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arXiv:quant-ph/0112004 · Physical Review Letters

Entanglement Concentration Using Quantum Statistics

Nikola Paunković, Yasser Omar, Sougato Bose, Vlatko Vedral

Published Apr 18, 2002• 45 citations
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Abstract

We propose an entanglement concentration scheme which uses only the effects of quantum statistics of indistinguishable particles. This establishes the fact that useful quantum information processing can be accomplished by quantum statistics alone. Because of the basis independence of statistical effects, our protocol requires less knowledge of the initial state than most entanglement concentration schemes. Moreover, no explicit controlled operation is required at any stage.

DOI
10.1103/physrevlett.88.187903

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We propose an entanglement concentration scheme which uses only the effects of quantum statistics of indistinguishable particles. This establishes the fact that useful quantum information processing can be accomplished by quantum statistics alone. Because of the basis independence of statistical effects, our protocol requires less knowledge of the initial state than most entanglement concentration schemes. Moreover, no explicit controlled operation is required at any stage.
We extend the idea of entanglement concentration protocol for pure states (Phys. Rev. Lett. 88 , 187903) to the case of entanglement distillation for mixed states. The scheme works only with particle statistics and local operations, without the need of any other interactions. We show that the maximally entangled state can be distilled out when the initial state is pure, otherwise the entanglement distilled depends on the off-diagonal element of density matrix of the initial state. Because of the requirement for density matrix, the entanglement distilled is always less than one, and this result is the same for both fermionic and bosonic particles. The distillation efficiency is a product of the diagonal elements of the initial state, it takes the maximum 50%, the same as that in the case for pure states.
Entanglement is one of the most useful resources in quantum information processing. If a sender and receiver share noiseless entanglement in the form of maximally entangled states, then Chapter 6 showed how they can teleport quantum bits between each other with the help of classical communication, or they can double the capacity of a noiseless qubit channel for transmitting classical information. We will see further applications in Chapter 20 where they can exploit noiseless entanglement to assist in the transmission of classical or quantum data over a noisy quantum channel. Given the utility of maximal entanglement, a reasonable question is to ask what a sender and receiver can accomplish if they share pure entangled states that are not maximally entangled. In the quantum Shannon-theoretic setting, we make the further assumption that the sender and receiver can share many copies of these pure entangled states. We find out in this chapter that they can “concentrate” these non-maximally entangled states to maximally entangled ebits, and the optimal rate at which they can do so in the asymptotic limit is equal to the “entropy of entanglement” (the von Neumann entropy of half of one copy of the original state). Entanglement concentration is thus another fundamental task in noiseless quantum Shannon theory, and it gives a different operational interpretation to the von Neumann entropy. Entanglement concentration is perhaps complementary to Schumacher compression in the sense that it gives a firm quantum information-theoretic interpretation of the term “ebit” (just as Schumacher compression did for the term “qubit”), and it plays a part in demonstrating how the entropy of entanglement is the unique measure of entanglement for pure bipartite states.
How to concentrate non-maximally entangled states for quantum communication is a fundamental problem in quantum information. In this paper, we will apply generalized measurements to entanglement concentration of known non-maximally entangled pure states in arbitrary dimensional system. How to design the generalized measurements for the unambiguous discrimination of linearly independent non-orthogonal states is crucial for the concentration of the known non-maximally entangled states. The result shows that, any known non-maximally entangled pure state (for arbitrary dimensional system) can be transformed to the maximally entangled state only by introducing a qubit as ancilla and a joint unitary transformation operation on one of the entangled particles and the ancilla. In addition, because the less entangled state of each fail round will be re-concentrated too, the entanglement waste during the concentration process will be greatly reduced.
A recent paper (Phys. Rev. A \textbf{86}, 034305 (2012)) proposed an entanglement concentration protocol (ECP) for distilling one pair of maximally entangled multi-photon Greenberger-Horne-Zeilinger (GHZ) state from two pairs of less-entangled multi-photon states with the photonic Faraday rotation. In this paper, we put forward an improved ECP for arbitrary less-entangled multi-photon GHZ state. In the ECP, we only require one pair of less-entangled multi-photon state and one auxiliary photon, and the whole concentration process only requires local operations. Moreover, our ECP can be used repeatedly to further concentrate the less-entangled multi-photon state and obtain a higher success probability. If consider the practical operation and imperfect detection, our protocol is more efficient. This ECP may be useful in current quantum information processing.
Quantum coherence, an essential feature of quantum mechanics allowing quantum superposition of states, is a resource for quantum information processing. Coherence emerges in a fundamentally different way for nonidentical and identical particles. For the latter, a unique contribution exists linked to indistinguishability that cannot occur for nonidentical particles. Here, we experimentally demonstrate this additional contribution to quantum coherence with an optical setup, showing that its amount directly depends on the degree of indistinguishability, and exploiting it in a quantum phase discrimination protocol. Furthermore, the designed setup allows for simulating fermionic particles with photons, thus assessing the role of exchange statistics in coherence generation and utilization. Our experiment proves that independent indistinguishable particles can offer a controllable resource of coherence and entanglement for quantum-enhanced metrology.