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We present a new scheme for the compression of one-way quantum messages, in the setting of coherent entanglement assisted quantum communication. For this, we present a new technical tool that we call the convex split lemma, which is inspired by the classical compression schemes that use rejection sampling procedure. As a consequence, we show new bounds on the quantum communication cost of single-shot entanglement-assisted one-way quantum state redistribution task and for the sub-tasks quantum state splitting and quantum state merging. Our upper and lower bounds are tight up to a constant and hence stronger than previously known best bounds for above tasks. Our protocols use explicit quantum operations on the sides of Alice and Bob, which are different from the decoupling by random unitaries approach used in previous works. As another application, we present a port-based teleportation scheme which works when the set of input states is restricted to a known ensemble, hence potentially saving the number of required ports. Furthermore, in case of no prior knowledge about the set of input states, our average success fidelity matches the known average success fidelity, providing a new port-based teleportation scheme with similar performance as appears in literature.
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The quantum entropy-typical subspace theory is specified. It is shown that any mixed state with von Neumann entropy less than h can be preserved approximately by the entropy-typical subspace with entropy= h. This result implies an universal compression scheme for the case that the von Neumann entropy of the source does not exceed h.
We propose a linear compression technique for the time interval distribution of photon pairs. Using a partially frequency-entangled two-photon (TP) state with appropriate mean time width, the compressed TP time interval width can be kept in the minimum limit set by the phase modulation, and is independent of its initial width. As a result of this effect, ultra-narrow TP time interval distribution can be compressed with relatively slow phase modulators to decrease the damage of the phase-instability arising from the phase modulation process.
Quantum addition channels have been recently introduced in the context of deriving entropic power inequalities for finite dimensional quantum systems. We prove a reverse entropy power equality which can be used to analytically prove an inequality conjectured recently for arbitrary dimension and arbitrary addition weight. We show that the relative entropic difference between the output of such a quantum additon channel and the corresponding classical mixture quantitatively captures the amount of coherence present in a quantum system. This new coherence measure admits an upper bound in terms of the relative entropy of coherence and is utilized to formulate a state-dependent uncertainty relation for two observables. Our results may provide deep insights to the origin of quantum coherence for mixed states that truly come from the discrepancy between quantum addition and the classical mixture.
For space-based laser communications, when the mean photon number per received optical pulse is much smaller than one, there is a large gap between communications capacity achievable with a receiver that performs individual pulse-by-pulse detection, and the quantum-optimal joint-detection receiver that acts collectively on long codeword-blocks of modulated pulses; an effect often termed superadditive capacity. In this paper, we consider the simplest scenario where a large superadditive capacity is known: a pure-loss channel with a coherent-state binary phase-shift keyed (BPSK) modulation. The two BPSK states can be mapped conceptually to two non-orthogonal states of a qubit, described by an inner product that is a function of the mean photon number per pulse. Using this map, we derive an explicit construction of the quantum circuit of a joint-detection receiver based on a recent idea of belief-propagation with quantum messages (BPQM) (arXiv:1607.04833). We quantify its performance improvement over the Dolinar receiver that performs optimal pulse-by-pulse detection, which represents the best classical approach. We analyze the scheme rigorously and show that it achieves the quantum limit of minimum average error probability in discriminating 8 (BPSK) codewords of a length-5 binary linear code with a tree factor graph. Our result suggests that a BPQM-receiver might attain the Holevo capacity of this BPSK-modulated pure-loss channel. Moreover, our receiver circuit provides an alternative proposal for a quantum supremacy experiment, targeted at a specific application that can potentially be implemented on a small, special-purpose, photonic quantum computer capable of performing cat-basis universal qubit logic.
We present a general theory of entanglement-assisted quantum convolutional coding. The codes have a convolutional or memory structure, they assume that the sender and receiver share noiseless entanglement prior to quantum communication, and they are not restricted to possess the Calderbank-Shor-Steane structure as in previous work. We provide two significant advances for quantum convolutional coding theory. We first show how to expand a given set of quantum convolutional generators. This expansion step acts as a preprocessor for a polynomial symplectic Gram-Schmidt orthogonalization procedure that simplifies the commutation relations of the expanded generators to be the same as those of entangled Bell states (ebits) and ancilla qubits. The above two steps produce a set of generators with equivalent error-correcting properties to those of the original generators. We then demonstrate how to perform online encoding and decoding for a stream of information qubits, halves of ebits, and ancilla qubits. The upshot of our theory is that the quantum code designer can engineer quantum convolutional codes with desirable error-correcting properties without having to worry about the commutation relations of these generators.
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