[Paper Review] Recycling the resource: Sequential usage of shared state in quantum teleportation with weak measurements

Saptarshi Roy, Anindita Bera+3 more|arXiv (Cornell University)|May 10, 2019

Quantum Information and CryptographyComputer Science57 references35 citations

TL;DR

This paper proposes a quantum teleportation protocol using weak measurements to recycle a shared entangled state across multiple sender-receiver pairs, preserving entanglement for reuse. By replacing standard projective Bell measurements with weak measurements—specifically, Bell measurements mixed with white noise—it demonstrates that up to six reattempts are possible with a maximally entangled initial state while maintaining quantum fidelity above the classical threshold, with the maximum reattempt number (MRN) remaining at six even for non-maximally entangled states with concurrence >0.91 ebits.

ABSTRACT

Complete measurements, while providing maximal information gain, results in destruction of the shared entanglement. In the standard teleportation scheme, the sender's measurement on the shared entangled state between the sender and the receiver has that consequence. We propose here a teleportation scheme involving weak measurements which can sustain entanglement upto a certain level so that the reusability of the shared resource state is possible. The measurements are chosen in such a way that it is weak enough to retain entanglement and hence can be reused for quantum tasks, yet adequately strong to ensure quantum advantage in the protocol. In this scenario, we report that at most six sender-receiver duos can reuse the state, when the initial shared state is entangled in a finite neighborhood of the maximally entangled state and for a suitable choice of weak measurements. However, we observe that the reusability number decreases with the decrease in the entanglement of the initial shared state. Among the weakening strategies studied, Bell measurement admixed with white noise performs better than any other low-rank weak measurements in this situation.

Motivation & Objective

• To address the inefficiency of standard teleportation, where shared entanglement is destroyed after a single use.
• To explore whether weak measurements can preserve residual entanglement, enabling reuse of the same resource state for multiple teleportation rounds.
• To identify the maximum number of reattempts (MRN) possible while maintaining quantum fidelity above classical limits.
• To compare different weak measurement strategies in terms of their ability to sustain reusable entanglement for sequential teleportation.

Proposed method

• Uses positive operator-valued measures (POVMs) as weak measurements to reduce disturbance to the shared entangled state.
• Applies a specific weak measurement strategy: mixing Bell states with white noise to create a noisy, weakly projective measurement.
• Employs a recursive fidelity calculation to track teleportation performance across rounds, ensuring fidelity remains above the classical benchmark (2/3).
• Analyzes the evolution of the effective state after each measurement, showing it evolves into an X-state, which is not optimally teleported by standard Bell measurements.
• Uses concurrence as a measure of entanglement to quantify residual entanglement in the reused state.
• Derives a recursion relation for the sharpness parameter λi to maintain a target fidelity of 2/3 across rounds.

Experimental results

Research questions

• RQ1 Can a shared entangled state be reused for multiple rounds of quantum teleportation without full projective measurement?
• RQ2 What is the maximum number of reattempts (MRN) possible when using weak measurements instead of projective measurements?
• RQ3 How does the initial entanglement of the resource state affect the number of reattempts?
• RQ4 Which weak measurement strategy maximizes the reattempt number while preserving quantum advantage?
• RQ5 To what extent does the effective state after measurement remain useful for subsequent teleportation?

Key findings

• The maximum reattempt number (MRN) for a maximally entangled initial state is six when using weak Bell measurements with white noise, maintaining fidelity above the classical threshold of 2/3.
• The MRN remains at six even for non-maximally entangled states with concurrence greater than 0.91 ebits, indicating robustness to entanglement degradation.
• For initial states with lower concurrence (e.g., α < 0.3008), the MRN decreases, with a clear inverse relationship between entanglement and reattempt count.
• Among various weak measurement strategies, Bell measurement admixed with white noise yields the highest MRN, outperforming low-rank weak measurements such as those from orthogonal support.
• When MRN = 6, the effective state after each round becomes separable (concurrence < 0.0007), indicating that entanglement is not necessary for high reattempt count.
• The sharpness parameter λ must be carefully tuned across rounds via a recursion relation to sustain fidelity, with λ1 = 1/3 required for maximally entangled states to achieve f = 2/3 in the first round.