27pages, 11figures. The 12page version will appear in 24th International Symposium on Theoretical Aspects of Computer Science (STACS 2007)
发表信息：
Proceedings of 24th International Symposium on Theoretical Aspects of Computer Science (STACS 2007), Lecture Notes in Computer Science 4393, pp. 610-621, 2007
Since quantum information is continuous, its handling is sometimes surprisingly harder than the classical counterpart. A typical example is cloning; making a copy of digital information is straightforward but it is not possible exactly for quantum information. The question in this paper is whether or not quantum network coding is possible. Its classical counterpart is another good example to show that digital information flow can be done much more efficiently than conventional (say, liquid) flow.
Our answer to the question is similar to the case of cloning, namely, it is shown that quantum network coding is possible if approximation is allowed, by using a simple network model called Butterfly. In this network, there are two flow paths, s_1 to t_1 and s_2 to t_2, which shares a single bottleneck channel of capacity one. In the classical case, we can send two bits simultaneously, one for each path, in spite of the bottleneck. Our results for quantum network coding include: (i) We can send any quantum state |psi_1> from s_1 to t_1 and |psi_2> from s_2 to t_2 simultaneously with a fidelity strictly greater than 1/2. (ii) If one of |psi_1> and |psi_2> is classical, then the fidelity can be improved to 2/3. (iii) Similar improvement is also possible if |psi_1> and |psi_2> are restricted to only a finite number of (previously known) states. (iv) Several impossibility results including the general upper bound of the fidelity are also given.
This paper shows how network coding and superdense coding can be combined to increase the classical data throughput by a factor $2-ε$ (for arbitrarily small $ε> 0$) compared to the maximum that could be achieved using either network coding or superdense coding alone. Additionally, a general decomposition of a ``mixed'' network (i.e., consisting of classical and quantum links) is given, and it is reasoned that, owing to the inherent hardness of finding network codes, this may well lead to an increase in classical data throughput in practise, should a scenario arise in which quantum networks are…
We present a proof for the quantum channel coding theorem which relies on the fact that a randomly chosen code space typically is highly suitable for quantum error correction. In this sense, the proof is close to Shannon's original treatment of information transmission via a noisy classical channel.
A two-receiver quantum dense coding scheme and an $N$-receiver quantum dense coding scheme, in the case of non-symmetric Hilbert spaces of the particles of the quantum channel, are investigated in this paper. A sender can send his messages to many receivers simultaneously. The scheme can be applied to quantum secret sharing and controlled quantum dense coding.
We analyze quantum superdense coding as would be seen in Everett's many worlds interpretation of measurement, and compare it to Everettian teleportation.
Quantum network coding on the butterfly network has been studied as a typical example of quantum multiple cast network. We propose secure quantum network coding on the butterfly network in the multiple unicast setting based on a secure classical network coding. This protocol certainly transmits quantum states when there is no attack. We also show the secrecy even when the eavesdropper wiretaps one of the channels in the butterfly network.
The sending station being the classical device can be eavesdropped by classical means. Dense coding and quantum nature of wave function give the additional resource to raise the safety of the quantum channel as a whole.
In this paper the quantum source coding theorem is obtained for a completely ergodic source. This results extends Shannon's classical theorem as well as Schumacher's quantum noiseless coding theorem for memoryless sources. The control of the memory effects requires earlier results of Hiai and Petz on high probability subspaces.
Quantum superdense coding enables a sender to encode a two-bit classical message in one qubit using the preshared entanglement. In this paper, we develop a superdense coding protocol using a dual quantum Zeno (DQZ) gate to take the full advantage of quantum superdense coding from the complete Bell-state analysis. We verify that the DQZ gate allows remote parties to achieve the distinguishability of orthonormal Bell states in a semi-counterfactual manner and the DQZ superdense coding achieves high throughput efficiency as a function of cycle numbers for the Bell-state analyzer.
