اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدAnalysis of the role of von Neumanns projection postulate in the canonical scheme of quantum teleportation and main quantum algorithms
68
0
0.0
(
0
)
تأليف
Andrei Khrennikov
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Modern development of quantum technologies based on quantum information theory stimulated analysis of proposed computational, cryptographic and teleportational schemes from the viewpoint of quantum foundations. It is evident that not all mathematical calculations performed in complex Hilbert space can be directly realized in physical space. Recently by analyzing the original EPR paper we found that they argument was based on the misuse of the von Neumanns projection postulate. Opposite to von Neumann, Einstein, Podolsky and Rosen (EPR) applied this postulate to observables represented by operators with degenerate spectra. It was completely forbidden by von Neumanns axiomatics of QM. It is impossible to repeat the EPR considerations in the von Neumanns framework. In this note we analyze quantum teleportation by taking into account von Neumanns projection postulate. Our analysis shows that so called quantum teleportation is impossible in von Neumanns framework. On the other hand, our analysis implies that the main quantum algorithms are totally consistent with von Neumanns projection postulate.
قيم البحث
اقرأ أيضاً
We study an electrostatic qubit monitored by a point-contact detector. Projecting an entire qubit-detector wave function on the detector eigenstates we determine the precision limit for the qubit measurements, allowed by quantum mechanics. We found t
hat this quantity is determined by qubit dynamics as well as decoherence, generated by the measurement. Our results show how the quantum precision limit can be improved by a proper design of a measurement procedure.
The concept of a classical player, corresponding to a classical random variable, is extended to include quantum random variables in the form of self adjoint operators on infinite dimensional Hilbert space. A quantum version of Von Neumanns Minimax th
eorem for infinite dimensional (or continuous) games is proved.
Quantum measurements can be interpreted as a generalisation of probability vectors, in which non-negative real numbers are replaced by positive semi-definite operators. We extrapolate this analogy to define a generalisation of doubly stochastic matri
ces that we call doubly normalised tensors (DNTs), and formulate a corresponding version of Birkhoff-von Neumanns theorem, which states that permutations are the extremal points of the set of doubly stochastic matrices. We prove that joint measurability arises as a mathematical feature of DNTs in this context, needed to establish a characterisation similar to Birkhoff-von Neumanns. Conversely, we also show that DNTs emerge naturally from a particular instance of a joint measurability problem, remarking its relevance in general operator theory.
Propagating quantum microwaves have been proposed and successfully implemented to generate entanglement, thereby establishing a promising platform for the realisation of a quantum communication channel. However, the implementation of quantum teleport
ation with photons in the microwave regime is still absent. At the same time, recent developments in the field show that this key protocol could be feasible with current technology, which would pave the way to boost the field of microwave quantum communication. Here, we discuss the feasibility of a possible implementation of microwave quantum teleportation in a realistic scenario with losses. Furthermore, we propose how to implement quantum repeaters in the microwave regime without using photodetection, a key prerequisite to achieve long distance entanglement distribution.
Bidirectional teleportation is a fundamental protocol for exchanging quantum information between two parties by means of a shared resource state and local operations and classical communication (LOCC). In this paper, we develop two seemingly differen
t ways of quantifying the simulation error of unideal bidirectional teleportation by means of the normalized diamond distance and the channel infidelity, and we prove that they are equivalent. By relaxing the set of operations allowed from LOCC to those that completely preserve the positivity of the partial transpose, we obtain semi-definite programming lower bounds on the simulation error of unideal bidirectional teleportation. We evaluate these bounds for three key examples: when there is no resource state at all and for isotropic and Werner states, in each case finding an analytical solution. The first aforementioned example establishes a benchmark for classical versus quantum bidirectional teleportation. We then evaluate the performance of some schemes for bidirectional teleportation due to [Kiktenko et al., Phys. Rev. A 93, 062305 (2016)] and find that they are suboptimal and do not go beyond the aforementioned classical limit for bidirectional teleportation. We offer a scheme alternative to theirs that is provably optimal. Finally, we generalize the whole development to the setting of bidirectional controlled teleportation, in which there is an additional assisting party who helps with the exchange of quantum information, and we establish semi-definite programming lower bounds on the simulation error for this task. More generally, we provide semi-definite programming lower bounds on the performance of bipartite and multipartite channel simulation using a shared resource state and LOCC.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
