Increasing singlet fraction with entanglement swapping

Abstract

We consider entanglement swapping for certain mixed states. We assume that the initial states have the same singlet fraction and show that the final state can have singlet fraction greater than the initial states. We also consider two quantum teleportations and show that entanglement swapping can increase teleportation fidelity. Finally, we show how this effect can be demonstrated with linear optics.PACS numbers: 03.67. Lx, 42.50.Dv Maximally entangled states are crucial for quantum information processing. If two parties share a pair of qubits in the maximally entangled state then they can perform quantum teleportation. However, usually the parties share nonmaximally entangled state ̺. One can define the singlet fraction F of the state ̺ as the maximal overlap of the state ̺ with the maximally entangled state, i.e.,where the maximum is taken over all maximally entangled states |Ψ . If one performs quantum teleportation with the state ̺ preprocessed by local unitary operations [1] then the optimal teleportation fidelity isIf F > 1 2 then the parties can perform quantum teleportation with the average fidelity of the teleported qubit exceeding classical limit 2 3 . However, it is well known that there are two-qubit entangled states which have F < 1 2 . The Horodecki family has proved that one can increase the singlet fraction of any two-qubit entangled state above 1 2 by non-trace preserving local operations and classical communication (LOCC) [2]. Verstraete and Verschelde have proved that one can do it even with trace preserving LOCC [3]. Moreover, they have found how to obtain optimal teleportation with any two-qubit state, i.e., how to find an LOCC protocol which gives the highest average fidelity of the teleported qubit. Let us now consider a string of nodes connected by nonmaximally entangled pairs of qubits. The first set of entangled pairs is distributed between nodes A and B, the second one is distributed between B and C and so on. In order to perform quantum teleportation from the first to the last node one first distills entanglement between A and B, then between B and C and so on [4]. Next, one performs entanglement swapping [5,6] at each node which creates entanglement between the first and the last node. Notice that usually many entangled pairs are needed between two nodes in order to distill entanglement. Finally, one performs quantum teleportation between the first and the last node. This strategy is crucial ingredient of quantum repeaters [7]. However, for pure nonmaximally entangled states there exists another strategy. Instead of distilling maximally entangled state between each pair of neighboring nodes and then performing entanglement swapping one first performs entanglement swapping and then distills entanglement between the first and the last node [8,9,10,11,12]. If each pair of neighboring nodes is connected by a single nonmaximally entangled pure state this strategy gives higher probability of obtaining maximally entangled state between the first and the last node.In this paper we conside...

Entanglement swapping of two arbitrarily degraded entangled states

“…Several past results have indicated that swapping could result in improved final entanglement for certain input states [9,[14][15][16]. Here we find one extremely broad class of input states (arbitrarily entangled completely pure state) is often capable of increasing the final concurrence above the product of the two initial concurrences.…”

“…II C. Note that over the last few years several papers have treated entanglement swapping for particularly restricted classes of partially mixed input states, nearly all of which fall into the broad category of X-states [13][14][15][16][17]. We ascertain that our general analytical solution of Eqs.…”

“…In any experimental implementation the generated entangled quantum states are not necessarily perfect and, in fact, could be further degraded by transmission through the communication channels. Entanglement swapping of certain classes of degraded states were considered recently [13][14][15][16][17]. However, the nature of the intrinsic imperfections of any quantum network and the exact decoherence mechanism of the transmission channel itself are implementation dependent [18][19][20][21].…”

Deterministic and probabilistic entanglement swapping of nonmaximally entangled states assisted by optimal quantum state discrimination

“…There is no dependence on their numerical values themselves as in the case of a deterministic protocol [see Eqs. (16) and (32)]. This is a nice feature of MC measurements among equally likely symmetric states, where our confidence for identifying each state in the set depends only on the dimension of the subspace spanned by the states (N s ) and the number of states in the set (D A ), through the ratio N s /D A [52,53].…”

“…This projects Alice's and Bob's systems onto a maximally entangled state irrespectively of Charlie's measurement result. Important applications of ES are quantum repeaters [10], which allow one to generate entanglement between distant users [11][12][13], as an entanglement concentration scheme [14][15][16][17], which allows one to increase probabilistically the amount of entanglement between two parties, and in experimental studies on nonlocality [9]. Further applications are generation of GreenbergerHorne-Zeilinger (GHZ) states via multiparticle ES [18,19], quantum secret sharing [20], and quantum communication protocols [21][22][23][24][25].…”