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Private Quantum Channels
 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
, 2000
"... We investigate how a classical private key can be used by two players, connected by an insecure oneway quantum channel, to perform private communication of quantum information. In particular we show that in order to transmit n qubits privately, 2n bits of shared private key are necessary and sucien ..."
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Cited by 54 (0 self)
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We investigate how a classical private key can be used by two players, connected by an insecure oneway quantum channel, to perform private communication of quantum information. In particular we show that in order to transmit n qubits privately, 2n bits of shared private key are necessary and sucient. This result may be viewed as the quantum analogue of the classical onetime pad encryption scheme. 1 Introduction Secure transmission of classical information is a well studied topic. Suppose Alice wants to send an nbit message M to Bob over an insecure (i.e. spiedon) channel, in such a way that the eavesdropper Eve cannot obtain any information about M from tapping the channel. If Alice and Bob share some secret nbit key K, then here is a simple way for them to achieve their goal: Alice exclusiveors M with K and sends the result M 0 = M K over the channel, Bob then xors M 0 again with K and obtains the original message M 0 K = M . Eve may see the encoded message M 0 , ...
The universal composable security of quantum key distribution
 Theory of Cryptography: Second Theory of Cryptography Conference, volume 3378 of Lecture
, 2005
"... The existing unconditional security definitions of quantum key distribution (QKD) do not apply to joint attacks over QKD and the subsequent use of the resulting key. In this paper, we close this potential security gap by using a universal composability theorem for the quantum setting. We first deriv ..."
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Cited by 51 (3 self)
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The existing unconditional security definitions of quantum key distribution (QKD) do not apply to joint attacks over QKD and the subsequent use of the resulting key. In this paper, we close this potential security gap by using a universal composability theorem for the quantum setting. We first derive a composable security definition for QKD. We then prove that the usual security definition of QKD still implies the composable security definition. Thus, a key produced in any QKD protocol that is unconditionally secure in the usual definition can indeed be safely used, a property of QKD that is hitherto unproven. We propose two other useful sufficient conditions for composability. As a simple application of our result, we show that keys generated by repeated runs of QKD degrade slowly. 1
Randomizing Quantum States: Constructions and Applications
 COMMUNICATIONS IN MATHEMATICAL PHYSICS
, 2004
"... The construction of a perfectly secure private quantum channel in dimension d is known to require 2 log d shared random key bits between the sender and receiver. We show that if only nearperfect security is required, the size of the key can be reduced by a factor of two. More specifically, we show ..."
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Cited by 48 (8 self)
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The construction of a perfectly secure private quantum channel in dimension d is known to require 2 log d shared random key bits between the sender and receiver. We show that if only nearperfect security is required, the size of the key can be reduced by a factor of two. More specifically, we show that there exists a set of roughly d log d unitary operators whose average effect on every input pure state is almost perfectly randomizing, as compared to the d 2 operators required to randomize perfectly. Aside from the private quantum channel, variations of this construction can be applied to many other tasks in quantum information processing. We show, for instance, that it can be used to construct LOCC data hiding schemes for bits and qubits that are much more efficient than any others known, allowing roughly log d qubits to be hidden in 2 log d qubits. The method can also be used to exhibit the existence of quantum states with locked classical correlations, an arbitrarily large amplification of the correlation being accomplished by sending a negligibly small classical key. Our construction also provides the basic building block for a method of remotely preparing arbitrary ddimensional pure quantum states using approximately log d bits of communication and log d ebits of entanglement.
A New Proof for the Existence of Mutually Unbiased Bases
, 2001
"... We develop a strong connection between maximally commuting bases of orthogonal unitary matrices and mutually unbiased bases. A necessary condition of the existence of mutually unbiased bases for any finite dimension is obtained. Then a constructive proof of the existence of mutually unbiased bases f ..."
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Cited by 30 (1 self)
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We develop a strong connection between maximally commuting bases of orthogonal unitary matrices and mutually unbiased bases. A necessary condition of the existence of mutually unbiased bases for any finite dimension is obtained. Then a constructive proof of the existence of mutually unbiased bases for dimensions that are powers of primes is presented. It is also proved that in any dimension d the number of mutually unbiased bases is at most d + 1. An explicit representation of mutually unbiased observables in terms of Pauli matrices are provided for d = 2 . 1
Quantum Digital Signature based on quantum oneway functions
, 2004
"... Abstract. A quantum digital signature protocol based on quantum mechanics is proposed in this paper. The security of the protocol relies on the existence of quantum oneway functions by quantum information theorem. This protocol involves a socalled arbitrator who validates and authenticates the sig ..."
