Optimal Visible Compression Rate For Mixed States Is Determined By Entanglement Of Purification

Compressing Mixed-State Sources by Sending Classical Information

We consider visible compression for discrete memoryless sources of mixed quantum states when only classical information can be sent from Alice to Bob. We assume that Bob knows the source statistics, and that Alice and Bob have identical random number generators. We put in an information theoretic framework some recent results on visible compression for sources of states with commuting density operators, and remove the commutativity requirement. We derive a general achievable compression rate, which is for the noncommutative case still higher than the known lower bound. We also present several …

混合态压缩的强逆界

Strong Converse Bounds for Compression of Mixed States

本文研究混合态可见与盲压缩的强逆界，定义新的Rényi推广量，证明可扩展态下纯化纠缠可加性，并给出一般态在超单位解码器下的强逆界。

混合态的率失真理论

Rate-Distortion Theory for Mixed States

本文研究带边信息的混合量子态系综压缩的率失真问题，推导了不同纠缠辅助场景下的率失真函数与完整率区域，压缩方案可适配多种压缩模型。

Entanglement-Assisted Quantum Data Compression

Ask how the quantum compression of ensembles of pure states is affected by the availability of entanglement, and in settings where the encoder has access to side information. We find the optimal asymptotic quantum rate and the optimal tradeoff (rate region) of quantum and entanglement rates. It turns out that the amount by which the quantum rate beats the Schumacher limit, the entropy of the source, is precisely half the entropy of classical information that can be extracted from the source and side information states without disturbing them at all ("reversible extraction of classical informat…

From Quantum Source Compression to Quantum Thermodynamics

This thesis addresses problems in the field of quantum information theory. The first part of the thesis is opened with concrete definitions of general quantum source models and their compression, and each subsequent chapter addresses the compression of a specific source model as a special case of the initially defined general models. First, we find the optimal compression rate of a general mixed state source which includes as special cases all the previously studied models such as Schumacher's pure and ensemble sources and other mixed state ensemble models. For an interpolation between the vis…

On the Entanglement Cost of One-Shot Compression

We revisit the task of visible compression of an ensemble of quantum states with entanglement assistance in the one-shot setting. The protocols achieving the best compression use many more qubits of shared entanglement than the number of qubits in the states in the ensemble. Other compression protocols, with potentially larger communication cost, have entanglement cost bounded by the number of qubits in the given states. This motivates the question as to whether entanglement is truly necessary for compression, and if so, how much of it is needed. Motivated by questions in communication complex…

Incompressibility of classical distributions

In blind compression of quantum states, a sender Alice is given a specimen of a quantum state $ρ$ drawn from a known ensemble (but without knowing what $ρ$ is), and she transmits sufficient quantum data to a receiver Bob so that he can decode a near perfect specimen of $ρ$. For many such states drawn iid from the ensemble, the asymptotically achievable rate is the number of qubits required to be transmitted per state. The Holevo information is a lower bound for the achievable rate, and is attained for pure state ensembles, or in the related scenario of entanglement-assisted visible compression…