scholarly journals LOCAL INVARIANTS AND PAIRWISE ENTANGLEMENT IN SYMMETRIC MULTIQUBIT SYSTEM

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1917-1933 ◽  
Author(s):  
A. R. USHA DEVI ◽  
M. S. UMA ◽  
R. PRABHU ◽  
SUDHA
Keyword(s):  
Classification Scheme ◽  
Spin Squeezing ◽  
Qubit System ◽  
Local Invariants ◽  
Complete Set ◽  
Qubit States

Pairwise entanglement properties of a symmetric multi-qubit system are analyzed through a complete set of two-qubit local invariants. Collective features of entanglement, such as spin squeezing, are expressed in terms of invariants and a classification scheme for pairwise entanglement is proposed. The invariant criteria given here are shown to be related to the recently proposed (Phys. Rev. Lett.95, 120502 (2005)) generalized spin squeezing inequalities for pairwise entanglement in symmetric multi-qubit states.

scholarly journals Parameter estimation of qubit states with unknown phase parameter

2015 ◽  
Vol 13 (01) ◽  
pp. 1450044 ◽  
Author(s):  
Jun Suzuki
Keyword(s):  
Parameter Estimation ◽  
Logarithmic Derivative ◽  
Mean Square ◽  
Level System ◽  
Optimal Measurement ◽  
Unknown Phase ◽  
Phase Parameter ◽  
Qubit System ◽  
Mean Square Errors ◽  
Qubit States

We discuss a problem of parameter estimation for quantum two-level system, qubit system, in presence of unknown phase parameter. We analyze trade-off relations for mean square errors (MSEs) when estimating relevant parameters with separable measurements based on known precision bounds; the symmetric logarithmic derivative (SLD) Cramér–Rao (CR) bound and Hayashi–Gill–Massar (HGM) bound. We investigate the optimal measurement which attains the HGM bound and discuss its properties. We show that the HGM bound for relevant parameters can be attained asymptotically by using some fraction of given n quantum states to estimate the phase parameter. We also discuss the Holevo bound which can be attained asymptotically by a collective measurement.

scholarly journals Geometric local invariants and pure three-qubit states

2011 ◽  
Vol 83 (6) ◽  
Author(s):  
Mark S. Williamson ◽  
Marie Ericsson ◽  
Markus Johansson ◽  
Erik Sjöqvist ◽  
Anthony Sudbery ◽  
...  
Keyword(s):  
Local Invariants ◽  
Qubit States

scholarly journals ON THE NON-EXISTENCE OF A UNIVERSAL HADAMARD GATE

2007 ◽  
Vol 05 (06) ◽  
pp. 845-855
Author(s):  
PREETI PARASHAR
Keyword(s):  
Fourier Transform ◽  
Higher Dimensions ◽  
Quantum Fourier Transform ◽  
Qubit System ◽  
Hadamard Gate ◽  
Qubit States ◽  
Hadamard Operation

We establish the non-existence of a universal Hadamard gate for an arbitrary qubit, by considering two different principles; namely, no-superluminal signalling and non-increase of entanglement under LOCC. It is also shown that these principles are not violated if and only if the qubit states belong to the special ensemble obtained recently. We then extend the non-existence of the Hadamard operation to a multi-qubit system. In higher dimensions, the analog of the Hadamard gate is the quantum Fourier transform. We show that it is not possible to design this gate for an arbitrary qudit.

Local invariants for multi-partite entangled states allowing for a simple entanglement criterion

2004 ◽  
Vol 4 (5) ◽  
pp. 383-395
Author(s):  
H. Aschauer ◽  
J. Calsamiglia ◽  
M. Hein ◽  
H.J. Briegel
Keyword(s):  
Physical Meaning ◽  
Entangled States ◽  
Mixed States ◽  
Polynomial Invariants ◽  
Partial Transposition ◽  
Straightforward Generalization ◽  
Local Invariants ◽  
Complete Set ◽  
New Criterion ◽  
Entanglement Criterion

We present local invariants of multi-partite pure or mixed states, which can be easily calculated and have a straight-forward physical meaning. As an application, we derive a new entanglement criterion for arbitrary mixed states of $n$ parties. The new criterion is weaker than the partial transposition criterion but offers advantages for the study of multipartite systems. A straightforward generalization of these invariants allows for the construction of a complete set of observable polynomial invariants.

scholarly journals Bipartite quantum measurements with optimal single-sided distinguishability

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 442
Author(s):  
Jakub Czartowski ◽  
Karol Życzkowski
Keyword(s):  
Composite System ◽  
Edge Length ◽  
Regular Simplex ◽  
Optimal Basis ◽  
Joint Measurement ◽  
Qubit System ◽  
Local Quantum ◽  
Complete Set ◽  
State Tomography ◽  
The One

