We show how to use decoherence-free subspaces over collective-noise quantum channels to convey classical information in perfect secrecy. We argue that codes defined over decoherence-free subspaces are codes for quantum wiretap channels in which the gain of information by a non-authorized third part is zero. We also show that if some symmetry conditions are guaranteed, the maximum rate on which such secret communications take place is equal to the ordinary capacity of a quantum channel to convey classical information. As a consequence of these results, we show how some protocols for secure communication can be simplified, reducing significantly the number of communications performed.We show how to use decoherence-free subspaces over collective-noise quantum channels to convey classical information in perfect secrecy. We argue that codes defined over decoherence-free subspaces are codes for quantum wiretap channels in which the gain of information by a non-authorized third part is zero. We also show that if some symmetry conditions are guaranteed, the maximum rate on which such secret communications take place is equal to the ordinary capacity of a quantum channel to convey classical information. As a consequence of these results, we show how some protocols for secure communication can be simplified, reducing significantly the number of communications performed.

IEEE Latin America TransactionsJun 1, 20150 citations

Unconditional Security with Decoherence-Free Subspaces

Elloá B. Guedes, Francisco de Assis

We show how to use decoherence-free subspaces over collective-noise quantum channels to convey classical information in perfect secrecy. We argue that codes defined over decoherence-free subspaces are codes for quantum wiretap channels in which the gain of information by a non-authorized receiver is zero. We also show that if some symmetry conditions are guaranteed, the maximum rate on which these secret communications take place is equal to the Holevo-Schumacher-Westmoreland capacity of the quantum channel.We show how to use decoherence-free subspaces over collective-noise quantum channels to convey classical information in perfect secrecy. We argue that codes defined over decoherence-free subspaces are codes for quantum wiretap channels in which the gain of information by a non-authorized receiver is zero. We also show that if some symmetry conditions are guaranteed, the maximum rate on which these secret communications take place is equal to the Holevo-Schumacher-Westmoreland capacity of the quantum channel.

arXiv:1204.3000Apr 13, 20121 citation

ON THE SECURITY OF DECOHERENCE-FREE SUBSPACES AND SUBSYSTEMS FOR CLASSICAL INFORMATION CONVEYING THROUGH QUANTUM CHANNELS

Elloá B. Guedes, Francisco de Assis

Decoherence is one of the main obstacles in quantum information processing. In cryptographic scenarios, in particular, decoherence is not only responsible for the loss of the quantum properties but also for information leakage out to a wiretapper. Given that decoherence must be fought in real-world quantum communication systems, we present a scheme, using decoherence-free subspaces and subsystems, to perform secure classical communications through noisy quantum channels. Using quantum information and wiretap theories, we establish a proof of unconditional security of our scheme. We illustrate our proposal with a non-trivial example and discuss some of its impacts on already existing quantum secure message exchange protocols. Furthermore, we present some up-to-date technologies that can be used for practical implementation of the scheme proposed.Decoherence is one of the main obstacles in quantum information processing. In cryptographic scenarios, in particular, decoherence is not only responsible for the loss of the quantum properties but also for information leakage out to a wiretapper. Given that decoherence must be fought in real-world quantum communication systems, we present a scheme, using decoherence-free subspaces and subsystems, to perform secure classical communications through noisy quantum channels. Using quantum information and wiretap theories, we establish a proof of unconditional security of our scheme. We illustrate our proposal with a non-trivial example and discuss some of its impacts on already existing quantum secure message exchange protocols. Furthermore, we present some up-to-date technologies that can be used for practical implementation of the scheme proposed.

International Journal of Quantum InformationMar 1, 20132 citations

Efficient quantum communication under collective noise

Michalis Skotiniotis, Dür, Wolfgang, Barbara Kraus

We introduce a new quantum communication protocol for the transmission of quantum information under collective noise. Our protocol utilizes a decoherence-free subspace in such a way that an optimal asymptotic transmission rate is achieved, while at the same time encoding and decoding operations can be efficiently implemented. The encoding and decoding circuit requires a number of elementary gates that scale linearly with the number of transmitted qudits, m. The logical depth of our encoding and decoding operations is constant and depends only on the channel in question. For channels described by an arbitrary discrete group G, i.e. with a discrete number, |G|, of possible noise operators, perfect transmission at a rate m/(m+r) is achieved with an overhead that scales at most as $\mathcal{O}(d^r)$ where the number of auxiliary qudits, r, depends solely on the group in question. Moreover, this overhead is independent of the number of transmitted qudits, m. For certain groups, e.g. cyclic groups, we find that the overhead scales only linearly with the number of group elements |G|.We introduce a new quantum communication protocol for the transmission of quantum information under collective noise. Our protocol utilizes a decoherence-free subspace in such a way that an optimal asymptotic transmission rate is achieved, while at the same time encoding and decoding operations can be efficiently implemented. The encoding and decoding circuit requires a number of elementary gates that scale linearly with the number of transmitted qudits, m. The logical depth of our encoding and decoding operations is constant and depends only on the channel in question. For channels described by an arbitrary discrete group G, i.e. with a discrete number, |G|, of possible noise operators, perfect transmission at a rate m/(m+r) is achieved with an overhead that scales at most as $\mathcal{O}(d^r)$ where the number of auxiliary qudits, r, depends solely on the group in question. Moreover, this overhead is independent of the number of transmitted qudits, m. For certain groups, e.g. cyclic groups, we find that the overhead scales only linearly with the number of group elements |G|.

