scholarly journals General classes of impossible operations through the existence of incomparable states

2007 ◽  
Vol 7 (4) ◽  
pp. 392-400
Author(s):  
I. Chattopadhyay ◽  
D. Sarkar
Keyword(s):  
Large Class ◽  
General Class ◽  
Inner Product ◽  
Entangled States ◽  
Unitary Operators ◽  
Joint System ◽  
Bipartite State ◽  
Local Operation ◽  
Information Conservation ◽  
Hadamard Gate

In this work we show that the most general class of anti-unitary operators are nonphysical in nature through the existence of incomparable pure bipartite entangled states. It is also shown that a large class of inner-product-preserving operations defined only on the three qubits having spin-directions along x,y and z are impossible. If we perform such an operation locally on a particular pure bipartite state then it will exactly transform to another pure bipartite state that is incomparable with the original one. As subcases of the above results we find the nonphysical nature of universal exact flipping operation and existence of universal Hadamard gate. Beyond the information conservation in terms of entanglement, this work shows how an impossible local operation evolve with the joint system in a nonphysical way.

Generalized three-party sharing of operations on remote single qutrit

2014 ◽  
Vol 12 (03) ◽  
pp. 1450011 ◽  
Author(s):  
Pengfei Xing ◽  
Yimin Liu ◽  
Chuanmei Xie ◽  
Xiansong Liu ◽  
Zhanjun Zhang
Keyword(s):  
Success Probability ◽  
Entangled States ◽  
Entangled State ◽  
Quantum Channels ◽  
Channel State ◽  
Classical Communication ◽  
Maximally Entangled State ◽  
Quantum Operations ◽  
Local Operation ◽  
Maximally Entangled States

Two three-party schemes are put forward for sharing quantum operations on a remote qutrit with local operation and classical communication as well as shared entanglements. The first scheme uses a two-qutrit and three-qutrit non-maximally entangled states as quantum channels, while the second replaces the three-qutrit non-maximally entangled state with a two-qutrit. Both schemes are treated and compared from the four aspects of quantum and classical resource consumption, necessary-operation complexity, success probability and efficiency. It is found that the latter is overall more optimal than the former as far as a restricted set of operations is concerned. In addition, comparisons of both schemes with other four relevant ones are also made to show their two features, including degree generalization and channel-state generalization. Furthermore, some concrete discussions on both schemes are made to expose their important features of security, symmetry and experimental feasibility. Particularly, it is revealed that the success probabilities and intrinsic efficiencies in both schemes are completely determined by the shared entanglement.

scholarly journals Absolute Quantum Theory (after Chang, Lewis, Minic and Takeuchi), and a Road to Quantum Deletion

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 174
Author(s):  
Koen Thas
Keyword(s):  
Quantum Theory ◽  
Finite Fields ◽  
Hilbert Spaces ◽  
Inner Product ◽  
Unitary Operators ◽  
Evolution Operators ◽  
Quantum Theories ◽  
Classical Quantum ◽  
Absolute Quantum ◽  
Made In

In a recent paper, Chang et al. have proposed studying “quantum F u n ”: the q ↦ 1 limit of modal quantum theories over finite fields F q , motivated by the fact that such limit theories can be naturally interpreted in classical quantum theory. In this letter, we first make a number of rectifications of statements made in that paper. For instance, we show that quantum theory over F 1 does have a natural analogon of an inner product, and so orthogonality is a well-defined notion, contrary to what was claimed in Chang et al. Starting from that formalism, we introduce time evolution operators and observables in quantum F u n , and we determine the corresponding unitary group. Next, we obtain a typical no-cloning result in the general realm of quantum F u n . Finally, we obtain a no-deletion result as well. Remarkably, we show that we can perform quantum deletion by almost unitary operators, with a probability tending to 1. Although we develop the construction in quantum F u n , it is also valid in any other quantum theory (and thus also in classical quantum theory in complex Hilbert spaces).

scholarly journals Spectral Theory of the Klein–Gordon Equation in Krein Spaces

2008 ◽  
Vol 51 (3) ◽  
pp. 711-750 ◽  
Author(s):  
Heinz Langer ◽  
Branko Najman ◽  
Christiane Tretter
Keyword(s):  
Gordon Equation ◽  
Main Tool ◽  
Inner Product ◽  
Continuous Group ◽  
Unitary Operators ◽  
Spectral Functions ◽  
Indefinite Inner Product ◽  
Krein Spaces ◽  
Klein Gordon ◽  
Klein Gordon Equation

AbstractIn this paper the spectral properties of the abstract Klein–Gordon equation are studied. The main tool is an indefinite inner product known as the charge inner product. Under certain assumptions on the potential V, two operators are associated with the Klein–Gordon equation and studied in Krein spaces generated by the charge inner product. It is shown that the operators are self-adjoint and definitizable in these Krein spaces. As a consequence, they possess spectral functions with singularities, their essential spectra are real with a gap around 0 and their non-real spectra consist of finitely many eigenvalues of finite algebraic multiplicity which are symmetric to the real axis. One of these operators generates a strongly continuous group of unitary operators in the Krein space; the other one gives rise to two bounded semi-groups. Finally, the results are applied to the Klein–Gordon equation in ℝn.

