Results 1  10
of
38
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 ..."
Abstract

Cited by 48 (8 self)
 Add to MetaCart
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.
The mother of all protocols: restructuring quantum information’s family tree
 Proc. R. Soc. A
, 2009
"... We give a simple, direct proof of the ‘mother ’ protocol of quantum information theory. In this new formulation, it is easy to see that the mother, or rather her generalization to the fully quantum Slepian–Wolf protocol, simultaneously accomplishes two goals: quantum communicationassisted entanglem ..."
Abstract

Cited by 43 (15 self)
 Add to MetaCart
We give a simple, direct proof of the ‘mother ’ protocol of quantum information theory. In this new formulation, it is easy to see that the mother, or rather her generalization to the fully quantum Slepian–Wolf protocol, simultaneously accomplishes two goals: quantum communicationassisted entanglement distillation and state transfer from the sender to the receiver. As a result, in addition to her other ‘children’, the mother protocol generates the statemerging primitive of Horodecki, Oppenheim and Winter, a fully quantum reverse Shannon theorem, and a new class of distributed compression protocols for correlated quantum sources which are optimal for sources described by separable density operators. Moreover, the mother protocol described here is easily transformed into the socalled ‘father ’ protocol whose children provide the quantum capacity and the entanglementassisted capacity of a quantum channel, demonstrating that the division of singlesender/singlereceiver protocols into two families was unnecessary: all protocols in the family are children of the mother.
Remote preparation of quantum states
, 2005
"... Remote state preparation is the variant of quantum state teleportation in which the sender knows the quantum state to be communicated. The original paper introducing teleportation established minimal requirements for classical communication and entanglement but the corresponding limits for remote s ..."
Abstract

Cited by 24 (9 self)
 Add to MetaCart
(Show Context)
Remote state preparation is the variant of quantum state teleportation in which the sender knows the quantum state to be communicated. The original paper introducing teleportation established minimal requirements for classical communication and entanglement but the corresponding limits for remote state preparation have remained unknown until now: previous work has shown, however, that it not only requires less classical communication but also gives rise to a tradeoff between these two resources in the appropriate setting. We discuss this problem from first principles, including the various choices one may follow in the definitions of the actual resources. Our main result is a general method of remote state preparation for arbitrary states of many qubits, at a cost of 1 bit of classical communication and 1 bit of entanglement per qubit sent. In this “universal” formulation, these ebit and cbit requirements are shown to be simultaneously optimal by exhibiting a dichotomy. Our protocol then yields the exact tradeoff curve for memoryless sources of pure states (including the case of incomplete knowledge of the ensemble probabilities), based on the recently established quantumclassical tradeoff for visible quantum data compression. A variation of that method allows us to solve the even more general problem of preparing entangled states between sender and receiver (i.e., purifications of mixed state ensembles). The paper includes an extensive discussion of our results, including the impact of the choice of model on the resources, the topic of obliviousness, and an application to private quantum channels and quantum data hiding.
Secure assisted quantum computation
 Quantum Information and Computation
, 2005
"... Suppose Alice wants to perform some computation that could be done quickly on a quantum computer, but she cannot do universal quantum computation. Bob can do universal quantum computation and claims he is willing to help, but Alice wants to be sure that Bob cannot learn her input, the result of her ..."
Abstract

Cited by 16 (0 self)
 Add to MetaCart
(Show Context)
Suppose Alice wants to perform some computation that could be done quickly on a quantum computer, but she cannot do universal quantum computation. Bob can do universal quantum computation and claims he is willing to help, but Alice wants to be sure that Bob cannot learn her input, the result of her calculation, or perhaps even the function she is trying to compute. We describe a simple, efficient protocol by which Bob can help Alice perform the computation, but there is no way for him to learn anything about it. We also discuss techniques for Alice to detect whether Bob is honestly helping her or if he is introducing errors. 1
Random quantum circuits are approximate 2designs
, 2008
"... Given a universal gate set on two qubits, it is well known that applying random gates from the set to random pairs of qubits will eventually yield an approximately Haardistributed unitary. However, this requires exponential time. We show that random circuits of only polynomial length will approxima ..."
Abstract

Cited by 14 (3 self)
 Add to MetaCart
(Show Context)
Given a universal gate set on two qubits, it is well known that applying random gates from the set to random pairs of qubits will eventually yield an approximately Haardistributed unitary. However, this requires exponential time. We show that random circuits of only polynomial length will approximate the first and second moments of the Haar distribution, thus forming approximate 1 and 2designs. Previous constructions required longer circuits and worked only for specific gate sets. As a corollary of our main result, we also improve previous bounds on the convergence rate of random walks on the Clifford group. 1
2005b, General paradigm for distilling classical key from quantum states, eprint quantph/0506189
"... states ..."
Everything you always wanted to know about LOCC (but were afraid to ask
 Comm. Math. Phys
"... ar ..."
Efficient simulation of random quantum states and operators
, 2005
"... c ○ Christoph Dankert 2005I hereby declare that I am the sole author of this thesis. I authorize the University of Waterloo to lend this thesis to other institutions or individuals for the purpose of scholarly research. ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
c ○ Christoph Dankert 2005I hereby declare that I am the sole author of this thesis. I authorize the University of Waterloo to lend this thesis to other institutions or individuals for the purpose of scholarly research.
Distinguishability of Quantum States by Separable Operations
, 2007
"... We study the distinguishability of multipartite quantum states by separable operations. We first present a necessary and sufficient condition for a finite set of orthogonal quantum states to be distinguishable by separable operations. An analytical version of this condition is derived for the case ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
We study the distinguishability of multipartite quantum states by separable operations. We first present a necessary and sufficient condition for a finite set of orthogonal quantum states to be distinguishable by separable operations. An analytical version of this condition is derived for the case of (D − 1) pure states, where D is the total dimension of the state space under consideration. A number of interesting consequences of this result are then carefully investigated. Remarkably, we show there exists a large class of 2 ⊗ 2 separable operations not being realizable by local operations and classical communication. Before our work only a class of 3 ⊗ 3 nonlocal separable operations was known [Bennett et al, Phys. Rev. A 59, 1070 (1999)]. We also show that any basis of the orthogonal complement of a multipartite pure state is indistinguishable by separable operations if and only if this state cannot be a superposition of 1 or 2 orthogonal product states, i.e., has an orthogonal Schmidt number not less than 3, thus generalize the recent work about indistinguishable bipartite subspaces [Watrous, Phys. Rev. Lett. 95, 080505 (2005)]. Notably, we obtain an explicit construction of indistinguishable subspaces of dimension 7 (or 6) by considering a composite quantum system consisting of two qutrits (resp. three qubits), which is slightly better than the previously known indistinguishable bipartite subspace with dimension 8.