اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدLower bounds on the squashed entanglement for multi-party systems
106
0
0.0
(
0
)
تأليف
Wei Song
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Squashed entanglement is a promising entanglement measure that can be generalized to multipartite case, and it has all of the desirable properties for a good entanglement measure. In this paper we present computable lower bounds to evaluate the multipartite squashed entanglement. We also derive some inequalities relating the squashed entanglement to the other entanglement measure.
قيم البحث
اقرأ أيضاً
In this paper, we present a quantum secure multi-party summation protocol, which allows multiple mutually distrustful parties to securely compute the summation of their secret data. In the presented protocol, a semitrusted third party is introduced t
o help multiple parties to achieve this secure task. Besides, the entanglement swapping of $d$-level cat states and Bell states is employed to securely transmit message between each party and the semitrusted third party. At last, its security against some common attacks is analyzed, which shows that the presented protocol is secure in theory.
Squashed entanglement is a measure for the entanglement of bipartite quantum states. In this paper we present a lower bound for squashed entanglement in terms of a distance to the set of separable states. This implies that squashed entanglement is fa
ithful, that is, strictly positive if and only if the state is entangled. We derive the bound on squashed entanglement from a bound on quantum conditional mutual information, which is used to define squashed entanglement and corresponds to the amount by which strong subadditivity of von Neumann entropy fails to be saturated. Our result therefore sheds light on the structure of states that almost satisfy strong subadditivity with equality. The proof is based on two recent results from quantum information theory: the operational interpretation of the quantum mutual information as the optimal rate for state redistribution and the interpretation of the regularised relative entropy of entanglement as an error exponent in hypothesis testing. The distance to the set of separable states is measured by the one-way LOCC norm, an operationally-motivated norm giving the optimal probability of distinguishing two bipartite quantum states, each shared by two parties, using any protocol formed by local quantum operations and one-directional classical communication between the parties. A similar result for the Frobenius or Euclidean norm follows immediately. The result has two applications in complexity theory. The first is a quasipolynomial-time algorithm solving the weak membership problem for the set of separable states in one-way LOCC or Euclidean norm. The second concerns quantum Merlin-Arthur games. Here we show that multiple provers are not more powerful than a single prover when the verifier is restricted to one-way LOCC operations thereby providing a new characterisation of the complexity class QMA.
New measures of multipartite entanglement are constructed based on two definitions of multipartite information and different methods of optimizing over extensions of the states. One is a generalization of the squashed entanglement where one takes the
mutual information of parties conditioned on the states extension and takes the infimum over such extensions. Additivity of the multipartite squashed entanglement is proved for bo
Given a finite dimensional pure state transformation restricted by entanglement assisted local operations and classical communication (ELOCC), we derive minimum and maximum bounds on the entanglement of an ancillary catalyst that allows that transfor
mation. These bounds are non-trivial even when the Schmidt number of both the original and ancillary states becomes large. We identify a lower bound for the dimension of a catalyst allowing a particular ELOCC transformation. Along with these bounds, we present further constraints on ELOCC transformations by identifying restrictions on the Schmidt coefficients of the target state. In addition, an example showing the existence of qubit ELOCC transformations with multiple ranges of potential ancillary states is provided. This example reveals some additional difficulty in finding strict bounds on ELOCC transformations, even in the qubit case. Finally, a comparison of the bounds in this paper with previously discovered bounds is presented.
Shors and Grovers famous quantum algorithms for factoring and searching show that quantum computers can solve certain computational problems significantly faster than any classical computer. We discuss here what quantum computers_cannot_ do, and spec
ifically how to prove limits on their computational power. We cover the main known techniques for proving lower bounds, and exemplify and compare the methods.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
