Simulations of closed timelike curves

Proposed models of closed timelike curves (CTCs) have been shown to enable powerful information-processing protocols. We examine the simulation of models of CTCs both by other models of CTCs and by physical systems without access to CTCs. We prove that the recently proposed transition probability CTCs (T-CTCs) are physically equivalent to postselection CTCs (P-CTCs), in the sense that one model can simulate the other with reasonable overhead. As a consequence, their information-processing capabilities are equivalent. We also describe a method for quantum computers to simulate Deutschian CTCs (but with a reasonable overhead only in some cases). In cases for which the overhead is reasonable, it might be possible to perform the simulation in a table-top experiment. This approach has the benefit of resolving some ambiguities associated with the equivalent circuit model of Ralph et al. Furthermore, we provide an explicit form for the state of the CTC system such that it is a maximum-entropy state, as prescribed by Deutsch.Comment: 15 pages, 1 figure, accepted for publication in Foundations of Physic

Extra Shared Entanglement Reduces Memory Demand in Quantum Convolutional Coding

We show how extra entanglement shared between sender and receiver reduces the memory requirements for a general entanglement-assisted quantum convolutional code. We construct quantum convolutional codes with good error-correcting properties by exploiting the error-correcting properties of an arbitrary basic set of Pauli generators. The main benefit of this particular construction is that there is no need to increase the frame size of the code when extra shared entanglement is available. Then there is no need to increase the memory requirements or circuit complexity of the code because the frame size of the code is directly related to these two code properties. Another benefit, similar to results of previous work in entanglement-assisted convolutional coding, is that we can import an arbitrary classical quaternary code for use as an entanglement-assisted quantum convolutional code. The rate and error-correcting properties of the imported classical code translate to the quantum code. We provide an example that illustrates how to import a classical quaternary code for use as an entanglement-assisted quantum convolutional code. We finally show how to "piggyback" classical information to make use of the extra shared entanglement in the code.Comment: 7 pages, 1 figure, accepted for publication in Physical Review

Coherent Communication with Continuous Quantum Variables

The coherent bit (cobit) channel is a resource intermediate between classical and quantum communication. It produces coherent versions of teleportation and superdense coding. We extend the cobit channel to continuous variables by providing a definition of the coherent nat (conat) channel. We construct several coherent protocols that use both a position-quadrature and a momentum-quadrature conat channel with finite squeezing. Finally, we show that the quality of squeezing diminishes through successive compositions of coherent teleportation and superdense coding.Comment: 4 pages, 3 figure

Quantum state cloning using Deutschian closed timelike curves

We show that it is possible to clone quantum states to arbitrary accuracy in the presence of a Deutschian closed timelike curve (D-CTC), with a fidelity converging to one in the limit as the dimension of the CTC system becomes large---thus resolving an open conjecture from [Brun et al., Physical Review Letters 102, 210402 (2009)]. This result follows from a D-CTC-assisted scheme for producing perfect clones of a quantum state prepared in a known eigenbasis, and the fact that one can reconstruct an approximation of a quantum state from empirical estimates of the probabilities of an informationally-complete measurement. Our results imply more generally that every continuous, but otherwise arbitrarily non-linear map from states to states can be implemented to arbitrary accuracy with D-CTCs. Furthermore, our results show that Deutsch's model for CTCs is in fact a classical model, in the sense that two arbitrary, distinct density operators are perfectly distinguishable (in the limit of a large CTC system); hence, in this model quantum mechanics becomes a classical theory in which each density operator is a distinct point in a classical phase space.Comment: 6 pages, 1 figure; v2: modifications to the interpretation of our results based on the insightful comments of the referees; v3: minor change, accepted for publication in Physical Review Letter

Encoding One Logical Qubit Into Six Physical Qubits

We discuss two methods to encode one qubit into six physical qubits. Each of our two examples corrects an arbitrary single-qubit error. Our first example is a degenerate six-qubit quantum error-correcting code. We explicitly provide the stabilizer generators, encoding circuit, codewords, logical Pauli operators, and logical CNOT operator for this code. We also show how to convert this code into a non-trivial subsystem code that saturates the subsystem Singleton bound. We then prove that a six-qubit code without entanglement assistance cannot simultaneously possess a Calderbank-Shor-Steane (CSS) stabilizer and correct an arbitrary single-qubit error. A corollary of this result is that the Steane seven-qubit code is the smallest single-error correcting CSS code. Our second example is the construction of a non-degenerate six-qubit CSS entanglement-assisted code. This code uses one bit of entanglement (an ebit) shared between the sender and the receiver and corrects an arbitrary single-qubit error. The code we obtain is globally equivalent to the Steane seven-qubit code and thus corrects an arbitrary error on the receiver's half of the ebit as well. We prove that this code is the smallest code with a CSS structure that uses only one ebit and corrects an arbitrary single-qubit error on the sender's side. We discuss the advantages and disadvantages for each of the two codes.Comment: 13 pages, 3 figures, 4 table

Duality in Entanglement-Assisted Quantum Error Correction

The dual of an entanglement-assisted quantum error-correcting (EAQEC) code is defined from the orthogonal group of a simplified stabilizer group. From the Poisson summation formula, this duality leads to the MacWilliams identities and linear programming bounds for EAQEC codes. We establish a table of upper and lower bounds on the minimum distance of any maximal-entanglement EAQEC code with length up to 15 channel qubits.Comment: This paper is a compact version of arXiv:1010.550

The squashed entanglement of the noiseless quantum Gaussian attenuator and amplifier

We determine the maximum squashed entanglement achievable between sender and receiver of the noiseless quantum Gaussian attenuators and amplifiers and we prove that it is achieved sending half of an infinitely squeezed two-mode vacuum state. The key ingredient of the proof is a lower bound to the squashed entanglement of the quantum Gaussian states obtained applying a two-mode squeezing operation to a quantum thermal Gaussian state tensored with the vacuum state. This is the first lower bound to the squashed entanglement of a quantum Gaussian state and opens the way to determine the squashed entanglement of all quantum Gaussian channels. Moreover, we determine the classical squashed entanglement of the quantum Gaussian states above and show that it is strictly larger than their squashed entanglement. This is the first time that the classical squashed entanglement of a mixed quantum Gaussian state is determined