We analyse orthogonal bases in a composite N×N Hilbert space describing a bipartite quantum system and look for a basis with optimal single-sided mutual state distinguishability. This condition implies that in each subsystem the N2 reduced states form a regular simplex of a maximal edge length, defined with respect to the trace distance. In the case N=2 of a two-qubit system our solution coincides with the elegant joint measurement introduced by Gisin. We derive explicit expressions of an analogous constellation for N=3 and provide a general construction of N2 states forming such an optimal basis in HN⊗HN. Our construction is valid for all dimensions for which a symmetric informationally complete (SIC) generalized measurement is known. Furthermore, we show that the one-party measurement that distinguishes the states of an optimal basis of the composite system leads to a local quantum state tomography with a linear reconstruction formula. Finally, we test the introduced tomographical scheme on a complete set of three mutually unbiased bases for a single qubit using two different IBM machines.

scholarly journals Effect of Entanglement on Geometric Phase for Multi-Qubit States

2009 ◽  
Vol 16 (02n03) ◽  
pp. 305-323 ◽  
Author(s):  
Mark S. Williamson ◽  
Vlatko Vedral
Keyword(s):  
Hilbert Space ◽  
Geometric Phase ◽  
Correction Term ◽  
Entangled State ◽  
Cluster States ◽  
W States ◽  
Local Invariants ◽  
Projective Hilbert Space ◽  
Classical Correlations ◽  
Qubit States

When a multi-qubit state evolves under local unitaries it may obtain a geometric phase, a feature dependent on the geometry of the state projective Hilbert space. A correction term to this geometric phase, in addition to the local subsystem phases, may appear from correlations between the subsystems. We find that this correction term can be characterized completely either by the entanglement or by the classical correlations for several classes of entangled state. States belonging to the former set are W states and their mixtures, while members of the latter set are cluster states, GHZ states and two classes of bound entangled state. We probe the structures of these states more finely using local invariants and suggest that the cause of the entanglement correction is a recently introduced gauge field-like SL(2,ℂ)-invariant called twist.

Computational power of single qubit discrete-time quantum walk

2021 ◽  
Author(s):  
Shivani Singh ◽  
Prateek Chawla ◽  
Anupam Sarkar ◽  
C. M. Chandrashekar
Keyword(s):  
Discrete Time ◽  
Quantum Walk ◽  
Quantum Gates ◽  
Computational Power ◽  
Position Space ◽  
Single Qubit ◽  
Qubit System ◽  
Time Quantum ◽  
Universal Quantum ◽  
Qubit States

Abstract Quantum walk has been regarded as a primitive to universal quantum computation. By using the operations required to describe the single particle discrete-time quantum walk on a position space we demonstrate the realization of the universal set of gates on two-and three-qubit system. The idea is to reap the effective Hilbert space of the single qubit and the position space on which it evolves in superposition of position space in order to realize multi-qubit states and universal set of quantum gates on them. Realization of many non-trivial gates in the form of engineering arbitrary states is simpler in the proposed quantum walk model when compared to the circuit based model of computation. We will also discuss the scalability of the model and some propositions for using lesser number of qubits in realizing larger qubit systems.

Qubit masking in multipartite qubit system

2021 ◽  
pp. 2150156
Author(s):  
Wei-Min Shang ◽  
Fu-Lin Zhang ◽  
Jie Zhou ◽  
Hui-Xian Meng ◽  
Jing-Ling Chen
Keyword(s):  
Recent Work ◽  
Quantum Entanglement ◽  
Quantum Correlation ◽  
Entangled States ◽  
Qubit System ◽  
Qubit States

The no-masking theories show that it is impossible to mask the set of all qubit states into the quantum correlation of bipartite qubit system or tripartite qubit system. In this paper, we give a new proof of the no-masking situation of the tripartite qubit system. Recent work has shown that there exists a universal masker which can mask an arbitrary set of qubit states in four-qubit systems perfectly by means of the maximum entangled states. Here we show that there exist more than one masking scheme even for the same multipartite qubit system. Basing on the maximum entangled states we give the deterministic masking scenario for N-qubit system. In practice, decoherence hinders us from obtaining the maximum entangled states. From this viewpoint, the masking scenario based on non-maximum entangled states becomes more universal. Furthermore, we provide an approximate quantum masking scenario and investigate the relation between approximate masking and quantum entanglement.

scholarly journals Bell’s inequality, generalized concurrence and entanglement in qubits

2019 ◽  
Vol 34 (06n07) ◽  
pp. 1950032 ◽  
Author(s):  
Po-Yao Chang ◽  
Su-Kuan Chu ◽  
Chen-Te Ma
Keyword(s):  
Upper Bound ◽  
Entanglement Entropy ◽  
Qubit State ◽  
Bell’S Inequality ◽  
Bell's Inequality ◽  
Qubit System ◽  
Maximal Violation ◽  
Topological Entanglement Entropy ◽  
Qubit States

It is well known that the maximal violation of the Bell’s inequality for a two-qubit system is related to the entanglement formation in terms of a concurrence. However, a generalization of this relation to an [Formula: see text]-qubit state has not been found. In this paper, we demonstrate some extensions of the relation between the upper bound of the Bell’s violation and a generalized concurrence in several [Formula: see text]-qubit states. In particular, we show the upper bound of the Bell’s violation can be expressed as a function of the generalized concurrence, if a state can be expressed in terms of two variables. We apply the relation to the Wen-Plaquette model and show that the topological entanglement entropy can be extracted from the maximal Bell’s violation.

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