scholarly journals Ramsey interferometry with generalized one-axis twisting echoes

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 268 ◽  
Author(s):  
Marius Schulte ◽  
Victor J. Martínez-Lahuerta ◽  
Maja S. Scharnagl ◽  
Klemens Hammerer
Keyword(s):  
Large Class ◽  
General Class ◽  
Particle Number ◽  
Sensitivity Enhancement ◽  
Local Sensitivity ◽  
Before And After ◽  
Phase Signal

We consider a large class of Ramsey interferometry protocols which are enhanced by squeezing and un-squeezing operations before and after a phase signal is imprinted on the collective spin of N particles. We report an analytical optimization for any given particle number and strengths of (un-)squeezing. These results can be applied even when experimentally relevant decoherence processes during the squeezing and un-squeezing interactions are included. Noise between the two interactions is however not considered in this work. This provides a generalized characterization of squeezing echo protocols, recovering a number of known quantum metrological protocols as local sensitivity maxima, thereby proving their optimality. We discover a single new protocol. Its sensitivity enhancement relies on a double inversion of squeezing. In the general class of echo protocols, the newly found over-un-twisting protocol is singled out due to its Heisenberg scaling even at strong collective dephasing.

Deterministic entanglement of assistance in quantum networks

2006 ◽  
Vol 84 (6-7) ◽  
pp. 639-644
Author(s):  
B C Sanders ◽  
G Gour ◽  
D A Meyer
Keyword(s):  
Entangled States ◽  
Maximum Probability ◽  
Quantum Networks ◽  
Classical Communication ◽  
Bipartite State ◽  
Operational Interpretation ◽  
Entanglement Distribution ◽  
Entanglement Of Assistance ◽  
03.65 Ud ◽  
03.67 Mn

We present a powerful theorem for tripartite remote entanglement distribution protocols, which provides an operational interpretation of concurrence as a type of entanglement capacity, and we establish that concurrence of assistance, which we show is an entanglement monotone, identifies capabilities of and limitations to producing pure bipartite entangled states from pure tripartite entangled states. In addition, we show that, if concurrence of assistance for the pure tripartite state is at least as large as the concurrence of the desired pure bipartite state, then the former may be transformed to the latter via local operations and classical communication, and we calculate the maximum probability for this transformation when this condition is not met.PACS Nos.: 03.67.Mn, 03.67.Hk, 03.65.Ud

ENTANGLEMENT OF FORMATION FOR A CLASS OF SPECIAL QUANTUM STATES

2007 ◽  
Vol 05 (03) ◽  
pp. 343-352 ◽  
Author(s):  
HUI ZHAO ◽  
ZHI-XI WANG
Keyword(s):  
Lower Bound ◽  
Large Class ◽  
Special Kind ◽  
Quantum States ◽  
The Other ◽  
High Dimensional ◽  
Entangled States ◽  
Mixed States ◽  
Density Matrices ◽  
Entanglement Of Formation

The entanglement of formation for a class of high-dimensional quantum mixed states is investigated. A special kind of D-computable states is defined and the lower bound of entanglement of formation for a large class of density matrices whose decompositions lie in these D-computable quantum states is obtained. Moreover we present a kind of construction for this special state which is defined by a class of special matrices with two non-zero different eigenvalues and the other eigenvalues are zero. Making use of the D-computable we construct a class of bound entangled states.

scholarly journals Stabilizing entangled states with quasi-local quantum dynamical semigroups

2012 ◽  
Vol 370 (1979) ◽  
pp. 5259-5269 ◽  
Author(s):  
Francesco Ticozzi ◽  
Lorenza Viola
Keyword(s):  
Large Class ◽  
Output Feedback ◽  
Pure State ◽  
Entangled States ◽  
Input State ◽  
Quantum Dynamical ◽  
Quantum Dynamical Semigroups ◽  
Markovian Dynamics ◽  
Local Quantum

We provide a solution to the problem of determining whether a target pure state can be asymptotically prepared using dissipative Markovian dynamics under fixed locality constraints. Besides recovering existing results for a large class of physically relevant entangled states, our approach has the advantage of providing an explicit stabilization test solely based on the input state and constraints of the problem. Connections with the formalism of frustration-free parent Hamiltonians are discussed, as well as control implementations in terms of a switching output-feedback law.

scholarly journals Geometry of the Faces for Separable States Arising from Generalized Choi Maps

2012 ◽  
Vol 19 (02) ◽  
pp. 1250009 ◽  
Author(s):  
Kil-Chan Ha ◽  
Seung-Hyeok Kye
Keyword(s):  
Large Class ◽  
Convex Cone ◽  
Entangled States ◽  
Geometric Structures ◽  
Separable States ◽  
Ppt States

We exhibit examples of separable states which are on the boundary of the convex cone generated by all separable states but in the interior of the convex cone generated by all PPT states. We also analyze the geometric structures of the smallest face generated by those examples. As a byproduct, we obtain a large class of entangled states with positive partial transposes.

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