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Channel Estimation with Noisy Entanglement

Bschorr, T C, Fischer, D G, Freyberger, M

Published Aug 8, 2001• 12 citations
OpenAlex

Abstract

We analyze the Pauli-channel estimation with mixed nonseparable states. It turns out that within a specific range entanglement can serve as a nonclassical resource. However, this range is rather small, that is entanglement is not very robust for this application. We further show that Werner states yield the best result of all Bell diagonal states with the same amount of entanglement.

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We analyze the Pauli-channel estimation with mixed nonseparable states. It turns out that within a specific range entanglement can serve as a nonclassical resource. However, this range is rather small, that is entanglement is not very robust for this application. We further show that Werner states yield the best result of all Bell diagonal states with the same amount of entanglement.
We begin this thesis by expanding the technique of teleportation simulation, which adds noise to the entangled resource state to mimic channel effects. By introducing classical noise in the communication step, we show it is possible to simulate more than just Pauli channels using teleportation. This new class is characterised, and studied in detail for a particular resource state, leading to a family of simulable channels named "Pauli-Damping channels" whose properties are analysed. Also introduced are a new family of quantum states, "phase Werner" states, whose entanglement properties relate to the interesting conjecture of bound entangled states with a negative partial transpose. Holevo-Werner channels, to which these states are connected, are shown to be teleportation covariant. We exploit this to present several interesting results, including the optimal estimation of the channel-defining parameter. The minimal binary-discrimination error for Holevo-Werner channels is bounded for the first time with the analytical form of the quantum Chernoff bound. We also consider the secret key capacity of these channels, showing how different entanglement measures provide a better upper bound for different regions of these channels. Finally, a method for generating new Bell inequalities is presented, exploiting nonphysical probability distributions to obtain new inequalities. Tens of thousands of new inequivalent inequalities are generated, and their usefulness in closing the detection loophole for imperfect detectors is examined, with comparison to the current optimal construction. Two candidate Bell inequalities which may equal or beat the best construction are presented.
We investigate teleportation of bipartite pure entanglement through two equally noisy quantum channel states, namely, a mixture of Bell states. There is a particular mixed-state channel for which all pure entangled states in a known biorthogonal product basis remain entangled after this inexact teleportation, which occurs for the duration of the entanglement. The Werner state channel lacks both these features. The relation of these noisy channels to the violation of Bell's inequality and quantum two-entropy inequality is studied.
The discovery of super dense coding paved the way for future quantum communications that exploit the power of entanglement. The protocol lets users communicate two classical bits using a pre-shared entangled pair of qubits called a Bell pair. However, the protocol assumes that a noiseless channel exists between end users. Moreover, perfect Bell pairs may not always be created in any experimental set up. We study the single shot communication properties of partially entangled Werner state and partially entangled pure bipartite states by considering the two-Pauli channel. The two-Pauli channel accommodates for both bit flips and phase flips that qubits may suffer during transmission. Quantification of entanglement is done via entanglement of formation and its dependence on capacity is analyzed.
Entanglement of quantum states is a very important resource in quantum communication systems. For many special tasks, entanglement is found to be helpful. But it is still a problem how to find the relationship between the amount of entanglement and the effect of doing the task. In this work, we consider a particular task—trying to send a single classical bit as effective as possible through a noisy quantum channel and two transmissions through the channel are available as a resource. For two special channels—amplitude damping channel and two-Pauli channel, we separately establish the quantitative connections, and try to find whether the relationship is always monotonous, i.e., the states with the larger entanglement necessarily result in the better effect. Unfortunately, this is not true. At the same time, we can get the optimal codes for the task using this method.
Establishing the limits of precision in the estimation of parameters for noisy quantum channels probed by qubits is important for many areas of quantum information, such as quantum sensing, computation, and communication. Here we consider the estimation of parameters characterizing a general class of noisy Pauli channels. We show that two entangled qubits, such that only one of them probes the channel, may lead, under an entangling measurement, to strong enhancement of the precision in the estimation, as compared to the precision corresponding to sending the pair, entangled or not, through the channel. We prove that entanglement plays an essential role, as does the entangling detection procedure, consisting in projecting the final state onto a Bell-state basis. We also prove that quantum advantage is obtained only when the output state, after interaction with the sample, is not entangled anymore. This behavior has striking similarities with quantum illumination, where initial entanglement of probe and ancilla beams, followed by an entangling measurement, lead to enhancement of the sensitivity of photodetection, even after the output beams are disentangled. Similarities and differences with ghost imaging are also discussed.