Equally-distant partially-entangled alphabet states for quantum channels

Each Bell state has the property that by performing just local operations on one qubit, the complete Bell basis can be generated. That is, states generated by local operations are totally distinguishable. This remarkable property is due to maximal quantum entanglement between the two particles. We present a set of local unitary transformations that generate out of partially entangled two-qubit state a set of four maximally distinguishable states that are mutually equally distant. We discuss quantum dense coding based on these alphabet states.Comment: 7 revtex pages, 2 eps figures, to appear in Phys. Rev. A 62, 1 November (2000

Realization of a collective decoding of codeword states

This was also extended from the previous article quant-ph/9705043, especially in a realization of the decoding process.Comment: 6 pages, RevTeX, 4 figures(EPS

Quantum privacy and quantum coherence

We derive a simple relation between a quantum channel's capacity to convey coherent (quantum) information and its usefulness for quantum cryptography.Comment: 6 pages RevTex; two short comments added 7 October 199

Nonorthogonal Quantum States Maximize Classical Information Capacity

I demonstrate that, rather unexpectedly, there exist noisy quantum channels for which the optimal classical information transmission rate is achieved only by signaling alphabets consisting of nonorthogonal quantum states.Comment: 5 pages, REVTeX, mild extension of results, much improved presentation, to appear in Physical Review Letter

A Full Characterization of Quantum Advice

We prove the following surprising result: given any quantum state rho on n qubits, there exists a local Hamiltonian H on poly(n) qubits (e.g., a sum of two-qubit interactions), such that any ground state of H can be used to simulate rho on all quantum circuits of fixed polynomial size. In terms of complexity classes, this implies that BQP/qpoly is contained in QMA/poly, which supersedes the previous result of Aaronson that BQP/qpoly is contained in PP/poly. Indeed, we can exactly characterize quantum advice, as equivalent in power to untrusted quantum advice combined with trusted classical advice. Proving our main result requires combining a large number of previous tools -- including a result of Alon et al. on learning of real-valued concept classes, a result of Aaronson on the learnability of quantum states, and a result of Aharonov and Regev on "QMA+ super-verifiers" -- and also creating some new ones. The main new tool is a so-called majority-certificates lemma, which is closely related to boosting in machine learning, and which seems likely to find independent applications. In its simplest version, this lemma says the following. Given any set S of Boolean functions on n variables, any function f in S can be expressed as the pointwise majority of m=O(n) functions f1,...,fm in S, such that each fi is the unique function in S compatible with O(log|S|) input/output constraints.Comment: We fixed two significant issues: 1. The definition of YQP machines needed to be changed to preserve our results. The revised definition is more natural and has the same intuitive interpretation. 2. We needed properties of Local Hamiltonian reductions going beyond those proved in previous works (whose results we'd misstated). We now prove the needed properties. See p. 6 for more on both point

Fidelity and the communication of quantum information

We compare and contrast the error probability and fidelity as measures of the quality of the receiver's measurement strategy for a quantum communications system. The error probability is a measure of the ability to retrieve classical information and the fidelity measures the retrieval of quantum information. We present the optimal measurement strategies for maximizing the fidelity given a source that encodes information on the symmetric qubit-states

The capacity of the noisy quantum channel

An upper limit is given to the amount of quantum information that can be transmitted reliably down a noisy, decoherent quantum channel. A class of quantum error-correcting codes is presented that allow the information transmitted to attain this limit. The result is the quantum analog of Shannon's bound and code for the noisy classical channel.Comment: 19 pages, Submitted to Science. Replaced give correct references to work of Schumacher, to add a figure and an appendix, and to correct minor mistake

Compressibility of Mixed-State Signals

We present a formula that determines the optimal number of qubits per message that allows asymptotically faithful compression of the quantum information carried by an ensemble of mixed states. The set of mixed states determines a decomposition of the Hilbert space into the redundant part and the irreducible part. After removing the redundancy, the optimal compression rate is shown to be given by the von Neumann entropy of the reduced ensemble.Comment: 7 pages, no figur

Minimum-error discrimination between three mirror-symmetric states

We present the optimal measurement strategy for distinguishing between three quantum states exhibiting a mirror symmetry. The three states live in a two-dimensional Hilbert space, and are thus overcomplete. By mirror symmetry we understand that the transformation {|+> -> |+>, |-> -> -|->} leaves the set of states invariant. The obtained measurement strategy minimizes the error probability. An experimental realization for polarized photons, realizable with current technology, is suggested.Comment: 4 pages, 2 figure