arXiv subjects

Mark M. Wilde

Publications and source records attributed to Mark M. Wilde.

At least 289 records · Page 16Linked to original sources

arXiv2009

Nonlocal quantum information in bipartite quantum error correction

We show how to convert an arbitrary stabilizer code into a bipartite quantum code. A bipartite quantum code is one that involves two senders and one receiver. The two senders exploit both nonlocal and local quantum resources to encode quantum information with local encoding circuits. They transmit their encoded quantum data to a single receiver who then decodes the transmitted quantum information. The nonlocal resources in a bipartite code are ebits and nonlocal information qubits and the local resources are ancillas and local information qubits. The technique of bipartite quantum error correction is useful in both the quantum communication scenario described above and in fault-tolerant quantum computation. It has application in fault-tolerant quantum computation because we can prepare nonlocal resources offline and exploit local encoding circuits. In particular, we derive an encoding circuit for a bipartite version of the Steane code that is local and additionally requires only nearest-neighbor interactions. We have simulated this encoding in the CNOT extended rectangle with a publicly available fault-tolerant simulation software. The result is that there is an improvement in the "pseudothreshold" with respect to the baseline Steane code, under the assumption that quantum memory errors occur less frequently than quantum gate errors.

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arXiv2009

Could light harvesting complexes exhibit non-classical effects at room temperature?

Mounting experimental and theoretical evidence suggests that coherent quantum effects play a role in the efficient transfer of an excitation from a chlorosome antenna to a reaction center in the Fenna-Matthews-Olson protein complex. However, it is conceivable that a satisfying alternate interpretation of the results is possible in terms of a classical theory. To address this possibility, we consider a class of classical theories satisfying the minimal postulates of macrorealism and frame Leggett-Garg-type tests that could rule them out. Our numerical simulations indicate that even in the presence of decoherence, several tests could exhibit the required violations of the Leggett-Garg inequality. Remarkably, some violations persist even at room temperature for our decoherence model.

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arXiv2009

Can Classical Noise Enhance Quantum Transmission?

A modified quantum teleportation protocol broadens the scope of the classical forbidden-interval theorems for stochastic resonance. The fidelity measures performance of quantum communication. The sender encodes the two classical bits for quantum teleportation as weak bipolar subthreshold signals and sends them over a noisy classical channel. Two forbidden-interval theorems provide a necessary and sufficient condition for the occurrence of the nonmonotone stochastic resonance effect in the fidelity of quantum teleportation. The condition is that the noise mean must fall outside a forbidden interval related to the detection threshold and signal value. An optimal amount of classical noise benefits quantum communication when the sender transmits weak signals, the receiver detects with a high threshold, and the noise mean lies outside the forbidden interval. Theorems and simulations demonstrate that both finite-variance and infinite-variance noise benefit the fidelity of quantum teleportation.

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arXiv2009

On the logical operators of quantum codes

I show how applying a symplectic Gram-Schmidt orthogonalization to the normalizer of a quantum code gives a different way of determining the code's logical operators. This approach may be more natural in the setting where we produce a quantum code from classical codes because the generator matrices of the classical codes form the normalizer of the resulting quantum code. This technique is particularly useful in determining the logical operators of an entanglement-assisted code produced from two classical binary codes or from one classical quaternary code. Finally, this approach gives additional formulas for computing the amount of entanglement that an entanglement-assisted code requires.

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arXiv2009

Quantum Shift Register Circuits

A quantum shift register circuit acts on a set of input qubits and memory qubits, outputs a set of output qubits and updated memory qubits, and feeds the memory back into the device for the next cycle (similar to the operation of a classical shift register). Such a device finds application as an encoding and decoding circuit for a particular type of quantum error-correcting code, called a quantum convolutional code. Building on the Ollivier-Tillich and Grassl-Roetteler encoding algorithms for quantum convolutional codes, I present a method to determine a quantum shift register encoding circuit for a quantum convolutional code. I also determine a formula for the amount of memory that a CSS quantum convolutional code requires. I then detail primitive quantum shift register circuits that realize all of the finite- and infinite-depth transformations in the shift-invariant Clifford group (the class of transformations important for encoding and decoding quantum convolutional codes). The memory formula for a CSS quantum convolutional code then immediately leads to a formula for the memory required by a CSS entanglement-assisted quantum convolutional code.