This paper considers quantum network coding, which is a recent technique that enables quantum information to be sent on complex networks at higher rates than by using straightforward routing strategies. Kobayashi et al. have recently showed the potential of this technique by demonstrating how any classical network coding protocol gives rise to a quantum network coding protocol. They nevertheless primarily focused on an abstract model, in which quantum resource such as quantum registers can be freely introduced at each node. In this work, we present a protocol for quantum network coding under w…
Quantum information theory predicts that when the transmission resource is doubled in quantum channels, the amount of information transmitted can be increased more than twice by quantum channel coding technique, whereas the increase is at most twice in classical information theory. This remarkable feature, the superadditive quantum coding gain, can be implemented by appropriate choices of code words and corresponding quantum decoding which requires a collective quantum measurement. Recently, the first experimental demonstration was reported [Phys. Rev. Lett. 90, 167906 (2003)]. The purpose of …
We construct a universal code for stationary and memoryless classical-quantum channel as a quantum version of the universal coding by Csiszár and Körner. Our code is constructed by the combination of irreducible representation, the decoder introduced through quantum information spectrum, and the packing lemma.
A protocol of quantum dense coding protection of two qubits is proposed in amplitude damping (AD) channel using weak measurement and reversal measurement. It is found that the capacity of quantum dense coding under the weak measurement and reversal measurement is always greater than that without weak measurement and reversal measurement. When the protocol is applied, for the AD channels with different damping coefficient, the result reflects that quantum entanglement can be protected and quantum dense coding becomes successful.
This paper is on identification of classical information by the use of quantum channels. We focus on simultaneous ID codes which use measurements being useful to identify an arbitrary message. We give a direct and a converse part of the appropriate coding theorem.
We present a quantum hyperdense coding protocol with hyperentanglement in polarization and spatial-mode degrees of freedom of photons first and then give the details for a quantum secure direct communication (QSDC) protocol based on this quantum hyperdense coding protocol. This QSDC protocol has the advantage of having a higher capacity than the quantum communication protocols with a qubit system. Compared with the QSDC protocol based on superdense coding with $d$-dimensional systems, this QSDC protocol is more feasible as the preparation of a high-dimension quantum system is more difficult th…
We define an anti-quantum bit state via analogous way as the anti-state in Particle Physics.We show the quantum information Feymann diagrams for the teleportations and superdense coding, which preserve the information flow. The role of information vacuum and anihilation between error information and anti-information is mentioned for the stability of quantum computing.
We investigate probabilistic dense coding in non-symmetric Hilbert spaces of the sender's and the receiver's particles. The sender and the receiver share the multipartite non-maximally quantum channel. We also discuss the average information.
Time coding quantum key distribution with coherent faint pulses is experimentally demonstrated. A measured 3.3 % quantum bit error rate and a relative contrast loss of 8.4 % allow a 0.49 bit/pulse advantage to Bob.
I introduce rate-distortion theory for quantum coding, and derive a lower bound, involving the coherent information, on the rate at which qubits must be used to encode a quantum source with a given maximum level of distortion per source emission. The convexity of the "information rate-distortion function" which defines this bound is also derived.
The weak converse coding theorems have been proved for the quantum source and channel. The results give the lower bound for capacity of source and the upper bound for capacity of channel. The monotonicity of mutual quantum information have also been proved. PACS numbers: 03.65.Bz
The quantum advantage of dense coding is studied, considering general encoding quantum operations. Particular attention is devoted to the case of many senders, and it is shown that restrictions on the possible operations on the senders' side may make some quantum state useless for dense-coding. It is shown, e.g., that some states are useful for dense coding if the senders can communicate classically (but not quantumly), yet they cannot be used for dense coding, if classical communication is not allowed. These no-go results are actually independent of the particular quantification of the quantu…
We investigate a scheme for implementing quantum dense coding via atomic ensembles, where prior distribution of the quantum entangled state is not needed. Our scheme also combines another two distinct advantages: atomic ensembles qubits with long coherent time serve as memory qubits and phtonic qubit as flying qubit. Thus our suggestion may offer a simple and easy way of demonstrating quantum dense coding experimentally via atomic ensembles.
This paper follows very closely a famous paper by Csiszár and Körner about classical (non-quantum) wiretap coding. Our paper gives a self-contained and slightly novel review of some important results of the paper by Csiszár and Körner. Then we present a generalization of those results to the quantum realm, thus giving one of the first half-decent treatments of quantum wiretap coding. Like Csiszár and Körner, we too find a capacity region (i.e., the maximal achievable region of rates) characterized in terms of one-letter informations. We try to make our treatment of quantum wiretap coding as pa…
A quantum key distribution protocol based on time coding uses delayed one photon pulses with minimum time-frequency uncertainty product. Possible overlap between the pulses induces an ambiguous delay measurement and ensures a secure key exchange.