arXiv:1204.0891Bulletin of the American Physical SocietyApr 4, 20120 citations

Efficient quantum communication under collective noise

Michalis Skotiniotis, Wolfgang Dür, Barbara Kraus

We introduce a new quantum communication protocol for the transmission of quantum information under collective noise. Our protocol utilizes a decoherence-free subspace in such a way that an optimal asymptotic transmission rate is achieved, while at the same time encoding and decoding operations can be efficiently implemented. The encoding and decoding circuit requires a number of elementary gates that scale linearly with the number of transmitted qudits, $m$ . The logical depth of our encoding and decoding operations is constant and depends only on the channel in question. For channels described by an arbitrary discrete group $G$ , i.e.~with a discrete number, $\lvert G\rvert$ , of possible noise operators, perfect transmission at a rate $m/(m+r)$ is achieved with an overhead that scales at most as $\mathcal{O}(d^r)$ where the number of auxiliary qudits, $r$ , depends solely on the group in question. Moreover, this overhead is independent of the number of transmitted qudits, $m$ . For certain groups, e.g.~cyclic groups, we find that the overhead scales only linearly with the number of group elements $|G|$ .We introduce a new quantum communication protocol for the transmission of quantum information under collective noise. Our protocol utilizes a decoherence-free subspace in such a way that an optimal asymptotic transmission rate is achieved, while at the same time encoding and decoding operations can be efficiently implemented. The encoding and decoding circuit requires a number of elementary gates that scale linearly with the number of transmitted qudits, $m$. The logical depth of our encoding and decoding operations is constant and depends only on the channel in question. For channels described by an arbitrary discrete group $G$, i.e.~with a discrete number, $\lvert G\rvert$, of possible noise operators, perfect transmission at a rate $m/(m+r)$ is achieved with an overhead that scales at most as $\mathcal{O}(d^r)$ where the number of auxiliary qudits, $r$, depends solely on the group in question. Moreover, this overhead is independent of the number of transmitted qudits, $m$. For certain groups, e.g.~cyclic groups, we find that the overhead scales only linearly with the number of group elements $|G|$.

Quantum Information and ComputationMar 1, 20134 citations

Quantum key distribution: defeating collective noise without reducing efficiency

Song Lin, Gongde Guo, Fei Gao +1 more

Decoherence-free subspace (DFS) is a valid solution to realize quantum communication over a collective noise channel, and has been widely studied. Generally speaking, replacing a qubit with a DFS state will cause the reduction of communication efficiency. However, in this letter, it is shown that some kinds of noises may not lower the transmission rate of quantum key distribution. To illustrate it, we propose two quantum key distribution protocols based on Bell states. Here, two nonorthogonal and unbiased sets in a DFS are constructed by linear combination of particles at different positions. Since $n-1$ classical bits are distributed by using $2n$ qubits in our protocols, the transmission rate is close to that of noiseless BB84 protocol. Furthermore, when considering the cost of transmitting classical bits, the efficiencies of these protocols are even higher than that of BB84 protocol.Decoherence-free subspace (DFS) is a valid solution to realize quantum communication over a collective noise channel, and has been widely studied. Generally speaking, replacing a qubit with a DFS state will cause the reduction of communication efficiency. However, in this letter, it is shown that some kinds of noises may not lower the transmission rate of quantum key distribution. To illustrate it, we propose two quantum key distribution protocols based on Bell states. Here, two nonorthogonal and unbiased sets in a DFS are constructed by linear combination of particles at different positions. Since $n-1$ classical bits are distributed by using $2n$ qubits in our protocols, the transmission rate is close to that of noiseless BB84 protocol. Furthermore, when considering the cost of transmitting classical bits, the efficiencies of these protocols are even higher than that of BB84 protocol.

Quantum Information and ComputationJul 1, 201412 citations

\mathcal{O}(d^r)

where the number of auxiliary qudits, r, depends solely on the group in question. Moreover, this overhead is independent of the number of transmitted qudits, m. For certain groups, e.g. cyclic groups, we find that the overhead scales only linearly with the number of group elements |G|.

m

. The logical depth of our encoding and decoding operations is constant and depends only on the channel in question. For channels described by an arbitrary discrete group

G

, i.e.~with a discrete number,

\lvert G\rvert

, of possible noise operators, perfect transmission at a rate

m/(m+r)

is achieved with an overhead that scales at most as

\mathcal{O}(d^r)

where the number of auxiliary qudits,

r

, depends solely on the group in question. Moreover, this overhead is independent of the number of transmitted qudits,

m

. For certain groups, e.g.~cyclic groups, we find that the overhead scales only linearly with the number of group elements

|G|

n-1

classical bits are distributed by using

2n

qubits in our protocols, the transmission rate is close to that of noiseless BB84 protocol. Furthermore, when considering the cost of transmitting classical bits, the efficiencies of these protocols are even higher than that of BB84 protocol.