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arXiv2009

Public and private communication with a quantum channel and a secret key

We consider using a secret key and a noisy quantum channel to generate noiseless public communication and noiseless private communication. The optimal protocol for this setting is the publicly-enhanced private father protocol. This protocol exploits random coding techniques and "piggybacking" of public information along with secret-key-assisted private codes. The publicly-enhanced private father protocol is a generalization of the secret-key-assisted protocol of Hsieh, Luo, and Brun and a generelization of a protocol for simultaneous communication of public and private information suggested by Devetak and Shor.

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arXiv2009

Optimal Entanglement Formulas for Entanglement-Assisted Quantum Coding

We provide several formulas that determine the optimal number of entangled bits (ebits) that a general entanglement-assisted quantum code requires. Our first theorem gives a formula that applies to an arbitrary entanglement-assisted block code. Corollaries of this theorem give formulas that apply to a code imported from two classical binary block codes, to a code imported from a classical quaternary block code, and to a continuous-variable entanglement-assisted quantum block code. Finally, we conjecture two formulas that apply to entanglement-assisted quantum convolutional codes.

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arXiv2009

Linear-Optical Hyperentanglement-Assisted Quantum Error-Correcting Code

We propose a linear-optical implementation of a hyperentanglement-assisted quantum error-correcting code. The code is hyperentanglement-assisted because the shared entanglement resource is a photonic state hyperentangled in polarization and orbital angular momentum. It is possible to encode, decode, and diagnose channel errors using linear-optical techniques. The code corrects for polarization "flip" errors and is thus suitable only for a proof-of-principle experiment. The encoding and decoding circuits use a Knill-Laflamme-Milburn-like scheme for transforming polarization and orbital angular momentum photonic qubits. A numerical optimization algorithm finds a unit-fidelity encoding circuit that requires only three ancilla modes and has success probability equal to 0.0097.

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arXiv2009

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.

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arXiv2009

Localized closed timelike curves can perfectly distinguish quantum states

We show that qubits traveling along closed timelike curves are a resource that a party can exploit to distinguish perfectly any set of quantum states. As a result, an adversary with access to closed timelike curves can break any prepare-and-measure quantum key distribution protocol. Our result also implies that a party with access to closed timelike curves can violate the Holevo bound.

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arXiv2008

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.

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arXiv2008

Protecting Quantum Information with Entanglement and Noisy Optical Modes

We incorporate active and passive quantum error-correcting techniques to protect a set of optical information modes of a continuous-variable quantum information system. Our method uses ancilla modes, entangled modes, and gauge modes (modes in a mixed state) to help correct errors on a set of information modes. A linear-optical encoding circuit consisting of offline squeezers, passive optical devices, feedforward control, conditional modulation, and homodyne measurements performs the encoding. The result is that we extend the entanglement-assisted operator stabilizer formalism for discrete variables to continuous-variable quantum information processing.

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arXiv2008

Quantum Coding with Entanglement

Quantum error-correcting codes will be the ultimate enabler of a future quantum computing or quantum communication device. This theory forms the cornerstone of practical quantum information theory. We provide several contributions to the theory of quantum error correction--mainly to the theory of "entanglement-assisted" quantum error correction where the sender and receiver share entanglement in the form of entangled bits (ebits) before quantum communication begins. Our first contribution is an algorithm for encoding and decoding an entanglement-assisted quantum block code. We then give several formulas that determine the optimal number of ebits for an entanglement-assisted code. The major contribution of this thesis is the development of the theory of entanglement-assisted quantum convolutional coding. A convolutional code is one that has memory and acts on an incoming stream of qubits. We explicitly show how to encode and decode a stream of information qubits with the help of ancilla qubits and ebits. Our entanglement-assisted convolutional codes include those with a Calderbank-Shor-Steane structure and those with a more general structure. We then formulate convolutional protocols that correct errors in noisy entanglement. Our final contribution is a unification of the theory of quantum error correction--these unified convolutional codes exploit all of the known resources for quantum redundancy.

