi-probability distribution, i.e., that its integral is one and that the marginal properties are satisfied. However, this is generally not true. We introduced a class of quantum states for which this property is satisfied; these states are dubbed “Feichtinger states” because they are defined in terms of a class of functional spaces (modulation spaces) introduced in the 1980s by H. Feichtinger. The properties of these states were studied, giving us the opportunity to prove an extension to the general case of a result due to Jaynes on the non-uniqueness of the statistical ensemble, generating a density operator.

scholarly journals Teleportation in an indivisible quantum system

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
E.O. Kiktenko ◽  
A.K. Fedorov ◽  
V.I. Man’ko
Keyword(s):  
Hilbert Space ◽  
Quantum System ◽  
Quantum State ◽  
Quantum Systems ◽  
High Dimensional ◽  
Dimensional System ◽  
Quantum State Transfer ◽  
State Transfer ◽  
The One ◽  
New Framework

AbstractTeleportation protocol is conventionally treated as a method for quantum state transfer between two spatially separated physical carriers. Recent experimental progress in manipulation with high-dimensional quantum systems opens a new framework for implementation of teleportation protocols. We show that the one-qubit teleportation can be considered as a state transfer between subspaces of the whole Hilbert space of an indivisible eight-dimensional system. We explicitly show all corresponding operations and discuss an alternative way of implementation of similar tasks.

Entanglement

2017 ◽  
Author(s):  
Richard Healey
Keyword(s):  
Quantum Theory ◽  
Quantum State ◽  
Physical Condition ◽  
Physical System ◽  
Polarization State ◽  
Quantum Systems ◽  
Ghz State ◽  
Mathematical Representation ◽  
Entangled State ◽  
Physical Relation

Often a pair of quantum systems may be represented mathematically (by a vector) in a way each system alone cannot: the mathematical representation of the pair is said to be non-separable: Schrödinger called this feature of quantum theory entanglement. It would reflect a physical relation between a pair of systems only if a system’s mathematical representation were to describe its physical condition. Einstein and colleagues used an entangled state to argue that its quantum state does not completely describe the physical condition of a system to which it is assigned. A single physical system may be assigned a non-separable quantum state, as may a large number of systems, including electrons, photons, and ions. The GHZ state is an example of an entangled polarization state that may be assigned to three photons.

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 Path-encoded high-dimensional quantum communication over a 2-km multicore fiber

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Beatrice Da Lio ◽  
Daniele Cozzolino ◽  
Nicola Biagi ◽  
Yunhong Ding ◽  
Karsten Rottwitt ◽  
...  
Keyword(s):  
Quantum Key Distribution ◽  
Quantum Communication ◽  
Error Rates ◽  
Quantum States ◽  
High Dimensional ◽  
Secret Key ◽  
System A ◽  
Reliable Transmission ◽  
Multicore Fiber ◽  
Interferometric Detection

AbstractQuantum key distribution (QKD) protocols based on high-dimensional quantum states have shown the route to increase the key rate generation while benefiting of enhanced error tolerance, thus overcoming the limitations of two-dimensional QKD protocols. Nonetheless, the reliable transmission through fiber links of high-dimensional quantum states remains an open challenge that must be addressed to boost their application. Here, we demonstrate the reliable transmission over a 2-km-long multicore fiber of path-encoded high-dimensional quantum states. Leveraging on a phase-locked loop system, a stable interferometric detection is guaranteed, allowing for low error rates and the generation of 6.3 Mbit/s of a secret key rate.

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