scholarly journals IMPOSSIBILITY OF PARTIAL SWAPPING OF QUANTUM INFORMATION

2007 ◽  
Vol 05 (04) ◽  
pp. 605-609 ◽  
Author(s):  
I. CHAKRABARTY
Keyword(s):  
Information Theory ◽  
Hilbert Space ◽  
Quantum Mechanics ◽  
Quantum Information ◽  
Higher Dimensions ◽  
Quantum Information Theory ◽  
Quantum States ◽  
Two Dimensional ◽  
Bloch Sphere ◽  
Two Parameters

It is a well–known fact that a quantum state |ψ(θ, ϕ)〉 is represented by a point on the Bloch sphere, characterized by two parameters θ and ϕ. Here in this work, we find out another impossible operation in quantum information theory. We name this impossibility as 'Impossibility of partial swapping of quantum information'. By this we mean that if two unknown quantum states are given at the input port, there exists no physical process, consistent with the principles of quantum mechanics, by which we can partially swap either of the two parameters θ and ϕ between these two quantum states. In this work, we provided the impossibility proofs for the qubits (i.e. the quantum states taken from two-dimensional Hilbert space) and this impossible operation can be shown to hold in higher dimensions also.

scholarly journals JENSEN–SHANNON DIVERGENCE AS A MEASURE OF THE DEGREE OF ENTANGLEMENT

2008 ◽  
Vol 06 (supp01) ◽  
pp. 715-720 ◽  
Author(s):  
A. P. MAJTEY ◽  
A. BORRAS ◽  
M. CASAS ◽  
P. W. LAMBERTI ◽  
A. PLASTINO
Keyword(s):  
Information Theory ◽  
Hilbert Space ◽  
Quantum Information ◽  
Quantum Information Theory ◽  
Quantum States ◽  
Jensen Shannon Divergence ◽  
Degree Of Entanglement

The notion of distance in Hilbert space is relevant in many scenarios. In particular, "distances" between quantum states play a central role in quantum information theory. An appropriate measure of distance is the quantum Jensen Shannon divergence (QJSD) between quantum states. Here we study this distance as a geometrical measure of entanglement and apply it to different families of states.

scholarly journals A Knot Theoretic Extension of the Bloch Sphere Representation for Qubits in Hilbert Space and Its Application to Contextuality and Many-Worlds Theories

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1135
Author(s):  
Stefan Heusler ◽  
Paul Schlummer ◽  
Malte S. Ubben
Keyword(s):  
Information Theory ◽  
Hilbert Space ◽  
Quantum Information ◽  
Knot Theory ◽  
Quantum Physics ◽  
Quantum Information Theory ◽  
Entangled States ◽  
Theoretic Model ◽  
Bloch Sphere ◽  
Many Worlds

We argue that the usual Bloch sphere is insufficient in various aspects for the representation of qubits in quantum information theory. For example, spin flip operations with the quaternions I J K = e 2 π i 2 = − 1 and J I K = + 1 cannot be distinguished on the Bloch sphere. We show that a simple knot theoretic extension of the Bloch sphere representation is sufficient to track all unitary operations for single qubits. Next, we extend the Bloch sphere representation to entangled states using knot theory. As applications, we first discuss contextuality in quantum physics—in particular the Kochen-Specker theorem. Finally, we discuss some arguments against many-worlds theories within our knot theoretic model of entanglement. The key ingredients of our approach are symmetries and geometric properties of the unitary group.

scholarly journals Reality, Indeterminacy, Probability, and Information in Quantum Theory

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 747
Author(s):  
Arkady Plotnitsky
Keyword(s):  
Information Theory ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Quantum Information ◽  
Quantum Correlations ◽  
Quantum Information Theory ◽  
Quantum Phenomena

Following the view of several leading quantum-information theorists, this paper argues that quantum phenomena, including those exhibiting quantum correlations (one of their most enigmatic features), and quantum mechanics may be best understood in quantum-informational terms. It also argues that this understanding is implicit already in the work of some among the founding figures of quantum mechanics, in particular W. Heisenberg and N. Bohr, half a century before quantum information theory emerged and confirmed, and gave a deeper meaning to, to their insights. These insights, I further argue, still help this understanding, which is the main reason for considering them here. My argument is grounded in a particular interpretation of quantum phenomena and quantum mechanics, in part arising from these insights as well. This interpretation is based on the concept of reality without realism, RWR (which places the reality considered beyond representation or even conception), introduced by this author previously, in turn, following Heisenberg and Bohr, and in response to quantum information theory.