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arXiv2008

Unified Quantum Convolutional Coding

We outline a quantum convolutional coding technique for protecting a stream of classical bits and qubits. Our goal is to provide a framework for designing codes that approach the ``grandfather'' capacity of an entanglement-assisted quantum channel for sending classical and quantum information simultaneously. Our method incorporates several resources for quantum redundancy: fresh ancilla qubits, entangled bits, and gauge qubits. The use of these diverse resources gives our technique the benefits of both active and passive quantum error correction. We can encode a classical-quantum bit stream with periodic quantum gates because our codes possess a convolutional structure. We end with an example of a ``grandfather'' quantum convolutional code that protects one qubit and one classical bit per frame by encoding them with one fresh ancilla qubit, one entangled bit, and one gauge qubit per frame. We explicitly provide the encoding and decoding circuits for this example.

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arXiv2008

Quantum Forbidden-Interval Theorems for Stochastic Resonance

We extend the classical forbidden-interval theorems for a stochastic-resonance noise benefit in a nonlinear system to a quantum-optical communication model and a continuous-variable quantum key distribution model. Each quantum forbidden-interval theorem gives a necessary and sufficient condition that determines whether stochastic resonance occurs in quantum communication of classical messages. The quantum theorems apply to any quantum noise source that has finite variance or that comes from the family of infinite-variance alpha-stable probability densities. Simulations show the noise benefits for the basic quantum communication model and the continuous-variable quantum key distribution model.

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arXiv2007

Coherent Communication with Linear Optics

We show how to implement several continuous-variable coherent protocols with linear optics. Noise can accumulate when implementing each coherent protocol with realistic optical devices. Our analysis bounds the level of noise accumulation. We highlight the connection between a coherent channel and a nonlocal quantum nondemolition interaction and give two new protocols that implement a coherent channel. One protocol is superior to a previous method for a nonlocal quantum nondemolition interaction because it requires fewer communication resources. We then show how continuous-variable coherent superdense coding implements two nonlocal quantum nondemolition interactions with a quantum channel and bipartite entanglement. We finally show how to implement continuous-variable coherent teleportation experimentally and provide a way to verify the correctness of its operation.

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arXiv2007

Convolutional Entanglement Distillation

We develop a theory of entanglement distillation that exploits a convolutional coding structure. We provide a method for converting an arbitrary classical binary or quaternary convolutional code into a convolutional entanglement distillation protocol. The imported classical convolutional code does not have to be dual-containing or self-orthogonal. The yield and error-correcting properties of such a protocol depend respectively on the rate and error-correcting properties of the imported classical convolutional code. A convolutional entanglement distillation protocol has several other benefits. Two parties sharing noisy ebits can distill noiseless ebits ``online'' as they acquire more noisy ebits. Distillation yield is high and decoding complexity is simple for a convolutional entanglement distillation protocol. Our theory of convolutional entanglement distillation reduces the problem of finding a good convolutional entanglement distillation protocol to the well-established problem of finding a good classical convolutional code.

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arXiv2007

Entanglement-Assisted Quantum Error Correction with Linear Optics

We construct a theory of continuous-variable entanglement-assisted quantum error correction. We present an example of a continuous-variable entanglement-assisted code that corrects for an arbitrary single-mode error. We also show how to implement encoding circuits using passive optical devices, homodyne measurements, feedforward classical communication, conditional displacements, and off-line squeezers.

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