We consider violation of CHSH inequality for states before and after entanglement swapping. We present a pair of initial states which do not violate CHSH inequality however the final state violates CHSH inequality for some results of Bell measurement performed in order to swap entanglement.
The two observables are complementary if they cannot be measured simultaneously, however they become maximally complementary if their eigenstates are mutually unbiased. Only then the measurement of one observable gives no information about the other observable. The spin projection operators onto three mutually orthogonal directions are maximally complementary only for the spin 1/2. For the higher spin numbers they are no longer unbiased. In this work we examine the properties of spin 1 Mutually Unbiased Bases (MUBs) and look for the physical meaning of the corresponding operators. We show that if the computational basis is chosen to be the eigenbasis of the spin projection operator onto some direction z, the states of the other MUBs have to be squeezed. Then, we introduce the analogs of momentum and position operators and interpret what information about the spin vector the observer gains while measuring them. Finally, we study the generation and the measurement of MUBs states by introducing the Fourier like transform through spin squeezing. The higher spin numbers are also considered.
We present an entanglement purification protocol for a mixture of a pure entangled state and a pure product state, which are orthogonal to each other. The protocol is a combination of bisection method and one-way hashing protocol. We give recursive formula for the rate of the protocol for different states, i.e., the number of maximally entangled two-qubit pairs obtained with the protocol per a single copy of the initial state. We also calculate numerically the rate for some states.Entanglement is a resource in quantum information. Maximally entangled states are a basic ingredient of fundamental quantum information protocols such as, e.g., quantum teleportation ͓1͔, dense coding ͓2͔, or Ekert's quantum cryptographic protocol ͓3͔. In these protocols the maximally entangled pair is shared by two parties and used to perform a certain task. However, in the real world the parties share noisy entangled pairs. Bennett et al. have shown that many pairs in mixed entangled states can be distilled to a smaller number of pairs in nearly maximally entangled states ͓4,5͔. In particular, they presented purification protocols that can be realized by means of local operations and classical communication. Let us suppose that the parties share n pairs of qubits, each of which is in the state . If in using a particular protocol the parties can obtain m pairs of qubits, each of which is in the maximal entangled state, from n pairs of qubits, each of which is in state , then the protocol has the rate m n for the state . Different protocols have different rates and moreover one needs different protocols for different states. The maximal rate for state , i.e., the rate of the optimal protocol for state , is called distillable entanglement. Distillable entanglement of mixed states is usually difficult to calculate, and it is only known for bound entangled states, maximally correlated states, and some other specific mixed states ͓6-11͔. For bound entangled states it is equal to zero ͓6͔ while for maximally correlated states it is equal to the relative entropy of entanglement ͓11-14͔ and can be distilled by the one-way hashing protocol ͓15,16͔. However, for many states only upper and lower bounds on distillable entanglement are known. Lower bounds are usually given by the rates of particular protocols. Upper bounds are given by entanglement measures known to be greater or equal to distillable entanglement, e.g., the relative entropy of entanglement.In this Brief Report we present an entanglement purification protocol for a mixture of a pure entangled state and a pure product state that are orthogonal to each other. The very first protocol for these states was presented in ͓5͔. Our protocol is a combination of Procrustean method of entanglement concentration ͓17͔, bisection method, and one-way hashing protocol ͓15,16͔.We assume that Alice and Bob share many copies of the stateis the maximal entangled state. State is a mixture of the maximal entangled state and a product state. The product state is orthogonal to the maximal entangled state. L...
Device independent dimension witnesses (DW) are a remarkable way to test the dimension of a quantum system in a prepare-and-measure scenario imposing minimal assumptions on the internal features of the devices. However, as the dimension increases, the major obstacle in the realization of DW arises due to the requirement of many outcome quantum measurements. In this article, we propose a new variant of a widely studied communication task (random access code) and take its average payoff as the DW. The presented DW applies to arbitrarily large quantum systems employing only binary outcome measurements. I. INTRODUCTIONRealizing higher-dimensional quantum systems with full control is one of the crucial barriers towards implementing many quantum information processing protocols and testing the foundations of physics. While the process of quantum tomography allows us to reconstruct a quantum system, however, it requires the assumption of fully characterized measurement devices. The device independent framework [1,2] in a prepare-and-measure experiment provides a methodology to obtain a lower bound on the dimension without assuming the internal features of the devices. Moreover, quantum advantages in information processing, for example, quantum communication complexity [3,4] are linked to this approach. Despite its merits, implementing device independent dimension witnesses (DWs) for higher dimensional quantum systems [5-9] faces several complications.
In every experimental test of a Bell inequality, we are faced with the problem of inefficient detectors. How we treat the events when no particle was detected has a big influence on the properties of the inequality. In this work, we study this influence. We show that the choice of post-processing can change the critical detection efficiency, the equivalence between different inequalities or the applicability of the non-signaling principle. We also consider the problem of choosing the optimal post-processing strategy. We show that this is a non-trivial problem and that different strategies are optimal for different ranges of detector efficiencies.
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