We extend the prepare-and-measure frequency-time coding quantum key distribution(FT-QKD) protocol to an entanglement based FT-QKD protocol. The latter can be implemented with a correlated frequency measurement scheme based on a time resolving single photon detector.
The quantum color coding scheme proposed by Korff and Kempe (quant-ph/0405086) is easily extended so that the color coding quantum system is allowed to be entangled with an extra auxiliary quantum system. It is shown that in the extended scheme we need only $\sim 2\sqrt{N}$ quantum colors to order $N$ objects in large $N$ limit, whereas $\sim N/e$ quantum colors are required in the original non-extended version. The maximum success probability has asymptotics expressed by the Tracy-Widom distribution of the largest eigenvalue of a random GUE matrix.
A new proof of the direct part of the quantum channel coding theorem is shown based on a standpoint of quantum hypothesis testing. A packing procedure of mutually noncommutative operators is carried out to derive an upper bound on the error probability, which is similar to Feinstein's lemma in classical channel coding. The upper bound is used to show the proof of the direct part along with a variant of Hiai-Petz's theorem in quantum hypothesis testing.
Coding theorems and (strong) converses for memoryless quantum communication channels and quantum sources are proved: for the quantum source the coding theorem is reviewed, and the strong converse proven. For classical information transmission via quantum channels we give a new proof of the coding theorem, and prove the strong converse, even under the extended model of nonstationary channels. As a by-product we obtain a new proof of the famous Holevo bound. Then multi-user systems are investigated, and the capacity region for the quantum multiple access channel is determined. The last chapter c…
A lower bound on the probability of decoding error of quantum communication channel is presented. The strong converse to the quantum channel coding theorem is shown immediately from the lower bound. It is the same as Arimoto's method exept for the difficulty due to non-commutativity.
Conditional pulse nulling (CPN) receiver is proposed by Dolinar to discriminate pulse position modulation (PPM) signals. The receiver using a beam splitter and an on-off photon detector can outperform the standard quantum limit (SQL) for PPM signals. In this paper, we apply this receiver to multi-pulse PPM (MPPM) and binary quantum coding signals, and use dynamic programming algorithm to optimize the control strategy. The MPPM signals is used to improve the band-utilization efficiency, and the binary quantum coding make the communication able to correct the error. Numerical simulation results …
We introduce a probabilistic version of the one-shot quantum dense coding protocol in both two- and multiport scenarios, and refer to it as conclusive quantum dense coding. Specifically, we analyze the corresponding capacities of two-qubit, two-qutrit, and three-qubit shared states. We identify cases where Pauli and generalized Pauli operators are not sufficient as encoders to attain the optimal one-shot conclusive quantum dense coding capacities. We find that there is a rich connection between the capacities, and the bipartite and multipartite entanglements of the shared state.
We derive the optimal exponent of the error probability of the quantum fixed-length pure state source coding in both cases of blind coding and visible coding. The optimal exponent is universally attained by Jozsa et al. (PRL, 81, 1714 (1998))'s universal code. In the direct part, a group representation theoretical type method is essential. In the converse part, Nielsen and Kempe (PRL, 86, 5184 (2001))'s lemma is essential.
We analyze a generalization of Huffman coding to the quantum case. In particular, we notice various difficulties in using instantaneous codes for quantum communication. Nevertheless, for the storage of quantum information, we have succeeded in constructing a Huffman-coding inspired quantum scheme. The number of computational steps in the encoding and decoding processes of N quantum signals can be made to be of polylogarithmic depth by a massively parallel implementation of a quantum gate array. This is to be compared with the O (N^3) computational steps required in the sequential implementatio…
We investigate a secure scheme for implementing quantum dense coding via cavity decay and liner optics devices. Our scheme combines two distinct advantages: atomic qubit sevres as stationary bit and photonic qubit as flying bit, thus it is suitable for long distant quantum communication.
The quantum analogues of classical variable-length codes are indeterminate-length quantum codes, in which codewords may exist in superpositions of different lengths. This paper explores some of their properties. The length observable for such codes is governed by a quantum version of the Kraft-McMillan inequality. Indeterminate-length quantum codes also provide an alternate approach to quantum data compression.
