A classical one-time pad allows two parties to send private messages over a public classical channel-an eavesdropper who intercepts the communication learns nothing about the message. A quantum one-time pad is a shared quantum state which allows two parties to send private messages or private quantum states over a public quantum channel. If the eavesdropper intercepts the quantum communication she learns nothing about the message. In the classical case, a one-time pad can be created using shared and partially private correlations. Here we consider the quantum case in the presence of an eavesdropper, and find the single-letter formula for the rate at which the two parties can send messages using a general quantum state as a quantum one-time pad. Surprisingly, the formula coincides with the distillable entanglement assisted by a symmetric channel, an important quantity in quantum information theory, but which lacked a clear operational meaning.
A classical one-time pad allows two parties to send private messages over a public classical channel-an eavesdropper who intercepts the communication learns nothing about the message. A quantum one-time pad is a shared quantum state which allows two parties to send private messages or private quantum states over a public quantum channel. If the eavesdropper intercepts the quantum communication she learns nothing about the message. In the classical case, a one-time pad can be created using shared and partially private correlations. Here we consider the quantum case in the presence of an eavesdropper, and find the single-letter formula for the rate at which the two parties can send messages using a general quantum state as a quantum one-time pad. Surprisingly, the formula coincides with the distillable entanglement assisted by a symmetric channel, an important quantity in quantum information theory, but which lacked a clear operational meaning.
We introduce and analyze an information theoretical task that we call the quantum multiple-access one-time pad. Here, a number of senders initially share a correlated quantum state with a receiver and an eavesdropper. Each sender performs a local operation to encode a classical message and sends their system to the receiver, who subsequently performs a measurement to decode the messages. The receiver will be able to decode the messages almost perfectly, while the eavesdropper must not be able to extract information about the messages even if they have access to the quantum systems transmitted. We consider a “conditional” scenario in which a portion of the receiver’s side information is also accessible to the eavesdropper. We investigate the maximum amount of classical information that can be encoded by each of the senders. We derive a single-letter characterization for the achievable rate region in an asymptotic limit of infinitely many copies and vanishingly small error.
We consider the private classical capacity of a quantum wiretap channel, where the users (sender Alice, receiver Bob, and eavesdropper Eve) have access to the resource of a shared quantum state, additionally to their channel inputs and outputs. An extreme case is maximal entanglement or a secret key between Alice and Bob, both of which would allow for one-time padding the message. But here both the wiretap channel and the shared state are general. In the other extreme case that the state is trivial, we recover the wiretap channel and its private capacity [N. Cai, A. Winter and R. W. Yeung, Probl. Inform. Transm. 40(4):318-336, 2004]. We show how to use the given resource state to build a code for secret classical communication. Our main result is a lower bound on the assisted private capacity, which asymptotically meets the multi-letter converse and which encompasses all sorts of previous results as special cases.
Suppose that Alice and Bob are located in distant laboratories, which are connected by an ideal quantum channel. Suppose further that they share many copies of a quantum state ρ_{ABE}, such that Alice possesses the A systems and Bob the BE systems. In our model, there is an identifiable part of Bob's laboratory that is insecure: a third party named Eve has infiltrated Bob's laboratory and gained control of the E systems. Alice, knowing this, would like use their shared state and the ideal quantum channel to communicate a message in such a way that Bob, who has access to the whole of his laboratory (BE systems), can decode it, while Eve, who has access only to a sector of Bob's laboratory (E systems) and the ideal quantum channel connecting Alice to Bob, cannot learn anything about Alice's transmitted message. We call this task the conditional one-time pad, and in this Letter, we prove that the optimal rate of secret communication for this task is equal to the conditional quantum mutual information I(A;B|E) of their shared state. We thus give the conditional quantum mutual information an operational meaning that is different from those given in prior works, via state redistribution, conditional erasure, or state deconstruction. We also generalize the model and method in several ways, one of which is a secret-sharing task, i.e., the case in which Alice's message should be secure from someone possessing only the AB or AE systems, but should be decodable by someone possessing all systems A, B, and E.
In Private Broadcasting, a single plaintext is broadcast to multiple recipients in an encrypted form, such that each recipient can decrypt locally. When the message is classical, a straightforward solution is to encrypt the plaintext with a single key shared among the parties, and to send each recipient a copy of the ciphertext. Surprisingly, the analogous method is insufficient in the case where the message is quantum (i.e. in Quantum Private Broadcasting (QPB)). In this work, we give three solutions to t-recipient QPB and compare them in terms of encryption key length. We examine independent encryption with the quantum one-time pad, unitary t-designs, and a new concept we define as symmetric unitary t-designs. Of these three, symmetric t-designs are the best choice when t is large, and these symmetric designs may be of independent interest beyond QPB.
In this paper, we propose a method of enciphering quantum states of two-state systems (qubits) for sending them in secrecy without entangled qubits shared by two legitimate users (Alice and Bob). This method has the following two properties. First, even if an eavesdropper (Eve) steals qubits, she can extract information from them with only a certain probability at most. Second, Alice and Bob can confirm that the qubits are transmitted between them correctly by measuring a signature. If Eve measures m qubits one by one from n enciphered qubits and sends alternative ones (the intercept/resend attack), the probability that Alice and Bob do not notice Eve's action is equal to (3/4) m or less. Passwords for decryption and the signature are given by classical binary strings and they are disclosed through a public channel. Enciphering classical information by this method is equivalent to the one-time pad method with distributing a classical key (random binary string) by the BB84 protocol. If Eve takes away qubits, Alice and Bob lose the original quantum information. If we apply our method to a state in iteration, Eve's success probability decreases exponentially. We cannot examine security against the case that Eve makes an attack using entanglement. This remains to be solved in the future.
In private broadcasting, a single plaintext is broadcast to multiple recipients in an encrypted form, such that each recipient can decrypt locally. When the message is classical, a straightforward solution is to encrypt the plaintext with a single key shared among all parties, and to send to each recipient a copy of the ciphertext. Surprisingly, the analogous method is insufficient in the case where the message is quantum [i.e., in quantum private broadcasting (QPB)]. In this work, we give three solutions to t-recipient quantum private broadcasting (t-QPB) and compare them in terms of key lengths. The first method is the independent encryption with the quantum one-time pad, which requires a key linear in the number of recipients, t. We show that the key length can be decreased to be logarithmic in t by using unitary t-designs. Our main contribution is to show that this can be improved to a key length that is logarithmic in the dimension of the symmetric subspace, using a concept that we define of symmetric unitary t-designs, which may be of independent interest.