Sub- and super-fidelity as bounds for quantum fidelity

2009 ◽  
Vol 9 (1&2) ◽  
pp. 103-130
Author(s):  
J.A. Miszczak ◽  
Z. Puchala ◽  
P. Horodecki ◽  
A. Uhlmann ◽  
K. Zyczkowski
Keyword(s):  
Quantum System ◽  
Quantum States ◽  
Concave Functions ◽  
Two Dimensional ◽  
Quantum Fidelity

We derive several bounds on fidelity between quantum states. In particular we show that fidelity is bounded from above by a simple to compute quantity we call super--fidelity. It is analogous to another quantity called sub--fidelity. For any two states of a two--dimensional quantum system (N=2) all three quantities coincide. We demonstrate that sub-- and super--fidelity are concave functions. We also show that super--fidelity is super--multiplicative while sub--fidelity is sub--multiplicative and design feasible schemes to measure these quantities in an experiment.Super--fidelity can be used to define a distance between quantum states. With respect to this metric the set of quantum states forms a part of a N^2-1 dimensional hypersphere.

Quasi-two-dimensional quantum states ofH2in stage-2 Rb-intercalated graphite

1996 ◽  
Vol 53 (15) ◽  
pp. 10187-10199 ◽  
Author(s):  
A. P. Smith ◽  
R. Benedek ◽  
F. R. Trouw ◽  
M. Minkoff ◽  
L. H. Yang
Keyword(s):  
Quantum States ◽  
Two Dimensional ◽  
Intercalated Graphite

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.

scholarly journals Probing Rényi entanglement entropy via randomized measurements

Science ◽  
2019 ◽  
Vol 364 (6437) ◽  
pp. 260-263 ◽  
Author(s):  
Tiff Brydges ◽  
Andreas Elben ◽  
Petar Jurcevic ◽  
Benoît Vermersch ◽  
Christine Maier ◽  
...  
Keyword(s):  
Quantum System ◽  
Entanglement Entropy ◽  
Quantum Systems ◽  
Quantum States ◽  
Many Body ◽  
Trapped Ion ◽  
Statistical Correlations ◽  
Quantum Simulator ◽  
Entanglement Structure ◽  
Arbitrary Quantum

Entanglement is a key feature of many-body quantum systems. Measuring the entropy of different partitions of a quantum system provides a way to probe its entanglement structure. Here, we present and experimentally demonstrate a protocol for measuring the second-order Rényi entropy based on statistical correlations between randomized measurements. Our experiments, carried out with a trapped-ion quantum simulator with partition sizes of up to 10 qubits, prove the overall coherent character of the system dynamics and reveal the growth of entanglement between its parts, in both the absence and presence of disorder. Our protocol represents a universal tool for probing and characterizing engineered quantum systems in the laboratory, which is applicable to arbitrary quantum states of up to several tens of qubits.

scholarly journals Tunable super- and subradiant boundary states in one-dimensional atomic arrays

2019 ◽  
Vol 2 (1) ◽  
Author(s):  
Anwei Zhang ◽  
Luojia Wang ◽  
Xianfeng Chen ◽  
Vladislav V. Yakovlev ◽  
Luqi Yuan
Keyword(s):  
Long Range ◽  
Quantum States ◽  
Two Dimensional ◽  
Edge States ◽  
Quantum Metrology ◽  
One Dimensional ◽  
Topological Quantum ◽  
Long Range Interactions ◽  
Boundary States ◽  
Quantum Optical

AbstractEfficient manipulation of quantum states is a key step towards applications in quantum information, quantum metrology, and nonlinear optics. Recently, atomic arrays have been shown to be a promising system for exploring topological quantum optics and robust control of quantum states, where the inherent nonlinearity is included through long-range hoppings. Here we show that a one-dimensional atomic array in a periodic magnetic field exhibits characteristic properties associated with an effective two-dimensional Hofstadter-butterfly-like model. Our work points out super- and sub-radiant topological edge states localized at the boundaries of the atomic array despite featuring long-range interactions, and opens an avenue of exploring an interacting quantum optical platform with synthetic dimensions.

scholarly journals Robust Phase Estimation of Gaussian States in the Presence of Outlier Quantum States

2020 ◽  
Vol 10 (16) ◽  
pp. 5475
Author(s):  
Yukito Mototake ◽  
Jun Suzuki
Keyword(s):  
Coherent State ◽  
Quantum System ◽  
Robust Statistics ◽  
Quantum States ◽  
Phase Estimation ◽  
Gaussian States ◽  
Statistical Framework

In this paper, we investigate the problem of estimating the phase of a coherent state in the presence of unavoidable noisy quantum states. These unwarranted quantum states are represented by outlier quantum states in this study. We first present a statistical framework of robust statistics in a quantum system to handle outlier quantum states. We then apply the method of M-estimators to suppress untrusted measurement outcomes due to outlier quantum states. Our proposal has the advantage over the classical methods in being systematic, easy to implement, and robust against occurrence of noisy states.

Quantum states in a nanotube quantum dot

2017 ◽  
Vol 31 (25) ◽  
pp. 1745023
Author(s):  
J. T. Wang ◽  
J. D. Fan
Keyword(s):  
Carbon Nanotube ◽  
High Efficiency ◽  
Energy Levels ◽  
Quantum States ◽  
Semiconductor Surface ◽  
Energy Structure ◽  
Two Dimensional ◽  
Quantum Energy ◽  
Quantum Bit ◽  
Computer Chips

In this paper, we carry out a theoretical calculation of quantum state and quantum energy structure in carbon nanotube embedded semiconductor surface. In this theoretical model, the electrons in the carbon nanotube are considered as in a two-dimensional cylindrical surface. Their motion, therefore, can be described by the Dirac equation. We solve the equation and find that the energy levels are quantized and are linearly dependent on the wave vectors along the [Formula: see text]-direction that is along the direction of the nanotube. This type of energy structure may have potential application for fabricating high efficiency solar cell or quantum bit in computer chips.

Distribution of x ⋅ p for quantum states on a circle

2015 ◽  
Vol 12 (07) ◽  
pp. 1550078
Author(s):  
Q. H. Liu ◽  
L. Qin ◽  
X. L. Huang ◽  
D. Y. Zhang ◽  
D. M. Xun
Keyword(s):  
Flat Space ◽  
Quantum States ◽  
Free Motion ◽  
Two Dimensional ◽  
Proper Definition ◽  
Dot Product ◽  
Definition Of

We first give the proper definition of the particle's position-momentum dot product, the so-called posmomx ⋅ p, to quantum states on a circular circle, in which the momentum turns out to be the geometric one that is recently intensively studied. Second, we carry out the posmom distributions for eigenstates of the free motion on the circle, i.e. [Formula: see text], (m = 0, ±1, ±2, …). The results are not only potentially experimentally testable, but also reflect a fact that the embedding of the circle S1 in two-dimensional flat space R2 is physically reasonable.

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