The information spectrum approach gives general formulae for optimal rates of various information theoretic protocols, under minimal assumptions on the nature of the sources, channels and entanglement resources involved. This paper culminates in the derivation of the dense coding capacity for a noiseless quantum channel, assisted by arbitrary shared entanglement, using this approach. We also review the currently known coding theorems, and their converses, for protocols such as data compression for arbitrary quantum sources and transmission of classical information through arbitrary quantum cha…
A controlled quantum dense coding scheme is investigated with a four-particle non-maximal quantum channel. The amount of classical information is shown to be capable of being controlled by the controllers through adjustments of the local measurement angles and to depend on the coefficients of the quantum channel; in addition, the four particles are distributed in two inverse ways in such an quantum channel. A restricted condition for distributing the particles to realize quantum dense coding in an arbitrary ($N+2$)-particle quantum channel is proposed.
To apply network coding for quantum computation, we study the distributed implementation of unitary operations over all separated input and output nodes of quantum networks. We consider a setting of networks where quantum communication between nodes is restricted to sending just a qubit, but classical communication is unrestricted. We analyze which N-qubit unitary operations are implementable over cluster networks by investigating transformations of a given cluster network into quantum circuits. We show that any two-qubit unitary operation is implementable over the butterfly network and the gr…
We report an experimental demonstration of Schumacher's quantum noiseless coding theorem. Our experiment employs a sequence of single photons each of which represents three qubits. We initially prepare each photon in one of a set of 8 non-orthogonal codeword states corresponding to the value of a block of three binary letters. We use quantum coding to compress this quantum data into a two-qubit quantum channel and then uncompress the two-qubit channel to restore the original data with a fidelity approaching the theoretical limit.
The quantum cost is a key ingredient to evaluate the quality of quantum protocols from a practical viewpoint. We show that the quantum cost of d-dimensional dense coding protocol is equal to d+3 when transmitting the classical message (0,0), and that is equal to d+4 when transmitting other classical message. It appears linear growth with the dimension and thus makes sense for implementation. In contrast, the quantum cost of high-dimensional teleportation protocols is equal to 13, which is the maximum value of the cost for the two-dimensional case. As an application, we establish the relation b…
Quantum network coding has been proposed to improve resource utilization to support distributed computation but has not yet been put in to practice. We investigate a particular implementation of quantum network coding using measurement-based quantum computation on IBM Q processors. We compare the performance of quantum network coding with entanglement swapping and entanglement distribution via linear cluster states. These protocols outperform quantum network coding in terms of the final Bell pair fidelities but are unsuitable for optimal resource utilization in complex networks with contention…
A complementarity relation is established between the capacity of multiport classical information transmission via quantum states and multiparty quantum correlation measures for three-qubit pure states. The multiparty quantum correlation measures considered are the generalized geometric measure, the tangle, and the discord monogamy score. The complementarity relation is revealed by the identification of a one-parameter family of pure three-qubit states, which we call the maximally dense coding capable family of states. These states have the maximal multiport dense coding capacity among all thr…
We investigate the usefulness of a recently introduced five qubit state by Brown $\it et al. \normalfont$ \cite{Brown} for quantum teleportation, quantum state sharing and superdense coding. It is shown that this five-qubit state can be utilized for perfect teleportation of arbitrary single and two qubit systems. We devise various schemes for quantum state sharing of an arbitrary single and two particle state via cooperative teleportation. We later show that this state can be used for superdense coding as well. It is found that five classical bits can be sent by sending only three quantum bits…
In a network, a channel introduces correlations to the parties that aim to establish a communication protocol. In this work, we present a framework of non-local network coding by exploiting a Bell scenario and show the usefulness of non-local and quantum resources in network coding. Two-sender and two-receiver interference channels are considered, for which network coding is characterized by two-input and four-outcome Bell scenarios. It is shown that non-signaling (quantum) correlations lead to strictly higher channel capacities in general than quantum (local) correlations. It is also shown th…
We prove direct quantum coding theorem for random quantum codes. The problem is separated into two parts: proof of distinguishability of codewords by receiver, and that of indistinguishability of codewords by environment (privacy). For a large class of codes, only privacy has to be checked.
