Continuous variable private quantum channel

Abstract

In this paper we introduce the concept of quantum private channel within the continuous variables framework (CVPQC) and investigate its properties. In terms of CVPQC we naturally define a "maximally" mixed state in phase space together with its explicit construction and show that for increasing number of encryption operations (which sets the length of a shared key between Alice and Bob) the encrypted state is arbitrarily close to the maximally mixed state in the sense of the Hilbert-Schmidt distance. We bring the exact solution for the distance dependence and give also a rough estimate of the necessary number of bits of the shared secret key (i.e. how much classical resources are needed for an approximate encryption of a generally unknown continuous-variable state). The definition of the CVPQC is analyzed from the Holevo bound point of view which determines an upper bound of information about an incoming state an eavesdropper is able to get from his optimal measurement.

upper bound on information Eve can get was revised and substantially lowered (chapter IV), part of chapter III rewritten, several typos corrected

References in corpus (18)

• Quantum information with continuous variables
• Continuous variable quantum cryptography using coherent states
• Quantum key distribution using gaussian-modulated coherent states
• Quantum computation over continuous variables
• Quantum Copying: Beyond the No-Cloning Theorem
• Teleportation of Quantum States
• Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
• Unknown Quantum States and Operations, a Bayesian View
• Quantum Distribution of Gaussian Keys with Squeezed States
• Randomizing quantum states: Constructions and applications
• Classical capacity of the lossy bosonic channel: the exact solution
• Optimal Encryption of Quantum Bits
• Universal cloning of continuous quantum variables
• Statistical properties of random density matrices
• Average fidelity between random quantum states
• Capacities of Quantum Channels and How to Find Them
• Secure Coherent-state Quantum Key Distribution Protocols with Efficient Reconciliation
• A method of enciphering quantum states

Cited by in corpus (6)

• Purification of Gaussian maximally mixed states
• Gaussian private quantum channel with squeezed coherent states
• Universal upper bounds for Gaussian information capacity
• Correspondence between maximally entangled states in discrete and Gaussian regimes
• Sample-size-reduction of quantum states for the noisy linear problem
• Approximate private quantum channels on fermionic Gaussian systems