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Cited by 9 (0 self)
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Abstract. A quantum digital signature protocol based on quantum mechanics is proposed in this paper. The security of the protocol relies on the existence of quantum oneway functions by quantum information theorem. This protocol involves a socalled arbitrator who validates and authenticates the signed message. In this protocol, we use privacy key algorithm to ensure the security of quantum information on channel and use quantum public keys to sign message. To guarantee the authenticity of the message, a family of quantum stabilizer codes are employed. Our protocol presents a novel method to construct ultimately secure digital system in future secure communication. 1
Invertible quantum operations and perfect encryption of quantum states
 Quantum Information & Computation 7(12), 103 (2007). Eprint arXiv:quantph/0605041v4
"... In this note, we characterize the form of an invertible quantum operation, i.e., a completely positive trace preserving linear transformation (a CPTP map) whose inverse is also a CPTP map. The precise form of such maps becomes important in contexts such as selftesting and encryption. We show that t ..."
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In this note, we characterize the form of an invertible quantum operation, i.e., a completely positive trace preserving linear transformation (a CPTP map) whose inverse is also a CPTP map. The precise form of such maps becomes important in contexts such as selftesting and encryption. We show that these maps correspond to applying a unitary transformation to the state along with an ancilla initialized to a fixed state, which may be mixed. The characterization of invertible quantum operations implies that oneway schemes for encrypting quantum states using a classical key may be slightly more general than the “private quantum channels” studied by Ambainis, Mosca, Tapp and de Wolf [1, Section 3]. Nonetheless, we show that their results, most notably a lower bound of 2n bits of key to encrypt n quantum bits, extend in a straightforward manner to the general case. 1
Private quantum channels and the cost of randomizing quantum information,” (22Mar00) preprint quantph/0003101
, 2000
"... We investigate how a classical private key can be used by two players, connected by an insecure oneway quantum channel, to perform private communication of quantum information. In particular we show that in order to transmit n qubits privately, 2n bits of shared private key are necessary and suffic ..."
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Cited by 5 (0 self)
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We investigate how a classical private key can be used by two players, connected by an insecure oneway quantum channel, to perform private communication of quantum information. In particular we show that in order to transmit n qubits privately, 2n bits of shared private key are necessary and sufficient. This result may be viewed as the quantum analogue of the classical onetime pad encryption scheme. From the point of view of the eavesdropper, this encryption process can be seen as a randomization of the original state. We thus also obtain strict bounds on the amount of entropy necessary for randomizing n qubits. 1
A new proof for the existence of mutually unbiased bases
 Algorithmica
"... We develop a strong connection between maximally commuting bases of orthogonal unitary matrices and mutually unbiased bases. A necessary condition of the existence of mutually unbiased bases for any finite dimension is obtained. Then a constructive proof of the existence of mutually unbiased bases f ..."
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Cited by 3 (0 self)
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We develop a strong connection between maximally commuting bases of orthogonal unitary matrices and mutually unbiased bases. A necessary condition of the existence of mutually unbiased bases for any finite dimension is obtained. Then a constructive proof of the existence of mutually unbiased bases for dimensions which are power of a prime is presented. It is also proved that in any dimension d the number of mutually unbiased bases is at most d + 1. An explicit representation of mutually unbiased observables in terms of Pauli matrices are provided for d = 2 m. 1
Additivity and distinguishability of random unitary channels
 Journal of Mathematical Physics
, 2008
"... A random unitary channel is one that is given by a convex combination of unitary channels. It is shown that the conjectures on the additivity of the minimum output entropy and the multiplicativity of the maximum output pnorm can be equivalently restated in terms of random unitary channels. This is ..."
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Cited by 3 (1 self)
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A random unitary channel is one that is given by a convex combination of unitary channels. It is shown that the conjectures on the additivity of the minimum output entropy and the multiplicativity of the maximum output pnorm can be equivalently restated in terms of random unitary channels. This is done by constructing a random unitary approximation to a general quantum channel. This approximation can be constructed efficiently, and so it is also applied to the computational problem of distinguishing quantum circuits. It is shown that the problem of distinguishing random unitary circuits is as hard as the QIPcomplete problem of distinguishing general mixed state circuits. 1
Computational Distinguishability of Quantum Channels
, 2009
"... The computational problem of distinguishing two quantum channels is central to quantum computing. It is a generalization of the wellknown satisfiability problem from classical to quantum computation. This problem is shown to be surprisingly hard: it is complete for the class QIP of problems that h ..."
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The computational problem of distinguishing two quantum channels is central to quantum computing. It is a generalization of the wellknown satisfiability problem from classical to quantum computation. This problem is shown to be surprisingly hard: it is complete for the class QIP of problems that have quantum interactive proof systems, which implies that it is hard for the class PSPACE of problems solvable by a classical computation in polynomial space. Several restrictions of distinguishability are also shown to be hard. It is no easier when restricted to quantum computations of logarithmic depth, to mixedunitary channels, to degradable channels, or to antidegradable channels. These hardness results are demonstrated by finding reductions between these classes of quantum channels. These techniques have applications outside the distinguishability problem, as the construction for mixedunitary channels is used to prove that the additivity problem for the classical capacity of quantum channels can be equivalently restricted to the mixed unitary channels.