We investigate the dense coding in the case of non-symmetric Hilbert spaces of the sender and receiver's particles sharing the quantum maximally entangled state. The efficiency of classical information gain is also considered. We conclude that when a more level particle is with the sender, she can get a non-symmetric quantum channel from a symmetric one by entanglement transfer. Thus the efficiency of information transmission is improved.
Quantum dense coding is one of the most important protocols in quantum communication. It derives from the idea of using quantum resources to boost the communication capacity and now serves as a key primitive across a variety of quantum information protocols. Here, we focus on the basic theoretical ideas behind quantum dense coding, discussing its development history from discrete and continuous variables to quantum networks, then to its variant protocols and applications in quantum secure communication. With this basic background in hand, we then review the main experimental achievements, from…
By sending a classical two-level system, one can transfer information about only \emph{two} distinguishable outcomes. Here we show that in quantum mechanics, using both the spin and path degrees of freedom of a spin-1/2 particle, and a Mach-Zehnder type interferometric arrangement with two suitable Stern-Gerlach detectors, it is possible to transfer information about \emph{four} distinguishable outcomes. This procedure does \emph{not} require using quantum entanglement as a resource as in the well-known protocol of dense coding, but instead hinges entirely on the quantum superposition principl…
In this paper, we study quantum dense coding between two arbitrarily fixed particles in a (N+2)-particle maximally-entangled states through introducing an auxiliary qubit and carrying out local measurements. It is shown that the transmitted classical information amount through such an entangled quantum channel usually is less than two classical bits. However, the information amount may reach two classical bits of information, and the classical information capacity is independent of the number of the entangled particles in the initial entangled state under certain conditions. The results offer …
We prove a theorem for coding mixed-state quantum signals. For a class of coding schemes, the von Neumann entropy $S$ of the density operator describing an ensemble of mixed quantum signal states is shown to be equal to the number of spin-$1/2$ systems necessary to represent the signal faithfully. This generalizes previous works on coding pure quantum signal states and is analogous to the Shannon's noiseless coding theorem of classical information theory. We also discuss an example of a more general class of coding schemes which {\em beat} the limit set by our theorem.
This paper presents a new encryption scheme called Compact Coding that encodes information in time, phase, and intensity domains, simultaneously. While these approaches have previously been used one at a time, the proposed scheme brings to bear for the first time their strengths simultaneously leading to an increase in the secure information transfer rate. The proposed scheme is applicable to both optical fibers and free space optics, and can be considered as an alternative to polarization coding. This paper applies the proposed compact coding scheme to multi-photon tolerant quantum protocols …
We derive universal classical-quantum superposition coding and universal classical-quantum multiple access channel code by using generalized packing lemmas for the type method. Using our classical-quantum universal superposition code, we establish the capacity region of a classical-quantum compound broadcast channel with degraded message sets. Our universal classical-quantum multiple access channel codes have two types of codes. One is a code with joint decoding and the other is a code with separate decoding. The former universally achieves corner points of the capacity region and the latter u…
This paper introduces a new quantum protocol for secure direct communication. This protocol is based on Entanglement and Super-Dense coding. In this paper we present some basic definitions of entanglement in quantum mechanics, present how to use the maximally entangled states known as Bell States, and super dense coding technique to achieve secure direct message communication. Finally, we will apply some error models that could affect the transmission of the quantum data on the quantum channels, and how to treat these errors and acquire a safe transmission of the data.
In this paper, we establish an interesting duality between two different quantum information-processing tasks, namely, classical source coding with quantum side information, and channel coding over c-q channels. The duality relates the optimal error exponents of these two tasks, generalizing the classical results of Ahlswede and Dueck. We establish duality both at the operational level and at the level of the entropic quantities characterizing these exponents. For the latter, the duality is given by an exact relation, whereas for the former, duality manifests itself in the following sense: an …
Quantum deletions, which are harder to correct than erasure errors, occur in many realistic settings. It is therefore pertinent to develop quantum coding schemes for quantum deletion channels. To date, not much is known about which explicit quantum error correction codes can combat quantum deletions. We note that {\em any} permutation-invariant quantum code that has a distance of $t+1$ can correct $t$ quantum deletions for any positive integer $t$ in both the qubit and the qudit setting. Leveraging on coding properties of permutation-invariant quantum codes under erasure errors, we derive corr…
