[Paper Review] The power of entangled quantum channels

Seth Lloyd|ArXiv.org|Dec 6, 2001

Quantum Computing Algorithms and Architecture3 references3 citations

TL;DR

This paper demonstrates that entangled quantum channels can transmit information at a rate √M times higher than unentangled parallel channels for the same power, enabling M qubits to be transferred in the same time and power required for a single qubit using a single channel. The enhancement arises from nonlinear coupling that creates a collective 'super-boson' state with 2^M internal states, leveraging quantum entanglement to achieve a power-efficient communication advantage.

ABSTRACT

All communication channels are at bottom quantum mechanical. Quantum mechanics contributes both obstacles to communication in the form of noise, and opportunities in the use of intrinsically quantum representations for information. This paper investigates the trade-off between power and communication rate for coupled quantum channels. By exploiting quantum correlations such as entanglement, coupled quantum channels can communicate at a potentially higher rate than unentangled quantum channels given the same power. In particular, given the same overall power, M coupled, entangled quantum channels can send M bits in the same time it takes a single channel to send a single bit, and in the same time it takes M unentangled channels to send $\sqrt M$ bits.

Motivation & Objective

• To investigate the trade-off between power and communication rate in coupled quantum channels.
• To determine whether entanglement can significantly enhance the capacity of parallel quantum channels under fixed power constraints.
• To explore the physical limits of quantum communication using entanglement and nonlinear dynamics.
• To establish a theoretical framework for entanglement-enhanced channel capacity beyond classical limits.

Proposed method

• Modeling quantum channels as qubit systems with unitary, Hamiltonian dynamics governed by the Margolus-Levitin theorem.
• Applying the Margolus-Levitin theorem to bound the minimum time required for state rotation, linking energy, time, and information transfer.
• Deriving the communication rate for unentangled parallel channels as C_M^C = √M × C_1, where C_1 is the single-channel capacity.
• Introducing a nonlinear Hamiltonian S̃_1…M that entangles M qubits, enabling collective evolution across the M-qubit Hilbert space.
• Using the entangled Hamiltonian to achieve a communication rate C_M^Q = βM√(P/ħ), where β ≈ √(2/π(1−2^−M)), yielding a √M speedup over unentangled channels.
• Analyzing the role of M-th order nonlinear interactions (e.g., σ_x^1σ_x^2…σ_x^M or a_A1a_B1†…a_AMa_BM† + H.C.) as necessary for maximal capacity gain.

Experimental results

Research questions

• RQ1 Can entanglement in coupled quantum channels lead to a substantial increase in communication rate under fixed power?
• RQ2 What is the theoretical upper bound on channel capacity when M quantum channels are entangled via nonlinear dynamics?
• RQ3 How does the use of entanglement compare to unentangled parallel channels in terms of power efficiency and transmission speed?
• RQ4 What kind of nonlinear interactions are required to achieve entanglement-enhanced capacity, and are they experimentally feasible?
• RQ5 Does the Margolus-Levitin theorem provide a tight bound on the minimum time for M-qubit transfer when entanglement is used?

Key findings

• For fixed power P, M entangled quantum channels can transmit information at a rate C_M^Q = βM√(P/ħ), where β ≈ √(2/π(1−2^−M)), significantly exceeding unentangled channels.
• The entanglement-enhanced rate scales linearly with M, while unentangled parallel channels scale only as √M, resulting in a √M speedup for the same power.
• M entangled channels can transmit M bits in the same time and power required for a single unentangled channel to send one bit, demonstrating a super-additive capacity gain.
• The enhancement arises from collective evolution in a high-dimensional Hilbert space, effectively forming a 'super-boson' with 2^M internal states.
• The required Hamiltonian involves M-th order nonlinear interactions, such as σ_x^1σ_x^2…σ_x^M for spin qubits or multi-mode photon operators, which are experimentally challenging to implement.
• While the theoretical capacity gain is substantial, the practical realization demands precise control over multi-body entangling operations, which remain difficult with current quantum technologies.