QUANTUM GATES AND PROTOCOLS WITH SPHERICAL WIGNER FUNCTIONS

2005 ◽  
Vol 03 (03) ◽  
pp. 501-509
Author(s):  
ORSOLYA KÁLMÁN ◽  
MIHÁLY G. BENEDICT
Keyword(s):  
Information Theory ◽  
Distribution Function ◽  
Quantum Information ◽  
Wigner Function ◽  
Quantum Information Theory ◽  
Quantum Gates ◽  
Bloch Sphere ◽  
Dense Coding ◽  
Space Formulation ◽  
Quasiprobability Distribution

The fundamental concepts and operations of quantum information theory are considered in the framework of a phase space formulation of quantum mechanics, where the states of one or several qubits are represented by a specific continuous quasiprobability distribution function on the Bloch sphere or on its generalizations. The function we use is the spherical Wigner function. It is shown that the usual transformations of quantum information theory are certain rotations or more general transformations of this Wigner function. We show that the standard teleportation and dense coding protocols can be appropriately formulated in terms of the Wigner function.

scholarly journals NATURAL METRIC FOR QUANTUM INFORMATION THEORY

2009 ◽  
Vol 07 (05) ◽  
pp. 1009-1019 ◽  
Author(s):  
P. W. LAMBERTI ◽  
M. PORTESI ◽  
J. SPARACINO
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Quantum Information Theory ◽  
Quantum States ◽  
Square Root ◽  
Mixed States ◽  
Basic Properties ◽  
Illustrative Application

We study in detail a very natural metric for quantum states. This new proposal has two basic ingredients: entropy and purification. The metric for two mixed states is defined as the square root of the entropy of the average of representative purifications of those states. Some basic properties are analyzed and its relation to other distances is investigated. As an illustrative application, the proposed metric is evaluated for one-qubit mixed states.

Thresholds for reduction-related entanglement criteria in quantum information theory

2015 ◽  
Vol 15 (13&14) ◽  
pp. 1165-1184
Author(s):  
Maria A. Jivulescu ◽  
Nicolae Lupa ◽  
Ion Nechita
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Quantum State ◽  
Random Matrix ◽  
Matrix Theory ◽  
Quantum Information Theory ◽  
Quantum States ◽  
Absolute Reduction ◽  
Open Questions ◽  
Pure Quantum State

We consider random bipartite quantum states obtained by tracing out one subsystem from a random, uniformly distributed, tripartite pure quantum state. We compute thresholds for the dimension of the system being traced out, so that the resulting bipartite quantum state satisfies the reduction criterion in different asymptotic regimes. We consider as well the basis-independent version of the reduction criterion (the absolute reduction criterion), computing thresholds for the corresponding eigenvalue sets. We do the same for other sets relevant in the study of absolute separability, using techniques from random matrix theory. Finally, we gather and compare the known values for the thresholds corresponding to different entanglement criteria, and conclude with a list of open questions.

Quantum information theory

2009 ◽  
Author(s):  
Stephen Barnett
Keyword(s):  
Information Theory ◽  
Quantum Mechanics ◽  
Quantum Information ◽  
Quantum Information Theory ◽  
Quantum Circuits ◽  
Classical Counterpart ◽  
Theory Of Information ◽  
The Many

The astute reader might have formed the impression that quantum in formation science is a rather qualitative discipline because we have not, as yet, explained how to quantify quantum information. There are three good reasons for leaving this important question until the final chapter. Firstly, quantum information theory is technically demanding and to treat it at an earlier stage might have suggested that our subject was more complicated than it is. Secondly, there is the fact that many of the ideas in the field, such as teleportation and quantum circuits, are unfamiliar and it was important to present these as simply as possible. Finally, and most importantly, the theory of quantum information is not yet fully developed. It has not yet reached, in particular, the level of completeness of its classical counterpart. For this reason we can answer only some of the many questions we would like a quantum theory of information to address. Having said this, we can say that however, there are beautiful and useful mathematical results and it seems certain that these will continue to form an important part of the theory as it develops. We noted in the introduction to Chapter 1 that ‘quantum mechanics is a probabilistic theory and so it was inevitable that a quantum information theory would be developed’. A presentation of at least the beginnings of a quantitative theory is the objective of this final chapter. The entropy or information derived from a given probability distribution is, as we have seen, a convenient measure of the uncertainty associated with the distribution. If many of the probabilities are large, so that many of the possible events are comparably likely, then the entropy will be large. If one probability is close to unity, however, then the entropy will be small. It is convenient to introduce entropy in quantum mechanics as a measure of the uncertainty, or lack of knowledge, of the form of the state vector. If we know that our system is in a particular pure state then the associated uncertainty or entropy should be zero. For mixed states, however, it will take a non-zero value.

scholarly journals Dimension-independent bounds for Hardy's experiment

2014 ◽  
Vol 12 (06) ◽  
pp. 1450039 ◽  
Author(s):  
Zhen-Peng Xu ◽  
Hong-Yi Su ◽  
Jing-Ling Chen
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Higher Dimensions ◽  
Quantum Information Theory ◽  
Fundamental Importance ◽  
Alternative Proof ◽  
Type Ii ◽  
Maximum Probability ◽  
Hardy's Paradox

Hardy's paradox is of fundamental importance in quantum information theory. So far, there have been two types of its extensions into higher dimensions: in the first type the maximum probability of nonlocal events is roughly 9% and remains the same as the dimension changes (dimension-independent), while in the second type the probability becomes larger as the dimension increases, reaching approximately 40% in the infinite limit. Here, we (i) give an alternative proof of the first type, (ii) study the situation in which the maximum probability of nonlocal events can also be dimension-independent in the second type and (iii) conjecture how the situation could be changed in order that (ii) still holds.

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