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Indistinguishability of elementary systems as resource for quantum information processing
Rosario Lo Franco, Giuseppe Compagno
TL;DR
Whether indistinguishability can provide useful entanglement for identical particles remains unsettled, despite their role as building blocks of quantum networks. The paper studies independently prepared identical particles with spatial overlap, using separated localized measurements to establish operational entanglement and demonstrate conditional teleportation.
Problem
For identical particles, there is no consensus on entanglement quantification or whether indistinguishability can yield useful entanglement for quantum information processing.
Source: p. 1Method
The authors use separated, spatially localized measurements to assess operational entanglement for independently prepared identical particles under generic spatial-overlap configurations.
Source: pp. 1–2Results
The operational entanglement can be exploited for conditional teleportation that beats the classical fidelity threshold 2/3.
Source: p. 4Takeaways & Limitations
The authors conclude that indistinguishability of identical elementary particles can serve as a resource for quantum information processing.
Source: p. 4
Abstract
from arXiv · showhide
Typical elements of quantum networks are made by identical systems, which are the basic particles constituting a resource for quantum information processing. Whether the indistinguishability due to particle identity is an exploitable quantum resource remains an open issue. Here we study independently prepared identical particles showing that, when they spatially overlap, an operational entanglement exists which can be made manifest by means of separated localized measurements. We prove this entanglement is physical in that it can be directly exploited to activate quantum information protocols, such as teleportation. These results establish that particle indistinguishability is a utilizable quantum feature and open the way to new quantum-enhanced applications.
Reduced density matrix
The reduced density matrix for region R is obtained by tracing over a localized basis in L, projecting onto R, and normalizing.
Reduced density matrix
- The procedure first traces the initial state over a localized basis in L, then projects the result onto region R.The calculation uses {|L ↑⟩, |L ↓⟩}; the procedure is symmetric under exchanging L and R.Source: Reduced density matrix · p. 5
- The projector onto R is the identity on that region’s spatial and pseudospin subspace.It is written as |R⟩⟨R| ⊗ (|↓⟩⟨↓| + |↑⟩⟨↑|).Source: Reduced density matrix · p. 6
- The reduced density matrix for R is normalized by dividing the unnormalized matrix by its trace.The unnormalized matrix is obtained after projecting onto R.Source: Reduced density matrix · p. 6
Concurrence of a two-qubit pure state
The section gives the standard pure-state concurrence formula and applies it to the two-qubit state expressed in the L-R basis.
Concurrence of a two-qubit pure state
- For a pure two-qubit state, concurrence is C(Φ) = 2|a00a11 − a01a10| in the computational basis.The coefficients aij are complex amplitudes of the basis states |ij⟩.Source: Concurrence of a two-qubit pure state · p. 6
- In the L-R basis, C(ΨLR) = 2|lr′l′r|/(|lr′|2 + |l′r|2).The expression follows by applying the general concurrence formula to |ΨLR⟩, with C(ΨLR) = 2|a01a10|.Source: Concurrence of a two-qubit pure state · p. 6
Teleportation protocol
The protocol rewrites the input using Bell-state components and localized operations on the identical-particle resource. Its conditional teleportation achieves total fidelity 5/6.
Teleportation protocol
- The Bell-state identity is inserted to rewrite the state, and the term with two identical particles in L is divided by 2 for normalization.The factor accounts for the number of identical particles in L.Source: Teleportation protocol · p. 6
- The notation |φ⟩d |φ1, φ2⟩ combines a distinguishable particle with two identical-particle states using the wedge product.The resulting state may require renormalization depending on the initial state.Source: Teleportation protocol · p. 6
- With probability 1/2, rejecting cases with zero or two particles in L leaves the state used for localized operations.The operations are on the state within the brace of the last four rows of Eq. (14).Source: Teleportation protocol · p. 6
- 5/6 is the total teleportation fidelity, exceeding the classical threshold 2/3.Each of two rejected cases occurs with probability 1/4 and attains the classical threshold; the remaining case contributes unit fidelity with probability 1/2.Source: Teleportation protocol · p. 6
Localized measurements of entangled distinguishable particles
For entangled distinguishable particles, individual measurements leave the concurrence unchanged, while the likelihood of obtaining entanglement across L and R depends on detection amplitudes.
Localized measurements of entangled distinguishable particles
- The concurrence remains C(ΨAB) = 2|ab| for every individual-measurement outcome, regardless of the spatial modes measured.This is the concurrence of the Bell-like state defined by amplitudes a and b.Source: Localized measurements of entangled… · pp. 6–7
- The probability of obtaining entanglement shared between L and R depends jointly on the detection probability amplitudes, making its appearance conditional.A quantum-information protocol involving those regions, such as teleportation, is consequently probabilistic.Source: Localized measurements of entangled… · p. 7